Experiments that held, and what they buy you

One hundred and seventy-six times, this project wrote down what it expected to measure — and what result would prove it wrong — before running the measurement. One hundred and sixty-nine of those are enforced by the compiler: crates/isomesh/src/experiment.rs refuses to build a harness whose id is not registered, so the prediction cannot be edited after the numbers arrive. The other seven are P-1…P-7, which predate the macro and live in FINDINGS.md as prose. These two numbers are counted from experiment.rs rather than remembered, because nothing gates this paragraph and it has rotted before: it read "one hundred and two" and "ninety-five" for a whole phase after they stopped being true, and "one hundred and twenty-two" and "one hundred and fifteen" for another after that.

This page is the scorecard, and the falsifications are the reason it is worth reading. The most useful thing in the whole record is still a bug that made two true hypotheses look false for a day.

If you only read one section, read the instrument story.

Why pre-register at all

A prediction written after the number is known is not evidence, and it reads exactly like one written before. This project has already caught itself writing expectations into docs that the measurement then disproved — twice, at ✗1 and ✗3.

So the prediction moved somewhere the compiler can see it:

use isomesh::experiment;

// This line does not compile if "P-8" is not in `PREREGISTERED`.
let p = experiment!("P-8");
assert!(p.hypothesis.starts_with("A weld gated"));

Three properties make it a gate rather than a habit:

Registering is a commit, so git carries the ordering that prose cannot. scripts/backlog_gate.sh checks that every registered id reaches FINDINGS.md, so the prose can elaborate and cannot contradict.

era how it was registered held falsified never ran
P-1 … P-7 prose in FINDINGS.md 5 2 —
P-8 … P-17 crates/isomesh/src/experiment.rs 5 4 1
P-18 … P-21 crates/isomesh/src/experiment.rs 3 1 —
P-22 … P-37 crates/isomesh/src/experiment.rs not tallied here — several split their verdict across clauses, and a column that rounds those to one word would be the kind of summary this page exists to distrust
P-38 … P-47 crates/isomesh/src/experiment.rs 3 7 —
P-48 … P-56 crates/isomesh/src/experiment.rs split, and tallied honestly below: 4 experiments held every clause, 2 were falsified outright, and 3 split — the phase's most useful result is a clause that failed
P-57 … P-60 crates/isomesh/src/experiment.rs 4 registrations, every one falsified on at least one clause and none on all — FINDINGS.md carries them (✗39–✗42); they are not summarised on this page
P-61 … P-72 crates/isomesh/src/experiment.rs 12 registered, 10 ran and 2 are blocked on a paper nobody can get — tallied below. 1 held every clause, 2 were falsified on every clause, and 7 split
P-73 … P-102 crates/isomesh/src/experiment.rs 30 registered and all 30 ran — tallied below. 6 held every clause, 2 were falsified on every clause, and 22 split, so 24 of the 30 carry at least one falsified clause
P-103 … P-122 crates/isomesh/src/experiment.rs 20 registered and all 20 ran — tallied below. Sixty clauses: 34 held, 24 falsified, 2 vacuous. 2 rows held every clause, 1 held every clause it could fire, and 17 of the 20 carry at least one falsified clause
P-123 … P-126 crates/isomesh/src/experiment.rs 4 registered and all 4 ran — tallied below. Twelve clauses: 9 held, 2 falsified, 1 vacuous. 2 rows held every clause, 2 carry a falsification, and 1 landed a source change, registered in advance

A page called "experiments that held" which quietly dropped the falsifications would be exactly the failure this machinery exists to prevent. They are all here.

Phase 19 is the worst era on this page and the most useful one. Seven of ten falsified, and four of those seven were falsified by their own registered falsifier naming the mechanism in advance. Two were falsified by an error in the registration itself — P-43's cost clause was wrong arithmetic and P-42's Gaussian clause was a tautology — which is the machinery catching the person operating it, and is the strongest evidence on this page that the practice is doing something.

The scorecard

prediction verdict what it means if you depend on this crate
P-11 — one canonical world_of_sample closes seam cracks at every cell size, not just powers of two held, both clauses (M-278) Chunk seams are exact only at power-of-two cell sizes today. Canonical reconstruction gives 0 unmatched seam edges at every spacing tried; what the crate can offer now gives 0 only at powers of two and 63–348 at 0.1, 1/12, 1/14. The weld hides it; an unwelded consumer gets it in full. The fix is priced and open as X-005
P-15 — more than half the dual mesher's cycles are in emit_quads held, and by more than it claimed (M-284) 45% of the instructions and 82% of the time, at r² = 0.995, predicted to +0.12% on a held-out shape. This is the measurement that made the 4.26× possible
P-9 — k-way weld order changes the output held The weld is not confluent, so vertex order is pinned deliberately rather than left to HashMap iteration. Your meshes reproduce byte-for-byte
P-13 — the non-convergent angle at a sharp feature is bounded below by the feature's dihedral held — after M-289 It is a property of sharp edges, not a defect with a location. Nothing to fix; something to know
P-16 — every past-90° vertex sits on a cell straddling the crease held, at 0% — after M-289 Same conclusion from the other side: two faces meeting inside one cell, not a winding bug
P-8 — a weld gated on the link condition reaches zero non-manifold output falsified, both clauses (E×4) The gate makes things worse. The crate does not ship one, and now you know why rather than wondering
P-12 — the dual's superlinearity is a cache-miss effect falsified (M-279) … and later true The best methodological lesson here. See below
P-14 — the residual non-manifold vertices are one-vertex-per-cell meeting two surface components falsified on clause one (M-275) The vertex-to-edge ratio came out exactly 2:1 on every row — 597/314, 99/48, 38/19, 106/53. There are not 597 defects plus 314 defects; there are 314, each counted twice more by the vertex walk
P-17 — Manifold Dual Contouring's residue is an interior ambiguity falsified (M-291) Interior::Joined fires on 100% of ambiguous-face pairs, offenders and control alike — no discriminating power at all. Bounded exhaustively instead (M-292), then reduced to a 48-sample fixture (M-294)
P-10 — vertex inflation from gate-plus-split is under 1% never ran Superseded. P-8 killed the gate P-10 presupposed before P-10 could measure its cost
P-19 — the winding number's on-demand crossover is set by row sharing, so Q* is of order N² not N³ held, both arms (M-303) Q*/N² came out 1.13–1.43 at 17³/33³/65³ against a registered 0.5×–4× band. The naive reading overstates the win by a factor of N: at 65³ the real crossover is 4,791 queries against 274,625 samples, so an on-demand field pays below about 1.7% of the grid. The hole-punched control moved Q*/N² to 13–42, and per-point cost tracked boundary-edge count to ×15.7 against ×16.2 — the mechanism confirmed by number, not by direction
P-20 — a weld key moves no topology metric beyond the splits it names held on both falsifiers, wording amended (M-305) A constant key moves nothing on 0 of 51 configurations, and non-manifold vertices never rise by more than the split count — so E×4's manufactured bowties do not come back. But boundary edges go 0 → 24 on a creased cube, which H said would not happen. That is not a defect: it is the split, seen from the edge column. The exact mirror of E×4, where a pairwise refusal did its damage in the vertex column
P-21 — a freshly extracted mesh separates exactly the sample pairs the field's own sign separates held, both clauses (M-307) Marching Cubes, MC+decider and Marching Tetrahedra seal 24 of 24 — eight fields × three resolutions, 9.15 M probes, zero holes and zero membranes. All three duals fail fbm_terrain with the identical count (92 / 138 / 190) and every one of those holes is on a face of the sampled domain: a dual's quad needs all four cells around a sign-changing grid edge and at the domain face only one or two exist. For a chunked world that face is the chunk seam, so a dual chunk's collider is not watertight on its own. The property that splits the family is not primal-versus-dual but does the method put its crossing on the probed grid edge — subgrid Marching Tetrahedra is primal and scores worst, 18 of 24
P-18 — every convex-decomposition precondition is already reported by ColliderReadiness falsified, and not where predicted (M-300) Registered expecting to die on self-intersection-freedom. It died on non-manifold vertices instead, and self-intersection-freedom turned out not to be an input precondition of anything (✗20). The audit was the product either way
P-61 — a crossing stored as an offset from the edge midpoint is bit-exactly antisymmetric, so a mirrored grid gives a mirrored vertex falsified on C1 and C2, held on C3 and C4 (✗49 / M-372) Your vertex positions moved in 0.0.10, and in exchange plain Marching Cubes is now equivariant under all 48 octahedral elements instead of 6. 0 mismatches on 5,800,000 straddling pairs against 1,035,808 for the old lower-corner form. 135 of the fixture's 216 hashes of the time were rebaselined; triangle counts, Hausdorff and self-intersections are unchanged to twelve digits, and 2,285 of 28,124 cut edges — 8.12% — moved by ≤ 268 ULP. If you hash meshes, 0.0.9's hashes will not match. C1 and C2 were cost clauses and both were priced wrong at registration
P-63 — O-12 is finite at 2¹⁸, and one sweep settles the vertex-link question for Marching Cubes held on C1 and C2; C3 falsified by its own block (M-374) The oldest open question in the ledger is half closed, by exhaustion rather than by sampling. Every face incident to an edge vertex comes from one of the four cells sharing that edge — 18 corners, 2¹⁸ = 262,144 patterns, the whole space — and not one produces a vertex with a split link, on both interior-ambiguity settings at four magnitude draws. The pre-fix defect reproduces 5,302 times in the same walk, so the zero means something. What is still open is the dual family, which needs 4³ = 64 corners and is filed as R-072
P-64 — bounded model checking proves the combinatorics the property tests only sample held, all three (M-379) The case table is proved indexable, not spot-checked. All 256 sign patterns in 2.04 s and all 16,384 (pattern, mask) pairs in 161 s. The useful half is the failure on the way: pointing Kani straight at the constructor ran CBMC out of 32 GB, and the proof only exists because the work was split between const evaluation over the real constructor and a model checker over the consumer. A #[kani::should_panic] control corrupts one triangle and reports the failure, so a vacuous proof cannot pass as a real one
P-68 — a running error bound turns a vertex position into a position and a certified interval falsified on C1 by one unit; held on C2, C3 and C4 (✗55 / M-382) The bound is sound at coefficient 3 and unsound at the registered 2 — 10 violations in 19,415, which is the kind of margin no sample size finds by luck. The ground truth is exact: f64 samples are dyadic rationals, so the true crossing is an exact rational and the error is computable in i128 with no floating point in the loop. That is what makes this a soundness statement rather than two approximations compared
P-69 — restructuring the sample loop autovectorises, with bit-identity as the gate falsified on C1, held on C2, C3 vacuous (✗51 / M-375) Nothing widened: total %ymm across all eleven monomorphisations is zero, and the prescribed shape is a 3–7% regression, so it was reverted. C1's 2× was arithmetically unreachable from the start — the loop is 11.6% of the marginal extraction cost, so its ceiling is 1.06×. The durable result was in no clause: there were three copies of that loop and they are now one (sdf::sample_grid), with the original arithmetic and all 216 hashes unchanged
P-70 — subgroup ballot compaction beats the Hillis-Steele scan falsified on C1 by arithmetic done at registration; held on C2 and C3 (✗54 / M-381) The mechanism is real — 1.4114× at 2 M elements, bit-identical, reproducing the literature's 1.33–1.49× band — and it is not shipped. Applied to the path it lives in it moves 1.27%, because scan_ms is 0.3657 of 8.3694 while upload_ms is 87.50%. A second WGSL path for 1.27% is what the one-path rule forbids, and naga 29.0.4 rejects enable subgroups; outright — and that 87.50% is the sample-grid upload on a path GPU-011a has since deleted (✗73 / M-405)
P-71 — the 83% is a blocking round-trip, and both targets can avoid it falsified on all three (✗52 / M-376) The largest piece of a GPU extraction is the geometry copy, not the count wait — 0.6663 ms of 1.1331 at 129³ against map-wait's 0.3191 — so extract_indirect removes 32%, not the registered 60%, and it removes it by not delivering the bytes. For a consumer that only draws, that is 100% of what it needs. For a collider consumer the copy is unavoidable, which is why DeferredGeometry ships in 0.0.10: measured under the frame-budget scheduler at 1.41 frames of latency, worst case 2
P-72 — the granularity of the active-cell structure is a parameter with an optimum held on C1 at 51×, falsified on C2 and C3 (M-377) Chunk size is the largest single knob in this crate and its optimum is interior at 4³. Eleven edits cost 4.59 ms at 4³ against 432.73 ms at 64³ at a fixed total cell count, because remesh is dirty_chunks × chunk_cells³ — 25,344 cells re-meshed against 8,126,464. The registered 8³–64³ range would have given the wrong shape entirely: it is monotone there with the minimum at the smallest granularity swept. The demos are not retuned on this, because the fixture excluded per-chunk entity and draw cost — and P-89 has since measured below it, at 4.36× and 1.76× against 1³ (✗69 / M-401)
P-62 — the Plantinga–Vegter certificate is sound against this crate's own tunnel classifier held on C1 and C2, falsified on C3 (M-378) Zero unsound certificates over 2,389 tunnel cells, from a predicate that refuses 95% of the population — so the zero is not the trivial one. It is not free: the cost is 21%, not the registered ceiling, and the reason is structural rather than fixable in isolation — a standalone pass re-gathers the eight corners the extractor already has in registers — fused into that gather it costs 0.0553 of extraction and certifies the same set (M-410)
P-66 — a derivative sign test is a usable under-resolution witness falsified on all three (✗53 / M-380) The third attempt at this line died too, and it died informatively. The witness is sound at k = 17 samples and unsound at k = 5, C2's second half was stated backwards, and thin_plate ranks last on the metric C3 predicted it would top. Two earlier attempts (P-43, P-44) were value witnesses; this was a derivative witness, and the family is now three for three. Nothing here changes what the crate does

Phase 19 — three that held, seven that did not, and two the registration itself got wrong

prediction verdict what it means if you depend on this crate
P-39 — a brush that provably cannot win the min/max chain inside a chunk can be deleted from the tape, bit-exactly held, all three clauses (M-341) Your edit history stops being a tax. Median 21 of 64 brushes survive per chunk, a chunk meshes 3.4× faster, and the mesh is byte-identical on 64 of 64 — because IEEE min/max select an operand rather than computing one. The bound costs 1.5 × 10⁻⁴ of what it saves. SmoothAdd is excluded from the losing-direction prune and that exclusion is load-bearing: prune it and 48 of 64 chunks change
P-40 — the active-cell test is one bit, so 64 cells decide at once demoted, then re-earned as a count (M-337 → M-348 → M-349) Registered as a ≥1.25× wall clock and recorded at 1.336×; an external audit found the committed CSV said 1.1925×, and three quiet-machine re-runs read 1.022× / 1.184× / 1.177×. The mechanism was never in doubt — what was wrong was gating it on a stopwatch, which ✗24 had already forbidden. Re-registered as P-50 and held as three exact equalities on 15 of 15 rows: gathers performed equals cells on the scalar path and active cells on the bitmap path, word groups equals cells_x.div_ceil(64)·cells_y·cells_z, and the two produce the same ordered active list. At 128³ it removes 99.07% of gathers on sphere — an integer, identical on every machine
P-41 — the sign lattice is not well-composed, and that is where the duals go non-manifold held, and the relation is a bijection (M-338) You can count the defects before the mesh exists. critical cells == non-manifold vertices, exactly, on every affected field — 602, 141, 58 — and exactly zero on the five clean ones, from both directions. Co-location 2442/2442 against a ~1% chance baseline. The census is a function of the sign bytes alone, so it is available at 13.5 ms against 63 ms to mesh the same grid
P-46 — repairing the sign lattice drives the duals to zero non-manifold output falsified, and the conditional it leaves is the product (M-344) The repair is free and total where critical cells are isolated (58 → 0 in one sweep, 141 → 0 in five, Hausdorff ratio 1.000000) and provably stuck where they are dense: an exhaustive walk over all 4,096 face-adjacent sign patterns finds 36 where no corner leaves both cells clean. Gate on maximum cluster size, not on count
P-47 — composed fields have a real gradient hole falsified in the mean, held on speed (M-345) The central difference is 7.6 × 10⁻⁵ degrees off on a 64-brush stack — three orders under the bar, so your normals are fine. But it reaches 4.365° exactly where a vertex's stencil straddles a CSG seam, and exact gradients are 2.8× cheaper anyway. Justified by cost, not by accuracy, which is not the reason anyone expected
P-45 — normal-cycle curvature measures are additive, so a per-chunk number composes falsified on two of three clauses (M-343) The two measures have opposite defects. The Gaussian one is chunk-local and does not sum — it overshoots by exactly π × excess chunk incidence, the missing −N(A∩B) term, because a partition of faces is not a partition of space. The mean one sums to 3 × 10⁻¹³ and needs a one-ring to compute
P-42 — the curvature residual falls inside a bound computed from the mesh falsified on convergence; the clause was a tautology (M-340) With B the whole closed surface, Σ(2π − α_v) = 2πχ identically, so the residual is one f64 epsilon per vertex and grows ×4 per halving because the vertex count does. Theorem 6's bound does not converge here either: max circumradius is not O(h) because Marching Cubes' needles get relatively worse with resolution
P-43 — the max cell-centre residual witnesses under-sampling falsified, and the cost clause was wrong arithmetic (M-339) One C¹ crease cell in 2.1 million pins the maximum at every resolution, so it does not fall at all while the Hausdorff does. And "the structural ⅛" was per-cell corner accounting; this crate prefills one shared grid, so the real cost is (n−1)³/n³ — a doubling of the sampling work, not an eighth
P-44 — the mean residual witnesses it instead falsified out of sample (M-342) The correlation reproduced on all four untouched fields at r ≥ 0.98 and the line still dies: the exponent gap is the /h normalisation. A mean's convergence order is field-independent because it is set by the smooth bulk; a supremum's is field-dependent because it is set by the worst feature. No power of h reconciles them, and an r of 0.98 over four monotone points is a statement about monotonicity
P-38 — Marching Cubes carries the same 128³ aliasing defect the dual path was cured of falsified at 0.98 against 1.5 (M-336) A-024's size[0] \| 1 is correctly scoped and now that is measured. The 64 KiB plane stride is not the defect; the walk is. Marching Cubes streams eight corners and steps x; emit_quads walks every grid edge on three axes with endpoints a row and a plane apart. A future extractor inherits the pad only if it inherits the walk

Two of these were falsified by the registration rather than by the world, and that is the part worth keeping. P-43's cost clause was arithmetically wrong when it was written; P-42's Gaussian clause was unfalsifiable by construction, because taking B to be the whole closed surface turns the measurement into discrete Gauss–Bonnet. Neither error survived contact with a number, and neither was repaired by amending the prediction — both were re-registered under new ids (P-44, P-45) and both of those then failed too, honestly, on data they had not seen.

Phase 20 — where three of six were wrong before anything ran

Every registration in this phase was checked against the paper it cites before the harness was written. Three of six rested on a claim the source does not make. That is the cheapest error this project has ever caught, and it is worth more than any single verdict below.

what the registration cited what the source actually says
"edge Chamfer 0.0262 vs MC 0.417 — 13× on sharp features" No such figure exists. The tangency paper measures Hausdorff, Chamfer and its own energy, treats sharp features qualitatively, and its residual is a rank-3 point-to-point term, not the point-to-plane form that was registered
Custódio's = label reduces degenerate triangles by N The paper reports no degenerate-triangle count on any dataset, and its triangulator is a per-cube convex hull explicitly "without the need of a look up table"
Affine arithmetic is correlation-aware, with a measured tightening The paper contains no correlation argument, no tightening figure, and no min/max rule at all — and that last gap turned out to be the experiment
A monotone-edge certificate for 3D meshes The theorem is real and it is two-dimensional. Its pigeonhole step is "a triangle has only three edges", and it does not apply to the trilinear interpolant
prediction verdict what it means if you depend on this crate
P-54 — a correlation-aware bound rejects empty cells a Lipschitz ball cannot held, all three (M-354) A field whose global Lipschitz constant is worthless becomes cullable. gyroid 688 → 2,647 of 4,096 cells rejected, 3.85×, with 1,959 gained and zero lost. On gyroid_uncapped Hart's test rejects nothing at all and affine rejects 1,098. And where the field is built from min/max the gain is exactly zero — box_exact's two rejected sets are identical cell for cell — because the collapse to an interval destroys the correlation. Mesh byte-identical on 12 of 12, with a deliberately sabotaged bound proving the gate can fail. Costs ~12× the arithmetic: a capability, not a speedup
P-56 — a central difference across a CSG seam is wrong by at most half the crease angle held on C1 and C3 (M-350) The error has a closed form and it is attained. (180° − θ)/2, with median tightness 0.9748 over 24 rows and 9 rows above 0.99. It is provable, not fitted: the difference returns u − Λw for a diagonal Λ with entries ≤ ½. P-47's lone 4.365° outlier back-solves to a 171° seam against a 4.5° bound — explained, not excused. It does not shrink with resolution, because the stencil step does not
P-53 — a third corner label removes the degeneracy integer volumes create held, split, held (M-352) Every degenerate triangle traces to an exactly-equal corner — 164 of 164 on fuel, 58,097 of 58,097 on bonsai — and the repair moves no geometry at all (max_snap_distance is exactly 0). But it is only safe on one of the two volumes: on bonsai it welds 520 separate components, because 516 of 17,201 collapse groups join vertices that share no triangle. The shippable result is the precondition — one union-find over the baseline mesh — not the repair
P-51 — this crate's extractors violate the empty ball a distance sample asserts held, falsified, held (✗38 / M-355) They do not, and that closes four papers in one pass. Marching Cubes pierces 0 of 22,790 vertices and Dual Contouring 0 of 22,798, exhaustively, two margins negative. The other half is wide open: 2.9%–80.5% of samples have a sphere no vertex ever touches, with MC worse than DC on 5 of 5 fields and 16× worse on thin_plate. The worst misses are exact constants — √2 cells for MC on a box, because MC places no vertex on a box edge at all
P-52 — tangency placement beats the QEF on sharp features falsified on three of four (✗37 / M-353) 64.8× and 87.2× worse, and the algebra says why in one line: the least-squares point is (1 − λ)·mean(pᵢ) + λ·c, and the mean of a cube's eight corners is the cell centre. Confined to a cell, the tangency energy stops being about the surface. This confirms the source's own ablation — globality is its mechanism, not an implementation detail
P-55 — monotone mesh edges certify the critical-point structure falsified on all three (✗36 / M-351) The zero was unreachable by geometry, not by sampling. A mesh edge is a chord: on a convex field f runs 0 → negative → 0, so g(0) = r(cos θ − 1) < 0 and g(1) = r(1 − cos θ) > 0 for every pair of surface points. sphere flags 804 of 804 edges against a registered zero. 97.5% of flags were decided by the endpoints before any interior sample existed. The predicate belongs on the ambient complex

What this phase says about the practice, which is not the same as what it says about meshing. Four of the six registrations contained an error I put there: a bar copied from a figure that does not exist, a tolerance that scales by a quantity which is identically zero where it is applied, a curve fit where a scale-free equality was available, and a field list naming five members of a set with four. Every one was caught by the artefact rather than by review — and three of them were caught before the harness existed, by reading the paper. The registrations that needed no external claim, P-51 and P-56, were the two that could be written immediately and the two that needed no correction.

Phase 23 — twelve registered, ten run, and two blocked at the door

All twelve came out of a single audit of this project's own practice, and the audit's central finding turned up again inside the phase that exists to apply it: a clause stated as a ratio of a total must name the share of that total it can move. P-69 registered a 2× on a loop that is 11.6% of the cost it was denominated in, so its ceiling was 1.06× before anything ran. P-70 registered a speedup on a stage that is 4.4% of its own path. Both numbers were available at registration and neither was computed.

Two registrations are blocked, and they are blocked on acquisition rather than on a ticket.

blocked what it needs why no ticket can unblock it
P-65 — does MCPro's procedural construction resolve UnresolvedSixSaddle? Stahl & Grosso, GRAPP 2025, 10.5220/0013309800003912 Six acquisition routes were tried. What is in the library is a 383-character SciTePress landing page that the catalog reported as "converted, embedded" — so the pipeline's own status flag is not a presence oracle either (M-371). Running it would mean inventing the quadrant subdivision, halfedge assembly and third routing from an abstract
P-67 — does reduced affine arithmetic keep P-54's rejection rate in a fixed-size struct? Knoll et al., 10.1111/j.1467-8659.2008.01189.x C1 and C2 are runnable against this crate's own P-54 baseline. C3 is the informative clause and it is not — it exists to reproduce a measured 1.5–2× / 3–4× band and a superquadric case where intervals win, and reproducing a band from a summary is exactly the failure ✗21 records. Splitting the registration to run the easy two would measure that the method is cheaper without ever testing where it is not

Neither is on the scorecard above. A scorecard row implies a verdict, and these have none; they are registered in crates/isomesh/src/experiment.rs so the compiler holds the ids, their questions are on record in FINDINGS.md, and the unblocking event is external — a PDF appearing.

Three of the ten changed what ships. P-61 moved every vertex position and rebaselined 135 of 216 golden hashes, to buy bit-exact equivariance under all 48 octahedral elements. P-71 landed DeferredGeometry as a third extraction contract. P-72 measured the largest single knob in the crate — a 51× spread in edit-plus-remesh across chunk granularity at a fixed cell count — and deliberately retuned nothing, because its fixture excluded the per-chunk entity and draw cost a real demo pays.

One found a crash rather than an answer. P-63's exhaustive sweep panicked inside marching_cubes, in release, on an ordinary trilinear cell: MAX_PATCH_TRIANGLES was a sampled maximum of 24 where the triangulator's own buffer was the derived 40. Fixed under its own ticket before any number in the phase was committed, and it is in 0.0.10. An exhaustive harness is a fuzzer that knows when it is finished.

Phase 24 — thirty run, and twenty-four with a falsified clause

The largest phase in the record, and the one where the falsifications are the point. Six registrations held every clause. Two were falsified on every clause. The other twenty-two split, which is what a clause-level verdict is for: a row that reads "held" and a row that reads "falsified" would both be summaries of something more useful than either.

prediction verdict what it means if you depend on this crate
P-75 — per-vertex material weights, computed once inside the extraction walk, beat a per-fragment edit-log walk held, all three (M-387) Carry the weights on the vertex. They cost 3.11–3.16% of extraction and the share is flat across a 4× log; they beat the per-fragment walk by 12.93× to 40.89×, widening monotonically across M-50's four buckets; and interpolating them across a triangle misclassifies 0.18–0.35% of the surface with 99.36–99.73% of that inside one cell of a material boundary. C1 held only because the surface carries half the vertices the pre-run estimate assumed — the same estimate had predicted it falsified
P-76 — stochastic triplanar selection trades fetches for temporal accumulation, and a destructible world has already spent its temporal budget held on C1 and C3; C2 held on its own falsifier, vacuous as worded (M-388) Keep three planes, and every falsifier failed. The fetch count drops by 18 = 3 × 6 exactly and the fragment cost by 2.1115×; biplanar gets 0.5000 of the saving exactly in fetches and 0.5429 in wall clock. The recommendation survives all of that because stochastic selection manufactures 39,495 extra history rejections in a scene with no dig in it at all, against the dig's own 8,483. C2 as written is vacuous: no instrument in the file can price an image error against a millisecond
P-81 — golden-section search against the resident field beats the shipped TriMesh collider on query cost, deterministically held on C1 and C2; C3's TriMesh half held, its field half vacuous (M-393) 8.067× over TriMesh at 4.766 µs a query against a 3× / 20 µs bar, and bit-identical over 10⁶ queries across Zen 3 and an Apple M5 — so this path is not behind the wall every other float-sensitive one is. The TriMesh arm reports 93,298 ghost contacts over one 495-crossing fixture: if a mesh collider ships, internal-edge removal is not optional. But P-85 falsifies C1's registered share premise — the collider's 45% is construction to within 3.12e-5 — so this moves a moving body's per-frame collision budget and not the 45%
P-98 — the Plantinga–Vegter certificate, fused into the extractor's own eight-corner gather, costs what M-378 derived held, all three (M-410) The certificate is now shippable as a default rather than a debug gate. 0.0553 worst of extraction at 65³ against M-378's derived 0.0658, the same certified set on 25 of 25 rows with 0 unsound over 2,389 hidden-topology cells, and per-chunk aggregation at 0 extra passes. The catch is in what aggregates: the count pair, not the fraction — average the fractions and you are wrong by 12.9 points on noise_cavity. M-378's prose gloss on its own 0.0658 is not a recipe for it
P-99 — the under-resolution witness works once its denominator is the surface rather than the volume held, all three (M-411) The reformulation ✗53 asked for lands, and the two findings around it are worth more than the verdict. The single-root rate ranks thin_plate first at 0.441176 and 0.469697, fails to converge on thin_plate and converges on the other seven, and the clause ✗53 stated backwards holds in the direction the predicate allows: false negatives 322 / 94 / 8 / 1 / 0 against monotone non-decreasing false positives, over k = {2,3,5,9,17}. But C1's premise is off by two — rank_all_edges reads 6, not eighth — and the metric C1 endorses needs the oracle too, so the deployable LOD input is rate_sign_change, which reproduces the ranking on all 120 rows
P-102 — ✗43's withdrawn rate reproduces under P-63's exhaustive machinery held, all three (M-414) The shipped extractor is closed on 8,064 configurations, and the reproduction is worth less than it looks. 0 of 8,064 unclosed post-fix on five independent magnitude fixtures, 2 of 8,064 pre-fix at 6³ at t7c6o0+t9c6o0, and the ±1 arm reports VOID rather than a pass. But C2's share is fan_configurations = 2, so "exactly 2" was reachable by exactly 2 and "zero elsewhere" was arithmetically forced rather than measured
P-74 — sphere-tracing the resident field gives ambient occlusion under 2 ms, with no seam or halo error and no construction cost held on C1, split on C2, falsified on C3 (✗57 / M-386) The first lighting measurement in this repository: field AO is cheap and it is not free. ao_ms_field is 0.3996 / 0.1363 ms, still under the bar at 0.9406 / 1.2215 ms once the 42.49% / 11.16% coverage is corrected out — though the bar is an absolute millisecond and its own verdict flipped between two runs of one binary. SSAO's error is 1.52–19.09× the field arm's on all six sets, so the comparison holds, while both absolute halves fail: the field arm's own seam and halo error are 0.021313 / 0.034184 and 0.007323 / 0.028428, not zero. And the construction RTSDF pays is not already paid here — 10.41 / 12.74 ms of it — because raw_lipschitz is 1.4140 / 2.1793 and a sphere trace on the resident field is unsound
P-78 — probe invalidation is edit-proportional, and tracing the field beats tracing the extracted mesh for probe updates C1's factor falsified, C1's world-size falsifier held, C2 falsified inverted, C3 held (✗59 / M-390) Probe GI survives the question that would have killed it and loses the one it was expected to win. The invalidation factor is 3.36–8.38 with c1_holds true on 18 of 72 rows — but invalidation does not grow with the world: 1.391× against a world that grew 8.00×. C2 is falsified inverted: the parry3d BVH over the extracted mesh is 1.95–7.27× faster than sphere-tracing the field. And the topological event does have a lighting signature — a breakthrough dig invalidates strictly more probes on 36 of 36 pairs at 1.25–2.53×, on two digs matched to 171 samples exactly
P-79 — shadow-page invalidation is proportional to the brush's projected area, localised invalidation is pixel-identical, and caching beats Epic's uncached choice falsified on C1 and C2; C3 held at the registered configuration and falsified over the sweep (✗60 / M-391) For a world being dug away, page invalidation is a quantisation and not an area. The constant is 20.3718 against a bar of 3. Localised invalidation is not pixel-identical — 4 texels on one row, with a 66-of-96-arm geometric leak underneath it that a page-level test would have shipped; radius + 2√3·cell closes it at zero leak on 384/384. Caching is worth 3.96× on game_dig's own brush and loses on 189 of 384 rows, so Epic's uncached choice is right at the wheel's maximum and wrong at the default
P-80 — the fine-to-coarse residual is computable from the field alone, and a normal map baked from it restores what coarsening costs except where the loss is a silhouette falsified on C1 and C2; C3 held on thin_plate, falsified on gyroid (✗61 / M-392) The map works and the clause missed by two thirds of a degree. C1 fails on one field of eight — noise_cavity at 0.899724 and 0.836800 against 0.95, both halves of its falsifier firing — and holds on the other seven at a worst residual_p95_cells of 0.057262 against a 0.1 bar. C2 misses by 0.62° against a headroom of 0.94° its own reference left and nobody computed. C3's prediction holds on thin_plate at 28.60° and fails on gyroid at 13.22° — where the no-map arm is itself only 14.85°, so the clause's premise failed rather than the map succeeding: a mean shading-normal angle over the surviving coarse surface cannot see a silhouette
P-82 — a game_dig projectile tunnels a thinning wall and continuous collision stops it, at under 25 µs an element C1 falsified by its own falsifier; C2 held; C3 held as registered and falsified off that fixture (✗62 / M-394) The discrete path never tunnels, so there is nothing to buy. The capture window is 2R + t, not t: game_dig's 2-cell body radius makes 2R 4.0 cells against a fastest per-frame step of 2.4588 cells, giving 0 tunnels over 500,000 shots on all 25 scored thickness×speed combinations — and thinning the wall from 2 cells to a twentieth of a cell changes the zero not at all. Cost is 1.5644 µs/element tested against a 25 µs bar. The 8-swept-sphere proxy agrees to 0.1629 cells as registered and misses on a convex rim above aspect 8.0, where the registered fixture is support-exact and cannot tell the two apart
P-83 — the divergence-theorem surface integral gives mass properties to 1e-4, deterministically, at under 2% of extraction C1 falsified; C2 splits — determinism held, the asymmetry half falsified; C3 falsified (✗63 / M-395) The whole gap is Marching Cubes, and no integrator could have passed C1. Off by 44× to 2,275× at 33³ on all eight fields, while a volume integral over the same triangles agrees with the surface integral to 1.7e-13. Cross-machine determinism holds on 48 of 48 hashes across Zen 3 and an Apple M5; the paper's non-symmetric tensor does not reproduce — an exact 0.000000e0 on box_exact — so the symmetrisation step can be dropped. Cost fails on 20 of 24 rows, and the paper's surface form costs 2.14× the classical origin-fan it was registered as cheaper than. No swap is recommended
P-84 — a brush clipped against a precomputed convex-cell partition fractures in under 10 ms a fragment, and the partition is a pure function of the edit log C1 held by three to four orders; C2 falsified as registered and held under one named repair; C3 falsified (✗64 / M-396) Runtime convex decomposition is not the problem; ordering is. The fracture costs 10,464–12,726 cycles per fragment against M-116's 240.7–271.8 ms. The partition is a pure function of the edit log only if a crossing vertex is solved from its stable-id plane triple and coincident planes are collapsed — 6 / 6 / 2 / 1 distinct partitions over all 40,320 orderings, and one of those four arms is the shippable one. Piece count grows 6.412534 and 6.019270 at 16 cells a chunk against a 4× bar and 1.360286 and 1.381061 at 32, so the clause is resolution-dependent in a way the registration did not allow for
P-85 — one stage of the collider build is over half its cost, and it is the triangle copy rather than the BVH the docs blame held on C1; falsified twice over on C2; falsified on C3 (✗65 / M-397) The collider's 45% is this crate's own weld and readiness gate. One stage is 80.3–81.8% of the build, and it is neither candidate: the copy is 0.035–0.050%, the BVH does not dominate either, and all of parry3d is 18.2–19.7%. And the cost is predictable from triangle count — gyroid costs 1.017–1.047× sphere's against a 1.5× bar, at matched triangle and vertex count — which is the best available outcome for a scheduler and the opposite of what was registered
P-86 — slivers are what a capsule controller catches on falsified on C1; falsified by the letter of its column on C2; held weakly on C3 (✗66 / M-398) The recorded degenerate_triangles metric has no gameplay consequence. 3.01% of controller stops land on the bottom aspect-ratio decile against a 20% bar — and that bar was 15.29× chance rather than 2×, because a capsule hits a sliver at 2.30× its area share, which is real enrichment and still six times too little. The seam column reads 1.134, and 1.055 ± 0.101 over episodes, which does not reopen M-133. C3 holds at 0 of 89 against a null expectation of 1.052 — a held clause with almost nothing behind it
P-87 — an octree navigation graph built on the sign bitmap repairs a dig locally, edit-proportionally, and merges convexly by 5× held on C1 and C2, falsified on C3 (✗67 / M-399) Navigation on this crate's own sign bitmap is affordable and it never touches a triangle. P-72's eleven-edit dig repairs in 0.1433–0.4366 ms for the worst single edit and 0.8793–2.5396 ms for all eleven, over a repair set 1.50–1.83× the crate's own dirty-cell count, growing 1.6355× while the world grows 512×. The convexity-preserving merge gives 2.5492–3.8597×, not the registered 5×, with gyroid worst as predicted — because the order of magnitude is in the octree, not in the merge
P-88 — an octree of free cells gives CALIBRE's clearance without a medial axis, locally, and never overstates it C1 falsified; C2 held for the cheap reading and falsified for the tight one; C3 held on the analytic fixtures and falsified on the reference fields (✗68 / M-400) The octree does give a clearance number without a medial axis, and there is no version of it that is both accurate enough and local. Within one voxel on 0.688892 and 0.831008 of samples against a 0.90 bar. λ-membership flips stay at 0.8482 of the changed samples, well inside the 4× bar, but the flip set is a subset of P-87's repair set only for the region reading — ball puts 149–682 flips outside it at every λ ≥ 1.0. And the one-sided clause dies where it matters: 62 / 649 overstatements on the reference fields, 0 on the 480,000 analytic samples. A gate that lies in the permissive direction is worse than no gate, so CALIBRE still needs ρ
P-89 — 1³ is worse than 2³, and M-377's two-term model extrapolates there held on C1, falsified on C2 (✗69 / M-401) M-377's 4³ optimum is now interior with measured neighbours on both sides and nothing left untested below it. 1³ loses by 4.36× on gyroid and 1.76× on fbm_terrain. The two-term model that fitted a stencil of exactly 6 on all twelve of M-377's arms does not extrapolate to c = 1 — 267% and 46% error — because at one cell a chunk the cost stops being field evaluations
P-90 — Lipschitz brush pruning still pays at a 4³ brick, the per-brick list is under 8 bytes, and the two culls compose held on C1, falsified on C2 and C3 (✗70 / M-402) Pruning survives the small brick; the bookkeeping does not, and the second cull is the first one twice. C1 reads 6.3916× and 10.4802× on the registered 46–60 bucket, but only at the brick: P-39's chunk-level cull alone reads 1.5799× and 1.8825×, under its own 2× bar and under its own clock-free evaluation ratios of 1.5956 and 1.8993. The list costs 9.398804 and 10.996338 bytes per brick, lost to the index and not the payload. C3 is the registered null — additional_removed 0 on 8 of 8 — because the brick enclosure is nested inside the chunk's and the two culls are one test at two scales
P-91 — geomorph works on terrain and fails on caves, and dither is the expensive option falsified on C1's terrain half and C2's cost half; held on C2's pop half and, by sign only, on C3 (✗71 / M-403) Item 3.6's prediction is exactly inverted. Geomorph FAILS on fbm_terrain at 25.0771 px and the gyroid half it was predicted to lose is the one that held, at 4.1900 px — because Lengyel's containing-cell rule is missing a morph target on 39.69% of terrain fine vertices against the < 1% the clause needs. Dither, registered as the expensive option, costs 3.49× less temporal history (123,769 against geomorph's best case 431,578) and gets 0.9683 px on gyroid. C3 holds by sign at 1.002476 against a fixture ceiling of 1.075770, which is additivity to engineering precision
P-92 — re-extracting a chunk is cheaper than decoding an encoded mesh of it falsified on C1 on every reading; held on C2 and C3 (✗72 / M-404) You do not choose between extracting and decoding. Marginal extraction is 3.00× the 7.3 ns bar at the cheapest field and 58.4× at a dug chunk, and it misses by 3.41× even against a decode measured on this machine rather than quoted. But the field plus edit log is 77.6–246.2× smaller than meshopt's encoding of the same triangles, and a replay is byte-identical across an Apple M5 and the Zen 3 at 0 differing bytes over 10,000 edits. So the title inverts: you already extracted because the chunk was dug, and the answer is send the log, keep the mesh local, regenerate because the extraction was going to happen anyway
P-93 — there is a crossover rate below which 64³ wins on total frame cost, because 4³ uploads more vertex data falsified on C1 and C3, held on C2 by 509× (✗73 / M-405) 4³ wins unconditionally, and granularity is settled rather than a trade. C1 was denominated in a quantity that no longer exists: the registration's 87.50% is the sample-grid upload on a path GPU-011a deleted, while the vertex upload C1 is actually about is 1.71% of a 12.5 edits/s frame at the 4³ optimum — reaching the window floor of 0.1 edits/s would need a bus 20.7× slower than this rig's. The weld does cost more than the upload it saves, by 509×. And a mixed per-chunk granularity beats neither fixed choice: 0.2376× and 0.1171× against a 1.5× bar
P-94 — an hour of digging is under 2 MB, coaxial edits collapse, and a bespoke coder beats a general-purpose one C1 held — its constancy half with no instrument — C2 and C3 falsified (✗74 / M-406) The log is small, and it does not collapse. An hour of continuous digging is 415,038 B and a saturated hour is 734,400 B against a 2 MB bar; the per-edit constancy half is 17.000000 bytes on all ten rows and could not have come out otherwise, which is said out loud rather than scored. All 200 of 200 coaxial capsules are individually necessary bit-exactly, so ✗41's survivor arithmetic does not transfer to a real stroke. And the bespoke coder beats zstd -19 by only 1.42–1.53× while zstd on the same residuals lands within 1.39–1.43× of it — the whole win is the model and not the coder, so the format is not worth writing
P-95 — undo beats a re-fold below some stable edit separation, and M-50's curve gives the checkpoint cadence falsified on C1 and C2, held on C3 (✗75 / M-407) Undo is always a re-fold, so the checkpoint cadence is the only knob. Re-folding from a checkpoint is cheaper at every separation — 16.3×/15.9×/19.0× at d = 0 and still 1.30×/1.29×/1.55× at d = 127 — and the fitted crossover lies 40.95 / 38.50 / 73.86 edits past the bottom of the log, which is no crossover at all. M-50's curve predicts a cadence of 193.8 against a fit-free measured 32, and the disagreement is a shape difference, not a scale factor. Undo is bit-exact: 0 hash mismatches over 3,654 undo/redo round trips
P-96 — smooth union's 40,320 orderings differ by less than a tenth of a cell, and the spread is a function of the blend radius C1 vacuous on M-38's own fixture, then held and falsified on a fixture that can move; C2 and C3 held (✗76 / M-408) M-38 is retired rather than confirmed. Its 40,317 distinct results are meshes 2.2e-16 world units apart, in a branch where no smoothing happens at all. On a fixture that can move, the spread holds to 0.0375 of blend radius and is falsified from 0.075, reaching 0.656099534 at M-38's own k = 0.15; it falls with k, recovers M-36's single result at k = 0 exactly, and stays inside the 10k seam shell. So smooth union is gameplay-commutative below half a cell of blend radius, and the ordering authority M-38 seemed to demand is needed only above it
P-97 — a hundred-thousand-edit trace replays byte-identically across machines, and if it does not, bisection names the edit falsified on C1 and C2, held on C3 (✗77 / M-409) The fold is bit-identical and two of the meshes are not. C1 fails on 2 of 8 fields by exactly 3 bytes each, and C2 fails with an empty divergence population — first_differing_edit is NONE on all eight and the folded grid differs by 0 bytes over 287,496 each, so there is no differing edit to find. The f64 fold agrees across x86-64 and AArch64 at every one of 100,000 prefixes on all eight fields; the only divergence in 2,470,824 compared bytes is the sign bit of a NaN that unit_gradient emits in release from a plateau M-31's zero-edit fixtures cannot have. Replay is linear at 1.0055–1.0173× against a 1.2 bar
P-100 — a 24-tetrahedron barycentric split reaches full octahedral equivariance where the six-tet split is stuck at 12 held on C1 and C3, falsified on both halves of C2 (✗78 / M-412) M-372's obstruction is real and it is in the decomposition. The barycentric split reaches 48 of 48 with worst_component_ulp 0, bit-exactly, where both six-tet arms read 12 on 32 of 32 in the same run — and it still tiles across chunk seams at 0 open edges, against a mismatched-diagonal control reading 80–3,765 on the same 80 rows. Removing the obstruction costs 2.4405× the six-tet split and 7.9353× Marching Cubes against registered bars of 2× and 6×. Invariance is purchasable; the price is a CAD price, not a game's
P-101 — accumulating dual crossings in a relabelling-invariant order takes the duals from 3 of 16 to 12, for free falsified on C1 and C3; held on C2 at a stated cost (✗79 / M-413) The registered key reorders a reduction A-016 already made invariant. dual_contouring stays at 3 of 16, identical to its own baseline, and is worse than shipped on 9 of them. The reordering is free exactly as promised — a stated cost of 40 of 48 golden dual hashes, max_hausdorff_delta 3.008704396734e-14, topology identical on 320 of 320 — and manifold_dual_contouring does not do worse: the two duals agree on 64 of 64 row-pairs. The one reduction that is not invariant is vec3::length, and changing only that takes both duals to pure_permutation_exact 6 of 6 on 32 of 32 rows
P-73 — every connectivity-weighted normal is far worse than a central difference, and the acos in it is a golden-hash liability falsified on all three (✗56 / M-385) The 2005 result does not transfer to trilinear output, and the determinism objection does not exist. 28 of 60 testable rows are under 3×, and the clause is separately vacuous on 6 of 16 cases where the gradient median is exactly zero. The off-surface canary predicts nothing — 0 of 7 fields clear ρ = 0.7, the best ρ anywhere in the file is 0.584622, and fbm_terrain is negative. And the connectivity route moves 0 of 18 hashes between an Apple M5 and the Zen 3. Nothing in src/ changed, and that is the finding: do not build the dossier's ~40-line pseudonormal
P-77 — a dig's TAA history rejection is five times steady state and persists, k-DOP clipping recovers half of it, and it is concentrated at the brush falsified on all three (✗58 / M-389) A dig's temporal debt is one frame. The post-edit rate is 2.8997× steady against a fixture ceiling of 2.9852 computed before the run, and the spike lasts a single frame — both halves of C1's own falsifier. k-DOP recovers exactly 0 on all 140 rows, by the paper's own containment guarantee, and its cost half is vacuous because no GPU TAA resolve pass exists in this crate. Concentration is 67.23% against an 80% bar, while the mechanism the clause was reaching for holds at 1.000000 on the edit-attributable denominator: under locomotion there is no history left to owe

Seven of the thirty were decided by arithmetic that was available before the harness existed, which is Phase 23's central finding turning up again in the phase that was supposed to have absorbed it. P-93's C1 was denominated in an 87.50% belonging to a path GPU-011a had already deleted. P-92's own gloss on C1 was arithmetically unreachable before the run. P-83's C1 could not have been passed by any integrator, because the gap it measures is Marching Cubes rather than the quadrature. P-82's capture window is 2R + t and the clause was written against t. P-86's 20% bar was 15.29× chance rather than the 2× it reads as. P-94's constancy half is 17.000000 bytes an edit and could not have come out otherwise. And P-102's C2 was "exactly 2" against a population of exactly 2. None of those needed a machine; all of them needed the number to be written down where a reader could check it, which is the only thing this page has ever claimed for pre-registration.

The vacuity machinery earned its keep, and it is the reason six of these rows are readable at all. C1 of P-96 is vacuous on M-38's own fixture — 40,317 distinct results in a branch where no smoothing happens — and the row is only a result because a second fixture that can move was run beside it. P-102's ±1 arm reports VOID rather than a pass. P-73 is vacuous on 6 of 16 cases where the denominator is exactly zero, P-81's C3 on a field arm with nothing to count, P-77's on a GPU pass this crate does not have, and P-95's on an N that does not exist to be stable. A clause that cannot fire is not a clause that held.

Phase 25 — twenty run, seventeen with a falsified clause, and one mechanism that won and was refused anyway

Twenty registrations drawn from a bit-packing and broadword survey, and not one of them was allowed to change crates/isomesh/src/. That was the phase's condition rather than its outcome: every arm is a bench-local reimplementation, so no golden hash moved and no consumer-visible behaviour changed. A mechanism that earned landing was to get its own ticket afterwards, because a landing not registered in advance is V-45's failure mode.

Sixty clauses: 34 held, 24 falsified, 2 vacuous. Two rows held every clause (M-419, M-430), one held every clause that could fire (M-432), and the other seventeen carry at least one falsification.

prediction verdict what it means if you depend on this crate
P-106 — the twelve cut-edge flags of a cell are a fixed boolean circuit over its eight sign bits, so sixty-four cells' worth fit in one word each held, all three (M-419) The phase's one clean mechanism win, and it still should not be built yet. The circuit is 12 word operations and 24 including the plane build, against a bar of 24 — derived by executing the same source over a counting word type rather than by reading the code — and it agrees with the crate's own table on 256 of 256 patterns where a deliberately broken circuit misses 192. It costs 0.1204 of the byte table's instructions per cell, a 7.7–8.3× cut on classify. But the 256 cut masks take only 128 distinct values and every complement pair agrees, so the twelve flags carry strictly less information than the case index and cannot feed CASES — and the best extraction-level ceiling the saving buys is 2.4752× on one field and 1.0231× on another
P-117 — nothing on the hot path is FMA-contraction sensitive, and if something is, M-31's cross-machine golden hashes would already have moved held, all three (M-430) The risk is real, named, and unrealised — which is the only outcome that lets you stop worrying about it. Eleven contraction-sensitive expressions under crates/isomesh/src/, with measured divergence under deliberate fusion from 2 ULP (vec3::dot) to two sign-crossing divergences where an exact 0.0 becomes -4.44e-16 (marching_cubes::corner_position, dual::place_vertices). And 0 of 216 golden hashes differ across x86_64-unknown-linux-gnu and aarch64-apple-darwin, with mul_add_call_sites 0 — rustc does not contract a*b + c by default and this crate never asks it to. So a future +fma build, a -ffast-math equivalent, or one hand-written mul_add would move golden hashes at eleven known sites. That is a build-flag constraint, not a code change
P-119 — double-buffered welding removes P-9's chunk-order spread, under 1.25× cost, with the mesh invariant under every permutation C1 vacuous on the registered column; C2 and C3 held (M-432) The mechanism works and the registered perturbation had nothing to move. baseline_spread is 0 on 16 of 16 rows for chunk order, so C1 as worded cannot fire — and the census that explains it did not exist until this phase, because the harness declared it and populated none of it. buckets_of_three_or_more_spanning_chunks, the only bucket kind whose member count chunk append order can change, reads 0 on 16 of 16. Meanwhile on P-9's own within-bucket protocol the single-buffer arm reproduces the published spread on all 16 rows and double-buffering takes it to 0. Cost is 1.0888–1.1059× in instructions against a 1.25 bar, and peak_bytes_ratio is 2.86–4.28× — a real price for determinism that no clause bounded
P-114 — one bit per 64 cells gives a second level at a sixty-fourth the size, and two levels skip 4,096 cells per test held on C1 and C3; falsified on C2 on 21 of 32 rows (✗90 / M-427) This is the ✗51 shape: it wins its microbenchmark by 2.57× and earns no ticket. C1 holds on the sparsest field as measured in all three units — thin_plate at 1.612× (65³) and 2.568× (129³) against a 1.5× bar, and 2.129×/3.318× in instructions, so the instruction form is the larger margin. Then the share closes it: traversal_share_of_extraction is 0.000088–0.000994, so the extraction-level ceiling peaks at 1.00039× and dips below 1. The registration had inherited a 5.5× stage figure and asserted the stage mattered; the harness measured the share instead. And the win does not generalise — ratio is below 1 on all eight gyroid and noise_cavity rows, at 4–11% active fraction
P-121 — decompose extraction into float work and integer work, and a bit-work total under 15% closes three rows before anyone writes a harness held on C1 and C2; falsified on C3 on 18 of 72 rows (✗95 / M-434) The phase's gate, and the number three other rows are denominated in. Worst residual_share 0.005195 against a 0.05 bar, and max_reference_integer_share_at_65 0.724533 against 0.15 — so R-103, R-104 and R-106 were live rather than Amdahl-dead. C3's falsification is a qualification on every share this phase quotes: on 2 of 8 groups the surface-free arm does not separate classify from emit, so integer_share is a share of their sum and no row may quote classify alone as isolated. Several stage columns go negative — prefix differences inverted by clock movement, bounded to half a percent by C1's own bar
P-103 — FastLanes' Scalar_T64 beats naive scalar by up to 8×, and the one quantity already boolean here is a cell's eight corner signs falsified on C1 as a whole-fixture gate and on C2; held on C3 (✗80 / M-416) The mechanism did exactly what the paper says and it bought nothing. Sign tests per cell fall from 8.0000 to 1.0476–1.0967 — a 7.3–7.6× cut in precisely the quantity Scalar_T64 targets — and instruction_ratio still spans 0.579154–1.08354 against a bar of 0.5. The reason is in the comparand: the bit-sliced arm's instructions per cell span only 26.69–29.96 across all 32 rows while the byte arm's span 24.77–50.81, so every apparent win is the byte path paying an f64 penalty, and at 65³ f32 the bit-sliced arm loses outright
P-104 — the active-cell bitmap is FastLanes' horizontal layout, and M-287's stride tax says so C1 vacuous; C2 falsified; C3 held (✗81 / M-417) The layout the clause is about is unreachable through the public API, and a coincidence was retracted. row_stride(size) = size[0] | 1 since A-024, and an odd row greater than one can never divide a power of two, so no caller can reach the taxed layout. The first clean run appeared to reproduce M-287's published 3.37 at 3.3714; the re-run reads 8.1052 on the same measurement of the same binary, while c2_instruction_ratio_fold reads 1.8054 on both. Of the 65 columns the two datasets share, 30 are byte-identical and 35 moved — instruction columns by at most 0.006%, cycle columns by up to 221.8%
P-105 — nothing in the crate popcounts the bitmap, so Harley–Seal's carry-save reduction is worth pricing falsified on C1; held on C2; C3 vacuous on 28 of 32 rows and falsified on the rest (✗82 / M-418) LLVM already took the saving Harley–Seal is selling. The naive fold autovectorises to 35/4 = 8.75 instructions per word exactly; the carry-save chain's nine live accumulators keep it scalar at 145/16 = 9.0625. So the mechanism issues more instructions per word, and the null was measured in its best case — objdump finds zero popcnt in the binary, because the repository sets no target-cpu. C3 is vacuous because a four-point monotone trend spans less than one row's own five-window reproducibility, up to 25× less. And count_ones_in_dual_rs is 0, so the row prices a stage the crate would have to add
P-107 — Flying Edges spends a prefix-sum pass to turn per-row counts into output offsets, and a two-level rank directory makes it a lookup falsified on C1; held on C2 and C3 (✗83 / M-420) Amdahl-dead exactly the way ✗51 was, and the registration named it in advance. offset_share is 0.000328–0.009714 against a 0.05 bar, so the offset stage is at most 0.97% of extraction and the whole extraction-level ceiling is 1.0098× even if the stage were free. The structure is correct and cheap — overhead_fraction 0.032227 against 0.0351, a rank query folding at most 7 words at every resolution — and it buys random access, not throughput: the shipped sequential walk costs a fraction of an instruction per query against the rank query's ~127
P-108 — Vigna's broadword select needs neither PEXT/PDEP nor a table, and the walk it replaces is a registered expected null falsified on C1 as registered; held on C2 and C3 (✗84 / M-421) The null arrived, and the share was the real answer. Broadword select costs +48.9 to +61.0 instructions per set bit over dual.rs:489-497, an instruction ratio of 0.2085–0.3165. But walk_share_of_extraction is 0.000103–0.001462 — between one part in ten thousand and one and a half parts in a thousand — so deleting the walk entirely buys at most 1.00146×. The scored arm makes zero count_ones calls, and the unscored literal variant that does is priced: a hardware POPCNT narrows the gap from about 4× to about 3× and cannot close it
P-109 — Elias–Fano encodes a monotone sequence in about 2 + ⌈log₂(u/n)⌉ bits with O(1) access, and within-chunk edge indices are monotone falsified on C1 and C2; held on C3 (✗85 / M-422) Right structure, wrong sparsity, and the cost model forecloses it arithmetically. A 4-bit budget demands u/n ≤ 8; universe_per_crossing measures 16.5304–786.3330, so the fixture's densest row is already 2.07× past the ceiling. Measured 7.2959–12.6711 bits per crossing, with low_bits_width equal to ⌈log₂(u/n)⌉ on 24 of 24 and the total within one bit of Vigna's own model. Access costs 36.8–158.7× direct addressing in instructions. The encoding still beats the shipped structure's space by up to 563×, which is the number a future reader should quote rather than the bar
P-110 — Pibiri & Kanda's contribution is rank/select that supports flip(i) while staying fast, which is the shape a structure written during a sweep needs falsified on C1; held on C2 and C3 (✗86 / M-423) The order-independence proof is the durable half. Over 128 orderings of 4,096 flips, distinct_final_states is 1 on every row while the order-sensitive control reports 128 — so V-45's objection does not arise, and the control is what makes the 1 admissible. C1 fails in every unit: the rank-only conjunct is a 2.1–2.4% near miss whose sign the unit decides, and the flip-plus-rank conjunct decides the verdict at 2.24–2.38×. The cost is located structurally — static rank is flat across all 24 rows while mutable rank climbs monotonically with the top-level scan
P-111 — simdjson's 256-entry byte-to-permutation table, reduced to scalar, is a 2 KiB const this crate can actually have falsified on C1 in all four units and on C3 on 14 of 16 rows; held on C2 (✗87 / M-424) Decidable from a bit census with no clock at all. stores_per_set_bit_walk is 1.00000 on 16 of 16; stores_per_set_bit_table is 2.00000–22.17637, exactly 64·words_nonzero/set_bits. A mechanism issuing 2–22 stores per useful store cannot beat one issuing one. The loss is located rather than observed: a byte-skipping variant drops stores to near 1 and still loses on all 16 rows, so the cost is the lookup. And C3's L1 claim survives the instrument on only 11 of 16 rows — one row where the table genuinely reads fewer misses per set bit
P-112 — Billeter's count-scan-scatter has a prefix sum in the middle, and P-107's O(1) rank replaces it falsified on C1 and C2; held on C3 (✗88 / M-425) Closed by its own registered falsifier, and it left a method rule behind. The 70% scatter falsifier fires on 7 of 16 rows; scan_share is 0.036580–0.158941 against 0.20, whose scan-free ceiling is 1.1890× — under the 1.25 C1 asked for, so C2 makes C1 arithmetically unreachable. The rank arm is 2.2–8.6× slower. And the whole three-phase compaction is 0.0162%–0.4825% of an extraction, so a free scan buys 1.00063×. The R-085 residual bar fired twice before the dataset landed and the diagnosis is the transferable part: the decomposition is exact to the last retired instruction while its nanosecond form reads 4–8% with a field-dependent sign
P-113 — Roaring switches container type at 6.25% density and says a bitmap is the wrong structure below 0.1% falsified on C1 and C2; held on C3 (✗89 / M-426) The clause quantified over the wrong axis, and a span control passed anyway. Density is a function of chunk size, not of field: 0 of 4 granularities have the eight fields straddling 6.25%, and within any one granularity they never cross it. The density_span_over_fixture control cleared its one-decade bar and the span is generated entirely by chunk size — a span control proves the range is wide, not wide along the axis the clause is about. C2's two failures were decidable from size_of alone. And the walk timer is saturated on the array arm on 32 of 32 rows, so bitmap < array was unobservable and the verdict is carried by instructions
P-115 — Tree-Encoded Bitmaps are the only RLE-family scheme that preserves the random access rank needs falsified on C1; held on C2 and C3 (✗91 / M-428) One measurement retires TEB, WAH and EWAH for this crate, and the registration pre-committed to that reading. access_ratio is 57.77–115.77× the flat bitmap's against a bar of 2.0 — 29× to 58× past it — on both rank granularities and in instructions. Space compresses 2.37–563.75×, and the pairing is the finding: thin_plate 129³ is 563.75× smaller and 63.9× slower to read, against a flat bitmap whose entire size is 256 KiB. Subtracting the measured instrument floor makes the ratios worse, and the implementation is not a strawman — teb_bytes is below the fully-pruned variant on 6 of 16 rows
P-116 — GRAPHGEN synthesises the optimal decision tree over a decision table, compresses it to a DRAG, and emits code held on C1 and C3; falsified on C2 on 8 of 8 rows (✗92 / M-429) The synthesis is sound and inert, and that is a fact about the Marching Cubes case table. average_path_len is 8.000000 — the optimal tree is the complete eight-level tree — and min equals max over 6,561 DP states, so every ordering of the eight conditions is optimal. The DRAG then merges exactly one node of 511, and it is a leaf merge. With 256 patterns, 0 don't-cares and 255 distinct actions there is no redundancy to exploit. The emitted 1,311 lines compile under rustc, Kani discharges 62 checks in 2.04 s with a sabotage that fails as it must, and the generated form costs 1.65%–3.83% more
P-118 — Neal's superaccumulator is exactly order-independent, so it is a second route to P-101's question that needs no invariant key falsified on C1 and C2; held on C3 (✗93 / M-431) M-177 is closed: it is not an accumulation defect. With every reduction on the dual vertex path exact — twelve superaccumulated accumulators plus vec3::length's dot — pure_sign_flip_exact still reads 6 of 32, while the same arm takes pure_permutation_exact from 8 of 32 to 32 of 32. So the permutation half is entirely vec3::length and the sign-flip half is structural, as M-177 said. C1 was out of reach before the run and a column says so. C2 fails at 7.93× instructions against a 2× bar, with a named mechanism: twelve reductions per solve, each paying a whole 67-chunk read-out over about four terms. Incidentally measured for the first time: sum_equivariant costs 4.64× a naive ordered sum on the dual solve
P-120 — Wu, Otoo & Shoshani replace pointer-based equivalence trees with a flat array and report 5× to 100× falsified on C1 on 4 of 32 rows; held on C2 and C3 (✗94 / M-433) The ✗26 objection does not reproduce, and that is a claim about this union-find. order_independent, labels_consecutive and partition_identical are all true on 32 of 32 across three scan orders — but every arm here is per-chunk, bench-local, rebuilt from scratch and never asked to delete, and connectivity.rs:29-46's refusal is about an incrementally maintained structure asked to handle fill. C1 clears 2.0× on 28 of 32 rows and tops out at 2.3759×; the four failures are all fbm_terrain, the only field whose air fraction is near half, so its comparand gets cheap. On instructions the bar clears on only 14 of 32
P-122 — Stream VByte keeps a dense control stream and a variable-length data stream separate so the decoder never branches on payload falsified on C1; held on C2 and C3 (✗96 / M-435) The split never reduces mispredictions and is cheaper anyway. branch_miss_ratio spans 1.001214–1.983313 on 16 of 16 rows — it doubles them at worst — while instructions per cell fall by 2.9%–14.6%, and the harness closes the obvious alternative explanation by showing the split makes more corner gathers, not fewer. There was very little to remove: branch_misses_per_cell_single is 0.008008–0.250699, under one misprediction per 125 cells at the sparsest. And one of sixteen rows' verdict depends on which order the two arms were measured in, so the harness records both orderings and refuses to quote that row as firm

Eleven of the twenty were decided by arithmetic available before the harness existed, which is Phase 24's central finding turning up a third time. P-107's and P-108's and P-112's clauses are share bars against shares of under 1%. P-109's 4-bit budget needs u/n ≤ 8 against a measured 16.5–786.3. P-111's stores-per-set-bit ratio is 64·words_nonzero/set_bits and needs no clock. P-113's byte crossover is 1/(8·index_bytes) and its two failures fall exactly where size_of puts them. P-114's one-level rows cannot reach 4,096 by construction. P-116's DRAG has nothing to compress because the table has no don't-cares. P-118's C1 was closed by p-101.csv before experiment_p118.rs was written, and the file records that in a column. P-103's ceiling and P-121's own bar complete the eleven.

Five refute a figure this repository or a cited paper had already published. M-287's 3.37× stride tax is not reproducible as a cycle ratio — the same measurement of the same binary reads 3.3714 and 8.1052. M-337's 5.5× stage figure, which P-114's registration inherited, is a share of under 0.1% of extraction. M-306's rejected-brush shares were read as active-cell densities and are high by 12.5×. Roaring's 6.25% is the two-byte case only. And M-177's obstruction, which three separate mechanisms have now failed to move, is confirmed structural rather than arithmetic.

Two harnesses aborted on their own vacuity controls before their datasets landed, and both aborts were worth more than the clause they interrupted. experiment_p112.rs's residual bar fired twice and the diagnosis retired a wall-clock control in favour of an instruction one, with a mutant control attached to prove the resulting zero could have been non-zero. experiment_p116.rs's emitted-text cross-check was comparing the source against its own reverse, and the three-conjunct instrumentation located the defect in exactly one of them. A third defect — a committed CSV column recording a decimal digit count rather than a stride — was found by writing this page's row for P-104 against the dataset rather than against the run.

Phase 26 — four experiments the backlog had left unregistered, and two of them close a question

Not a sweep. These four were already in BACKLOG.md, unblocked, and had never been registered: R-027a split out of R-027 on V-45 in Phase 17, R-052 and R-053 left as the successors to R-050 and R-048 when Phase 20 closed, and R-072 named in O-12's own text and then filed by nobody. That last one is the reason the phase exists at all — an open question was invisible to scripts/backlog_gate.sh clause 6 for want of a P- id to be missing, which is exactly the drift the clause exists to surface and could not.

Three of the four are corrections to an experiment that already ran, and each names in its own registration the error it is not repeating. One landed a source change, registered in advance.

prediction verdict what it means if you depend on this crate
P-126 — O-12's remaining half: is the dual vertex link a single cycle, over all 2²⁷ sign patterns of a 3×3×3 block? held, all three (M-439) O-12 is closed by exhaustion, and the closure is a standing gate rather than a claim. worst_link_components reads 1 on every non-control arm over 134,217,728 patterns and 5,067,767,808 dual vertices, while all three controls read 2 with 99.9M–221.8M link-defective vertices. C1 is additionally proved: two lemmas checked exhaustively at start-up — a cycle's consecutive edges always share a cell face over 256 cases × 64 masks, and with the joined bit agreed the two cells sharing a face induce the identical pairing over 49,152 combinations — so the sweep's job is that no reachable pattern escapes the proof. control/open_block reproduces P-63's own vacuity as a measurement at the right block size: 5.07 G dual vertices of which only 860,880,896 carry a complete link
P-124 — port Finken et al.'s monotone-edge condition to the ambient complex, where ✗36 proved the mesh-edge reading is saturated held, all three (M-437) The detector has signal, and it is almost entirely in the edges a chord predicate cannot reach. At 65³ over 262,144 cells, diagonal_only_failures is 17,862 of 17,862 on sphere, 10,563 of 10,567 on box_exact and 12,669 of 13,693 on thin_plate — cells rejected by a tetrahedral diagonal with every axis edge monotone. The mesh-edge control runs the same predicate in the same run and reproduces ✗36's saturation, which is what makes the ambient count a property of the complex rather than of the tolerance. The tolerance was fixed at registration — scaled by max(|f(a)|, |f(b)|) — because a tolerance vanishing at the endpoints is precisely what ✗36 caught
P-123 — decompose M-318's 45× buffer-churn gap; if the order-only term dominates, a canonical reorder at emission recovers it held on C1, falsified on C2, C3 held on 3 rows and vacuous on 3 (✗97 / M-436) The gap is not ordering, and R-027 is closed for good. The order-only term is 0.0000%–0.137% of the churn; the predecessor-shift term is 97.9%–99.4%. sphere 129³ reproduces M-318 to the digit — churn_total 15,706, churn_geometric 346 — and spends 15,370 of it on slots shifted because an earlier cell emitted a different number of vertices. That is Acar's sequential-counter instability, and no reorder at emission touches it: the only remaining shape is the persistent edge→slot map V-45 refused, which makes extract_into stop being a pure function of its inputs. The vacuity control fired both ways — the canonical arm drove the order-only term to exactly 0 while leaving geometry unchanged, and a permuted arm drove the same detector non-zero
P-125 — ship the pinch predicate as a validate report, so a caller can ask whether the =-corner repair is safe on its data held on C1 and C2, falsified on C3 on 2 of 6 rows (✗98 / M-438) The clearance is sound and the count is not, and the difference matters. C1 reproduces M-352 exactly — 516 of 17,201 collapse groups on bonsai, 0 of 50 on fuel — from the baseline mesh alone with no repair applied, and C2 gives one identical census over every face permutation, which is ✗26's objection asked in advance. C3 fails because a pinch count is an upper bound: 516 pinches weld 129 components, since several pinches can weld the same pair and a pinch inside one component welds nothing. So zero pinches is a genuine clearance — confirmed on all three zero rows — and a non-zero count bounds what a weld could reach rather than predicting it

The four registrations were written the same day and three of them contained an error the harness author found and reported rather than amended. That is the machinery catching the person operating it, for the third phase running, and all three were available before any harness existed:

And one harness rejected its own first implementation on a measurement. P-125's report groups coincident vertices, and the obvious grouping is equality on the lattice cell key — a genuine equivalence relation, and MeshReport::weld_buckets' own notion. Measured against the shipped welder on sphere 25³, where M-48 recorded Welder::weld removing 48 vertices and 96 triangles at this very epsilon, it finds 30 of the 48 merges and 60 of the 96 folding faces, because a coincidence class straddling a cell face splits between two buckets. For a report whose entire job is issuing clearances, under-reporting is a false clearance. Rewritten as ε-connected components: 48 and 96, exactly the weld, and erring on the safe side because the welder's classes refine the closure.

Three of the four experiments contain no clock at all — every column is an integer count over an enumerated population — so M-280 has nothing to move and their clean re-runs could not have shifted a digit. P-126's wall_seconds sums to about 1,015 s, inside the ticket's own 4–45 minute estimate, and no clause reads it.

Phase 27 — fifty registrations from eighteen fields of mathematics, every one run

The largest phase by any measure: fifty pre-registered experiments, P-127…P-176, all fifty harnessed, all fifty run against a clean tree, all fifty CSVs committed with clean provenance. The registrations were transcribed from eighteen fields of mathematics before any harness existed — isomesh::experiment!("P-127") was a compile error until all fifty landed — and the phase changed nothing in crates/isomesh/src/** and moved no golden hash: every mechanism is bench-local, in benches/common/, driven through the public API.

Thirteen rows held on every clause, three failed on every clause they could fail, and thirty-four are mixed. Three registrations were nulls on purpose and came back null; three more came back not null, which is why they were worth registering.

prediction verdict what it means if you depend on this crate
P-127 — b*b - 4*a*c is identically Cayley's 2×2×2 hyperdeterminant held, all three (M-440) The headline. symbolic_difference_is_zero true, 12 terms against 12 at degree 4, all 3 pencil pairings agreeing, exact-rational deviation 0/1 over 3,481 trials — and f32_sign_disagreements 14, which is what keeps the exact-sign work alive. A shipped expression has been a classical invariant for the crate's whole life without anyone knowing
P-128 — the saddle count cannot depend on cell aspect ratio held, all clauses on 48 of 48 rows (M-441) count_disagreements, sign_disagreements and corner_value_mismatches all 0 over 7,077,888 cells at aspect ratios 1, 4 and 8. The GL(2)³ weight (det g₁ det g₂ det g₃)² is an exact i128 equality. Group D may vary cell aspect ratio without re-asking whether interior ambiguity moved
P-129 — invariance as algebra, 10× cheaper than the 48-element sweep falsified, C1 and C3 (✗99 / M-442) The Δ-invariance check costs one evaluation per element, not per cell, so relabellings_per_delta reads 0.980 and the bar was dead on an integer count before any clock ran. The harness's first draft compared the case word two ways and was a tautology — case_of(relabel(f)) and relabel_case(case_of(f)) are the same function by construction — which the vacuity control caught by measuring zero violations on a deliberately asymmetric tuple. The shipped sweep compares the shipped table's triangulation under the element instead
P-130 — does rank predict ambiguity better than the case index falsified, C1 and C2 (✗100 / M-443) delta_zero_share reaches 1.000000 on box_exact — every surface cell sits exactly on the hyperdeterminant hypersurface. C2 is arithmetically unreachable: ambiguous = g(case) makes I(R;A) ≤ I(R;K) a data-processing inequality, so no measurement could have made it hold
P-131 — the Δ = 0 branch fires and is not the tangency the comment describes held, all three (M-444) 143 hits on reference fields, of 3,858 branch hits 2,222 true rank 3 with border rank 2 — de Silva & Lim's W-state class, not the tangential touch the code comment describes. The registered W-state fixture reaches the branch with w_state_rank 3 against w_state_border_rank 2
P-132 — orbit class predicts T-001's defects falsified on C1, held hard on C2 (✗101 / M-445) Only three of six orbit labels populated — that is C1's death — but the chi-square reads 445.967 on dof 2 against a critical 5.991, with the decomposable stratum contributing 327.649 by itself at defect rate exactly 0. And the row's most reusable output: zero non-manifold edges, zero non-manifold vertices, zero self-intersecting pairs — T-001's entire defect population on these fields is degenerate triangles
P-133 — a filtered exact sign for Δ, under 1.5× falsified on C2 on an integer before any clock is read (✗102 / M-446) naive_ops 27 against filter_ops 65 is 2.407, already past the registered bar. And the deeper thing: a static filter cannot certify an exactly zero Δ, and three of eight fields put 84–100% of their surface cells there
P-134 — |Δ| / (max|fᵢ|)⁴ as a continuous ambiguity magnitude falsified on C2 at 3 of 8 fields against a bar of 4 (✗103 / M-447) box_exact is arithmetically excluded rather than counted as a miss: its normalised magnitude has variance 0 over all 1,352 surface cells because a polyhedron's |Δ| / (max|fᵢ|)⁴ is identically 0. C1 held exactly — dyadic-scale error 0 on 16 of 16
P-135 — where the multi-affine identity stops holding held, all three (M-448) The boundary is now a number: a tricubic residual of 56 named non-zero terms, and under smooth_min(k) the deviation tracks k as exactly k − (7/16)k² — 9.9956e-4 at k = 0.001 rising to 3.906e-1 at k = 0.5. The O(k) seam shell the 2026-08-23 memo measured, joining Group A's scope to M-38
P-136 — the hyperdeterminant resolves the interior test the registered null came back null (M-449) sign(Δ) is worth nothing on the interior test: the best sign-only rule scores 0.985600 against a base rate of 0.985600 — delta_information_gain 0.000000 — and the reason is a group action, not a fitted number: Δ is blind to face negation while that same negation moves the separated count from 225 to 4,113
P-137 — BKK mixed volume 2: at most two critical points held, all three (M-450) Mixed volume 8 − 6 + 0 = 2, reproduced independently as an eliminant of degree exactly 2 in w. And SADDLE_COUNT's 2 is a different theorem: grad_disc_degree 6 against repo_disc_degree 4, root sets differing on 31,883 census cells and agreeing on 7
P-138 — price the tricubic case explosion before anyone proposes it held, all three (M-451) Tricubic mixed volume 116 against the trilinear's 2, case space 2^8 → 2^64, case_space_tractable false. The unregistered triquadratic arm is the only rung with both order and a tabulable table: mixed volume 29 over 2^27 = 134,217,728
P-139 — is the Kuhn triangulation regular, so Viro patchworking transfers held on C1 and C3, C2 split 4 true / 12 false (M-452) Kuhn's six tetrahedra are regular, exhibited by the lifting w(S) = −|S|(|S|−1)/2 verified against all 24 inequalities and a 70-subset lower-hull enumeration. The registered PW/PV comparison disagrees on 22,841 of 99,932 active cells in both directions
P-140 — patchworked fields with prescribed genus, as bench-local fixtures held, all clauses on all 560 rows (M-453) Six fields with genus 1, 2, 3, 2, 3, 5 prescribed by construction, and every one of 7 extractors reproduces every prescribed χ — all 56 pairs correct at 49³. Its sharpest finding is not about genus: graph_cube_g5, the highest-genus fixture, is perfect at 7³ and 11³ and meshes literally nothing at 9³
P-141 — derive the case table by real quantifier elimination, offline held — C1 true on 2,112 of 2,304 queries, the 192 exceptions all the pre-registered outcome (M-454) z3 5.1.0 re-derived AMBIGUOUS_FACES entry by entry over every real corner assignment, cases_matching_table 1,536 of 1,536, cases_disagreeing 0 — and it refuted the shipped Separate default on 192 of 192 ambiguous faces in 1.185 s. The 192 timeouts are nested-quantifier witness queries at the 2 s cap, terminated=false, which is C1's registered second branch. 2,304 hash-stamped .smt2 certificates
P-142 — the gyroid's χ = −8N³ under periodic wrap held on C1 and C2, falsified on C3 as registered (✗104 / M-455) chi_measured −8 / −64 / −216 against predicted at N = 1, 2, 3, genus 1 + 4N³ = 5 / 33 / 109 on all 16 rows. C3's falsifier's own reason was too strong: what the gate needs is a second ValidateConfig constructor plus one fold pass, not a change to Extractor::extract_into
P-143 — Schwarz P −4 and Schwarz D −16 as second and third known-χ fields falsified on C1 at 1 of 10 rows, C2 held as an exact i128 polynomial identity (✗105 / M-456) The one miss: schwarz_p at N = 3 reading −102 against −108 with non_manifold_edges 6 and chi_pinch_corrected −108 exactly. The mechanism is a group action: Schwarz P's body-centring operation negates F_P rather than translating it, so P's lattice is simple_cubic beside space group Im-3m, and that apparent contradiction is the mechanism
P-144 — can a periodic value-noise terrain admit a χ oracle falsified by the three-octave half, and the falsification runs the interesting way (✗106 / M-457) At one octave χ converges on 5 of 5 seeds and oracle_exists is true on 35 of 140 rows, against a registration that named "no oracle" as the likely outcome. The gate must be per-seed exactly as registered: converged χ reads −8 on three seeds, −12 on one and −16 on one
P-145 — a digital-topology χ oracle where the crate has none held, all three (M-458) It reproduces χ = 2 on sphere and 0 on torus, reproduces P-142's analytic gyroid exactly (−8 / −64 / −216, disagreement_cells 0), and supplies a first ground truth on the two closed fields the crate declares unknowable — gyroid −24 stable across 33³ and 65³, noise_cavity 82 and −152 — at cost_ratio 0.4746–1.0648 of the extraction it grades. Etiene's DOI resolves through three routes to 10.1109/tvcg.2011.109
P-146 — a metric from the trilinear's own Hessian buys 25% fewer triangles at matched error falsified on C1 and C3 (✗107 / M-459) c1_winners 0 of a population of 4 — at matched Hausdorff the metric arm is never cheaper and is 2.298935× dearer on thin_plate, the most anisotropic measurable field. metric_share 0.332862–8.747515 against a 0.15 bar. And the finding about the roster: the one field where the mechanism demonstrably works, fbm_terrain at flat_axis_aligned_fraction 1.000000, is Unbounded and therefore ungradeable
P-147 — the exponent does not improve and the constant does falsified on all three (✗108 / M-460) The exponent moved by 0.352013 on fbm_terrain against a 0.1 bar; the fitted constant's correlation to the AM–GM gap is −0.095238 — negative, not merely under 0.7. And C3's csg_difference read exponent_difference 0.000000 because a permutation-symmetric field annihilates all three degrees of freedom a per-axis grid has
P-148 — metric interpolation across a seam held on C1 and C2, C3 split 84 true / 12 false (M-461) Component-wise determinant swell reaches 6.84e9 against log-Euclidean's 1.77e-7; C2 held on 48 of 48 geometries, so three transcendentals cost M-32 exactly nothing and hashes_moved 0. The twelve C3 failures are gyroid under both schemes — its seam correspondence is not injective (seam_vertices_a 295, seam_vertices_b 294), which is M-48 again and not the interpolant
P-149 — the saving is monotone in the principal-curvature ratio falsified where readable at all (✗109 / M-462) torus's saving is perfectly anti-monotone, Spearman −1.000000 at 65³, and fbm_terrain's umbilic bin — the control that was supposed to show no saving — costs −6.04. 70 of 112 rows read unmeasurable:arms_identical because five of eight fields make P-146's two arms one grid
P-150 — Cao's L¹ anomaly in Cao's own table the registered null came back null and then inverted (M-463) The anomaly did not reproduce — anomaly_reproduced false on all 384 rows, violations_in_l1 0 of 72 — because M_L1 wins all 96 groups in every norm. L¹ is the one column where the theory holds rather than the one place it fails
P-151 — goal-oriented adaptivity beats camera-distance LOD by 20% falsified on C1 and C2 at 16 true / 48 false, C3 falsified (✗110 / M-464) It holds on torus alone — and there it genuinely is the visibility mechanism, gain_near 0.244932 collapsing to gain_wide −0.010015. But sphere's goal arm is 10.655× worse at matched triangles, and the whole criterion costs 0.371498–3.055830 of extraction with adjoint_share 0.144361 against a 10% bar
P-152 — Jones' β is the planarity assumption the QEF never checks falsified on C1 and C2, C3 held on 6 rows of 16 (✗111 / M-465) β is not a fraction of an extraction — it is one to two extractions (beta_share 0.824659–1.693981 against a 0.10 bar) — but the signal it carries that the residual does not is 3 to 176 cells a row
P-153 — β beats curvature as a refinement criterion falsified on C1 and C2 (✗112 / M-466) The criterion this row was built to promote loses to the derivative it was built to discredit, on every field (beta_beats_curvature false on 8 of 8). And noise_cavity's refinement ladder is inverted — error goes up under refinement, 0.96 span — which is the sub-cell structure C2 was about, arriving as a measurement of the premise
P-154 — a triangle budget from a convergent sum falsified on C1, C2 held on 21 rows of 24 (✗113 / M-467) Unreachable at 4 fields — max_fields_any_constant 4, so no single k could ever have passed — and M-13's area law, with zero fitted parameters, gets 5 fields where the β-sum gets one. thin_plate divergent at all three resolutions
P-155 — predict M-12's constant from Strang–Fix instead of fitting it falsified on C2 at 0 of 8 against a bar of four — and the bar equalled the entire measurable population (✗114 / M-468) C1 HELD: order 2 derived and measured on 8 of 8, both — the hat reproduces constants and linears exactly and fails on quadratics. Two of the four measurable fields are polyhedra whose creases have no second derivative
P-156 — a compact prefilter instead of a truncated recursive one falsified on C1 at 5 of a population of 6 and C3 at one ulp (✗115 / M-469) csg_difference at +6.80% is the one miss. C3's failure is not the quasi-interpolant's: the shipped standard_trilinear arm loses seam bit-exactness on the same six fields with the same worst delta. footprint_probe_outside 0 on all 80 rows
P-157 — raise the order: the lever ✗42 did not pull falsified on C1, C2 and C3 held (✗116 / M-470) The tricubic Lagrange 4×4×4 filter is genuinely order-4 on its own zero set (recon_fitted_exponent 3.84 / 3.09 / 3.74 / 4.04), and the mesh's exponent still reads ~1.9 — with an infinite-order exact_oracle arm pinned at the same ~1.9: the second order belongs to the piecewise-linear mesh, and no filter can reach it. cases_invalidated 256 against a prediction of 256
P-158 — sparse grids need a regularity the sharp CSG fields have not got the null arrived exactly as registered (✗117 / M-471) C1 HELD with the mixed-derivative norm divergent on both CSG fields (norm_growth_exponent 5.000000 on box_exact, calibrated by a Lipschitz-kink arm reproducing its analytic 6/h^5 to 4.33e-15 relative). C2 FALSIFIED on 8 of 8: on the three qualifying fields the Smolyak arm is 4.19×, 4.94× and 2.26× worse while holding 4.13× fewer samples, and break_even_reads_per_eval 8,793.8 prices the mechanism out of this crate at any accuracy
P-159 — how far from optimal the extractor is the phase's most valuable null, now a null with page numbers (M-472) Against W_inf² — the class the trilinear model is second-order exact for — Marching Cubes is order-optimal: ratio 1.020157 on sphere and 0.991341 on torus, with the independent h fit reading 1.975 and 1.919 against minimal 2.000000. Only the constant is in play, and constant_gap bounds it at 7.25 and 6.26. Three things the source does not contain are carried in every row's class_assumptions rather than glossed
P-160 — does adaptivity beat uniform, given the factor-2 theorem does not apply held, all three (M-473) The octree-adaptive arm beats uniform on 12 of 12 measured rows, gain 1.23–16.97, with gain_exceeds_two true on 10 of 12 — and the factor-2 cap is measured not to apply rather than argued away: class_convex false at convex_midpoint_min_value 0.200000000, class_symmetric false at symmetry_signed_volume 4.179064172 against −4.179064155, operator_linear false, hypotheses_satisfied 1 of 4
P-161 — which approximation class A^s each field is in held, all three (M-474) s is estimable for both families on 8 of 8 fields over 2.03 decades, and the answer is field-dependent: lod_helps true on 3 (box_exact +0.32, csg_difference +0.17, thin_plate +0.61, each clearing its own combined half-width) and false on 5, with fbm_terrain's CI −0.181 to −0.012, strictly negative — greedy adaptivity is measurably worse than uniform there. The DOF are field evaluations, and the adaptive family is charged for its own error estimator
P-162 — BCC vs cubic: 0.2571 dB is a prediction, not a hope falsified on C1 and C2, C3 held (✗118 / M-475) fields_improved 3 of 8 against a bar of five, and the one field that met the prediction met it only because PROJECTION_STEPS moved 64 → 1024 — at 64 the projection aborted the run entirely (a CSG crease contracts at 0.965 per step) and flipped csg_difference's verdict from −0.177 dB to +0.417 dB. Stalls fell 240 → 86 with 80 of the 86 at one legitimate local minimum; verdicts identical at 512 and 1024. case_table_size 16 against 256
P-163 — FCC vs BCC is 0.011 dB, below the harness's scatter falsified, and the registered null came back not null (✗119 / M-476) fields_below_scatter 1 of 8 because measurement_scatter_db is exactly 0.000000 on 6 of 8 fields — a deterministic computation has no scatter, so gap_over_scatter reads inf and the clause is arithmetically false rather than narrowly missed — against measured_gap_db reaching +5.731155 dB on noise_cavity, 514× the registered prediction
P-164 — the BCC box-spline paper, finally opened held on C1, falsified on C2 — arithmetically unreachable (✗120 / M-477) c1_fields_held 8 of 8, both filters order 2, the derivation executed to affine_residual 4.441e-16. C2's bar cannot be cleared because P-162's non-control arm was already BCC plus the box spline — hausdorff reproduces p-162.csv to the last digit on all 16 rows, so the bar C2 must exceed is the measurement C2 makes
P-165 — greedy meshing against Eppstein's polynomial-time optimum held, all three (M-478) Greedy meshing is finished. Eppstein's optimum reproduces exhaustive search on 33,267 components with brute_disagreements 0, and the shipped mesher's worst distance from it in the whole sweep is ratio 1.027132 — 1.120% over optimal, exactly optimal on 8 of 21 rows — while cost_ratio drops to 0.424099: computing the optimum is cheaper than running the mesher on 9 of 24 rows
P-166 — greedy meshing is no matroid; the LOD budget might be submodular the registered negative held, the hoped-for guarantee did not (✗121 / M-479) is_matroid false on all 6 rows with augmentation failures 87 / 190 / 2,331 on exhaustively scanned fixtures — the minimal counterexample a 2×2 block, min_basis 1 against max_basis 4. C2 FALSIFIED on violating_chunks 92 of 221 on capped_gyroid and 155 of 186 on fbm_terrain against 0 of 152 on sphere, with marginal returns that increase at the third refinement
P-167 — the Walsh–Hadamard spectrum of the 256-case table falsified on C3 at eval_ms_ratio 953.694027, held on C1 and split on C2 (✗122 / M-480) The two informative bits of the shipped table are dense — spectral_terms 256 of 256 — while its twelve edge bits are each one degree-2 coefficient. The registration's own guess about C3 was right: a 256-entry table is already in L1
P-168 — noise stability against the wrong noise model, on purpose the registered null came back registered (M-481) C1 HELD on 240 of 240 with closed_form_max_gap 0.0 and stability computable a second way to 6e-15. The genuine artefact at ulp_perturbation 1 flips 0 corner signs on all eight fields, so the whole comparison lives on amplified error — and where the model agrees it agrees for a nameable reason: measured_response_per_corner_flip 8.000000000 against total_influence 8.0 on the parity bit
P-169 — per-corner influence as a cheap independent check on validate_table() falsified on C2, held on C1 in the strongest reading it can have (✗123 / M-482) symmetry_class_count is 1 — all eight corners are one orbit — so "equal within each octahedral symmetry class" means all eight equal, and influence_spread is 0.000000000 on every bit of triangle_counts with octahedral_violations 0 over 12,288 pairs. C1 holding is C2 failing: a function whose corner influences are all equal cannot rank corners, and refinement_priority_correlation reads exactly 0.000000 on 200 of 200. The corrupted-table control detects 2 of 4 planted corruptions, all four showing influence_shift_abs 0.007812500 = 2/256
P-170 — Marching Cubes' 1985 ancestor, and how much less it proves held, all three (V-51 / M-483) Every DOI resolved, including the registered trap: 10.1137/0722019 is T. Nanda on the QR algorithm, the article immediately preceding Allgower & Schmidt at 322–346 — trap_gap 1. AS85's is_homeomorphism is false: it constructs a PL manifold along which ‖H(x)‖_∞ < ε under a full-rank hypothesis at the seed. The repository counts are re-taken every run: descendant_citations_in_repo 21, root_citations_in_repo 4, of which 0 survive removing the registration layer that introduced the name
P-171 — how often transversality fails held on C1, falsified on C2, C3 split 6 true / 18 false (✗124 / M-484) box_exact's exact-zero samples make C1 non-vacuous. And the phase-wide fact lands here: the shipped MC emits zero non-manifold edges, zero non-manifold vertices and zero self-intersecting pairs on all eight fields at 17/33/65 — all 227 defect cells are degenerate triangles, on gyroid and noise_cavity only
P-172 — Conley index dies on plateaus; the census says how big the registered obstruction is real, one dimension lower than claimed, and does not stop Conley (M-485) plateau_fraction 0.500000 on box_exact at all three resolutions, constant_cells 0 — yet conley_applicable_fraction never falls below 0.957031. C2's ranking came back reversed, true on only 3 of 24, all three fbm_terrain at saturated equality — the one vacuous way C2 could hold, which the harness predicted in advance
P-173 — the curl of the Hermite data is what λ = 0.01 guesses about held on C1 — the curl residual is free, worst curl_share 0.008061907 — and does not predict M-60's cells (M-486) Of nine rows with a reachable AUC only gyroid at 33³ clears 0.8 at 0.914640664, and fbm_terrain at 25³ reads 0.270443196, worse than chance. The per-cell λ cuts noise_cavity's self-intersections from 388 to 195 at 33³. The harness header was pessimistic by ~2× against its own CSV, and the entry says so
P-174 — varifolds against the normal cycles already benched the registered null held: the normal-cycles incumbent beats discrete varifolds on 28 of 30 rows at matched cost (M-487) error_ratio 1.000821–3.358471; the two exceptions are the capsule at 129³ at 0.998923, a 0.1% win inside a C⁰ seam that dominates both arms. The one recommendation that does move is on a quantity C1 never scored: on the torus's Gaussian curvature the varifold overtakes at 47³ and is 1.59× better at 129³
P-175 — fix slivers without moving a vertex; hashes_moved predicted 0 falsified on C1 and C3, held on C2 — and C2 is the result (✗125 / M-488) 15,391 flips reach the intrinsic Delaunay fixed point on every row, remove 1,570 of 10,678 slivers, and reach nothing the crate reads — vertex_positions_moved 0, hashes_moved 0, extrinsic_geometry_identical true, against a positive control that moves the hash on all 18 rows where a flip happened. The worst-decile minimum angle rises by at most 1.642437° against a 10° bar
P-176 — caves percolate in 3D and cannot in 2D held on C1 and C3, C2 split 42 / 42 (M-489) The transition is now a number: on noise_cavity the giant component appears at percolation_isovalue 0.029340, and at iso = 0 one component holds 0.814493 of the air against 65 isolated pockets. Two instruments sharing no data structure agree on the component count, the air-sample count and the full sorted size multiset on 84 of 84 rows. The 2D/3D difference is present on noise_cavity (percolation_isovalue_2d none) and absent on fbm_terrain, whose 2D slices percolate too — which the registration named in advance as a real risk, fbm_terrain being hash-based lattice noise and not a Gaussian field

Five harnesses re-derived a registered threshold against a measurement rather than amending a registration, and all five stories are in their entries: common/lattice.rs's PROJECTION_STEPS 64 → 1024 (P-162); P-148's SELF_SWELL_TOLERANCE 1e-9 → 1e-5 (H_FLOOR puts the metric's condition number at ~1e9, so a log/exp round trip loses κ·ε ≈ 2e-7 and the old bound was unreachable by construction); P-153's LADDER_SPAN_FLOOR 1.2 → 1.01 and bidirectional (noise_cavity's ladder is inverted); P-156's three population exclusions with reasons; P-164's LADDER_DENSITY_TOLERANCE 0.05 → 0.08 (lattice site counts are quantised, worst rung 6.454%). No registration was amended. experiment.rs:26-31 forbids it once a run exists, and M-289/P-30/P-35 remain the precedent for re-asking with a corrected instrument.

The 4.26×, and not one triangle changed

Two changes, three days apart, on the same function.

A-023 made the loop axis a constant. DualMesher::emit_quads took axis, u and v as runtime values, so p[axis] = a was a dynamically indexed store. The coordinate array could not live in registers, and every iteration wrote three coordinates to the stack that linearize read straight back — a store-to-load forwarding chain. Splitting it into three const-generic monomorphisations left the same three passes in the same order over the same bounds:

emit_quads, per iteration before after
cycles 43.26 3.33
instructions 31.24 12.02
share of the mesher's cycles at 193³ 82% 27–32%

A-024 forced the row length odd. values was laid out by the caller's shape, so at 128 samples per axis the row stride was 512 bytes and the plane stride exactly 64 KiB — a cache-set aliasing period on this machine, twice over. The remedy is size[0] | 1, unconditional and idempotent. Unconditional because a pad applied only when the stride looks bad is a second layout reachable from one call; idempotent because a fixed pad of one would map every size[0] = 2ᵏ − 1 onto the very stride it is avoiding.

Together, on a sphere at 256³, f32, one thread, one binary, one run:

before after
Surface Nets 693.8 ms 162.7 ms — 4.26×
Surface Nets IPC 1.20 4.09
SN / MC 5.43× 1.26×
per-sample cost, 16³ → 256³ 29.63 → 41.35 ns (+40%) 8.71 → 9.70 ns (+11%)
cache misses per sample 3.72 1.56

Not one triangle changed. The golden hashes pass untouched — an optimisation that changes the mesh is a bug in the optimisation.

And it cost this repository one of its own beliefs. ✗14 read "Surface Nets never wins on Zen 3, at any resolution: 2.46× behind even at 16³." Surface Nets is now faster than Marching Cubes at 16³, 24³ and 32³:

n 16 24 32 48 64 96 128 192 256
Marching Cubes ns/sample 9.37 8.87 8.29 8.03 7.74 7.41 7.48 7.62 7.67
Surface Nets ns/sample 8.71 8.59 8.05 8.24 8.42 8.53 8.75 9.53 9.70
ratio 0.93 0.97 0.97 1.03 1.09 1.15 1.17 1.25 1.26

The reason it had been true was one missing const.

One bit of a row length, at the chunk size everybody uses

128³ is the canonical chunk size in voxel engines, and it was the worst possible one.

The diagnosis came before any code changed, by letting the caller arrange the pad — adding one sample moves the stride while changing the work by under 1%:

shape plane bytes cycles/sample vs 127³ and 129³
127³ 64,516 33.10 —
128³ 65,536 = 2¹⁶ 108.51 3.37×
129³ 66,564 31.39 —
129×128×128 — pad x 66,048 31.48 0.98×
128×129×128 — pad y 66,048 36.45 1.13×
128×128×129 — pad z, the control 65,536 = 2¹⁶ 107.89 3.35×

The z row is what makes this a measurement rather than a story. It adds the same 0.8% of work and touches neither stride, and it keeps the entire penalty. Without it, "adding a sample helped" would be indistinguishable from "the fixture got slightly different."

Measured on a field with no surface in it at all — a sphere entirely inside the domain — so this is the scaffolding, not the geometry.

When a measurement is impossible, suspect the instrument

This is the most useful entry in the file, and it is an entry about being wrong.

R-006 and R-008 both compared vertex normals against a reference gradient computed from an exact wedge SDF written for the experiment. Both came back falsified. P-16 missed its threshold by four times over. Two independent hypotheses about sharp features, both dead, on the same afternoon.

The reference gradient was returning noise.

Its exterior branch normalised away = q − dir·t guarded only by e > 0.0. For a point lying on the ray, that difference is a catastrophic-cancellation residue of order ε·|q| — a random direction with a plausible magnitude. About half of all Marching Cubes vertices land epsilon-outside the wedge, so about half were being compared against a random unit vector.

as reported corrected
past-90° vertices, Marching Cubes 6,959 472
past-90° vertices, Dual Contouring 4,868 232
rows containing one, of 168 75 8
P-13 falsified held
P-16 falsified at 4× its threshold held, at 0%

Both falsified entries are still in FINDINGS.md, with their original wrong text, under a banner pointing at the correction. Deleting them would delete the evidence that the instrument can be the thing that is broken.

The rule it earned, now in the method section: a reference implementation used as ground truth needs the same scrutiny as the thing it checks. And its shorter form — when a measurement is impossible, suspect the instrument before the world.

P-12 is the same lesson wearing different clothes. It predicted the dual's superlinearity was a cache effect; the miss rates came back flat and it was recorded falsified. That was a correct measurement of a machine whose bottleneck was somewhere else. Once A-023 removed the store-to-load stall that was covering it, the 128³ spike went from 1.24× — indistinguishable from noise — to 2.6×, and A-024 then took it to 1.01×. A null measured under a dominant confound is a statement about the confound.

The paper is wrong, and here is the fixture

Schaefer, Ju & Warren, Manifold Dual Contouring (IEEE TVCG 13(3), 2007), §3, on the uniform grid:

"this surface is always a manifold because the original MC algorithm always constructs a manifold and the dual preserves the topology of the surface."

Over the eight fields the roster held at the time, at three resolutions, no chunking and no weld, so there is only one mechanism in the count:

non-manifold edges non-manifold vertices
Marching Cubes 0 0
Marching Cubes + asymptotic decider 0 0
Manifold Dual Contouring, this crate's default table 143 —
Manifold Dual Contouring, the paper's decider-modified table 114 222

The premise holds here. The conclusion does not.

Every one of those defects is on noise_cavity, and the mechanism now fits in 48 samples. A 2×2×3 column of ±1 inside a 4×4×3 lattice, trilinear between the samples, everything else outside — its middle plane reads out, in, in, out, the face saddle. On those twelve hand-written values Marching Cubes emits 40 triangles and 0 non-manifold edges; both duals emit 20 triangles and 1, carrying four distinct faces.

Four quads meet on one dual edge because all four cut edges of the shared face land in one cycle on each side, so all four connect the same pair of vertices. And the manifold construction buys nothing here: splitting a cell by cycle cannot split a cell that has one cycle.

The sharper half is that the offending set is not a set of sign configurations. Scale the shared face's two inside corners — no sign moves — and the asymptotic decider's saddle crosses zero with the defect:

inside corners saddle s the face non-manifold edges triangles
−0.25 +0.375 separated 1 20
−1 0, an exact tie separated 1 20
−4 −1.5 joined 0 20

One configuration, two answers, chosen by the field rather than by the rule. Which is why a face rule still leaves 25–49 offending faces per resolution while being combinatorially capable of avoiding all of them — over all 4,096 two-cell sign patterns, not one offends under every consistent mask.

Reading the tiers

Every number in this repository's documentation carries one of these, and the legend matters because the tiers are not decoration:

tier means the bar
M measured here We ran it. Code and numbers in this repo, reproducible by checkout
V verified externally We read the primary source ourselves. DOI or file attached
R reported A credible source asserts it; we have not checked
F folklore Widely repeated, no verified primary source found
✗ falsified Tested and found false — including what we believed, and why

Never cite an R or F claim as justification for a design decision without saying which tier it is.

Two standing rules keep the ledger honest. Re-tier rather than rewrite — when an R becomes an M, the R text stays and the measurement goes below it, because the gap between what was reported and what was measured is itself data. And record the ones we got right for the wrong reason: ✗10 sits in the falsified section even though its outcome was fine, because the reasoning was wrong and the reasoning is what generalises.

Where the raw results live
the registrations crates/isomesh/src/experiment.rs
the full ledger, 512 entries FINDINGS.md
per-experiment result data docs/experiments/ — each CSV carries its # hypothesis: and # falsified by: header
timing and quality measurements docs/measurements/
what falsified beliefs cost FINDINGS.md Part 1 — 19 entries, and 79 falsified beliefs across the whole ledger, each recording where the wrong belief came from, because provenance predicts the next error