The falsification ledger

Pilot wave on the carve: can a vibrating excitation shell itself?

A discrete Couder/Fort analog: a bouncing droplet feels the field left by its own past splashes. D2 (shell-ness): dead — guided radial histograms are broad on every substrate at every memory (ent_norm 0.90–0.98, modal bin 3–5%); the sharpest radial peak in the whole experiment belongs to the sponge's random-walk control. D3 (carve-scale preference): dead, a clean 1/3 null. D1 confinement was weak and present on both carve and solid; D4 (memory dependence) was left as the one live thread, with two declared escape hatches — executed and closed in Q17.

Cone mapping: is the causal cone inherited from the carve?

Two layers: exact BFS cones and wave-arrival cones with a hard causality self-check. C1 confirmed: sponge interior cone volume grows with slope 2.749 — the Hausdorff dimension 2.727 within 1% — while the same substrate gives different cones at different positions (corner 2.255). Front speed confirmed slowed, 38–60% depending on position. Zero causality violations in all runs. Two honest nulls (no cone crumpling, no extra corner warping).

Unregistered find, labeled at the time: waveguide concentration ("slower but louder", 100% vs 31% reached at corner, θ = 0.02). It fell out of a threshold-robustness scan and was sent to Q10 for pre-registered confirmation before becoming load-bearing — where its absolute form died (see What died).

Waveguide confirmation at L4, and the prime ladder

The pre-registered confirmation run for Q9's find, on matched carve/solid pairs up to the 81-grid. W1 mixed: the carve/solid contrast partially survives scaling (corner 4.62× passes, interior 21.8× fails the 58× bar) but the absolute effect collapsed — the loudness was largely a small-size artifact. W2: a threshold-free decay advantage survives from corner sources (4/4 carves slower: p3 0.536 < 0.896, p5 0.374 < 0.469, p7 0.581 < 0.739, p9 0.750 < 0.896) and reverses from interiors (0/4). W3: the trend tracks carve density, not primality, and is size-confounded. W4: the census's "9-carve = two 3-carves" identity falsified by brute force (kept 495,616 vs 160,000).

Matched-N ladder + carrier-cell map

Four carves at matched surviving node count (within 1.3%). A0 rejected: matched N does not erase the ordering (Δα spread 0.322, five times the 0.06 kill bar) — the advantage is not a size artifact. A2 confirmed: primality is irrelevant (p7 vs p9 differ by −0.002 at matched everything). But the monotone density law dies too: p5 sits below p7/p9 despite removing twice their fraction. Part B: the far-field carrier map gives enrichment E = 1.038 — statistically overwhelming (p = 1.4e-26) yet inside the ≤ 1.1 kill band, so the strong "tunnels guide" mechanism is falsified as a far-field story.

Caveat labeled post-hoc: at L4, 86.7% of all kept cells touch void, so void-adjacency nearly saturates and E's ceiling was ~1.16; the measured lean is ~24% of maximum headroom.

Depth isolation: does the advantage follow recursion depth?

Same prime (p3), only recursion depth varied. D1 fired against both shallow arms: Δα = +0.188 (L1) → +0.215 (L2) → +0.360 (deep L4), monotone, with deep-minus-shallow gaps of +0.172 / +0.145 clearing the 0.1 bar. Honest decomposition: ~+0.19 is a generic "carved at all" baseline; ~+0.17 is the depth premium. Only clean grids used — no truncation edges.

Later history (Q16): on the open domain the registered depth premium fails its kill bar (+0.044 < 0.1) and the monotone ordering breaks; a labeled post-hoc convergence correction recovers only a weakened deep-vs-shallow gap (≥ +0.123).

Cross-prime depth ladder at matched density

Breaks Q12's depth↔density lock using clean carves on different primes. C1 inconclusive: the one feasible matched-density cross-prime depth pair gives −0.016, inside the ±0.05 band — no evidence the depth premium transfers off p3 at depths 1–2. C4 leans prime-dependent (deepening p5 nominally hurt: slope −0.052); C3 is density-inverted. What generalizes across primes is the baseline: every clean carve beats its own solid, Δα ∈ [+0.122, +0.360] across all 7 arms.

Why does the carve hurt interior sources?

Four source positions on the deep carve vs matched solid. The reversal replicates strongly (interior Δα = −0.725 vs corner +0.360). H1 killed 10× over the bar: a degree-3 interior source — same launch geometry as the corner — still lands at −0.657; the reversal is about position, not degree. H3 fires: interior fronts move at solid speed (slope ratio 1.041), so the effect is amplitude redistribution, not propagation failure. Mechanism: ~70% control-side — the closed solid box keeps its interior far field artificially loud by wall reverberation (α collapses to 0.19–0.21). Also measured: the carve has zero degree-1 cells — "trapped in dead ends" is dead as stated; there are no dead ends.

Spherical Menger: do the carve effects survive on a ball?

A ball has neither corners nor flat walls — the two features the cube results leaned on. P1 confirmed, 2.7× over the bar: the solid ball's center α rises to 0.472 (vs the cube's echo-inflated 0.19–0.21), direct support for the reverberation account. P2 falsified — the reversal is real: even against the honest spherical control the carve steepens interior decay by Δα = −0.356. P3 falsified: it is the ball domain, not the carve, that normalizes position (spreads 0.112 vs 0.125). P4 confirmed: the fractal cone exponent (2.685) survives the container change — boundary-indifference.

Carving curve vs cosmic history

Can a constant-retention fractal-removal curve reproduce the ΛCDM matter/Λ fraction history? No, on every bar. B1 fails by 26× (max deviation 1.3048 vs 0.05); the pure 20/27 curve is unphysical (Ω_m > 1) for over a decade of early history. B2 fails both clauses (best-fit k = 0.80085 is 3× off the Menger value, residual 0.5493). B3 fails even in the adversarially friendly crossover window. B4 — the real test: ΛCDM's ratio slope is exactly 3 (numeric check 3.6e-12); any constant-k carve predicts 0.3988 today — the whole family falsified, 5.2× over the kill bar.

Spherical Sierpiński generator: dimension → 2 with bounded area?

Icosahedral-subdivision sphere with three deterministic removal rules. P0 exact: the middle rule reproduces the gasket dimension log₂3 = 1.5850 to 2.2e−16 at all six generations, and the boundary ledger closes to 3.8e−16. P1/P2 pass: hole boundary diverges with the (3/2)ⁿ law (mean increment ratio 1.4978); hole placement changes nothing dimensionally. P3 passes all bars: the taper rule climbs D = 1.5850 → 1.9887 (rising toward 2), holds area at 0.5505·4π and converging, while the boundary diverges linearly (increments ≈ 21 per generation). P4: "dimension → 2 with area → ∞" is impossible on a sphere by geometry; the honest reformulation — dimension → 2 with diverging boundary and area bounded away from zero — is demonstrated.

The cone race on a carved expanding sphere (2-D surface)

The eternal-inflation mapping made measurable: sponge material = inflating region, holes = bubble universes, exact de Sitter expansion. All physics predictions fail. P1: median disconnection time drops only 1.5–2.5% from k=0 to k=6 and is flat from depth 2. P2: disconnection geography uncorrelated with hole proximity (Spearman ρ = 0.008 vs the 0.3 bar). P3: never-contactable fraction gap 0–2.4 points vs the 5-point bar. A 2-D surface carve barely warps metric geometry — detours are cheap. One escape hatch logged and executed: rerun in the 3-D bulk (Q15b).

The same race on the 3-D bulk carve — escape hatch closed

Identical race on the Q14 volume graphs. All physics predictions fail again: mean distance inflation 1.0452 vs the 1.10 bar; the median paired disconnection shift is exactly zero ticks; never-fraction gaps 3.37/3.90 points vs the 5-point bar; geography ρ = 0.039. The bulk null has a different mechanism — for ~79% of surviving node pairs a monotone geodesic survives the carve, so the median pair is metrically untouched. P5 passes, the entry's one real positive: at 20.9% density, far below site percolation, the carve ball is one connected component (0 of 56,000 isolated) while random-matched controls shatter to largest components of 86 and 68 nodes. The Menger rule is load-bearing for the existence of paths, not their length.

Open domain: which wave claims survive with reflections removed?

Absorbing boundaries plus a first-arrival cutoff ladder, re-measuring the three load-bearing claims. B1 — the depth premium fails as registered (+0.044 < 0.1); a labeled post-hoc convergence correction recovers ≥ +0.123 with the monotone ordering broken — weakened, not hardened; roughly half to two-thirds of every reflective Δα was differential reflection inflation. B2 — the interior penalty is confirmed hardened: −0.725 → −0.889 (source-distance sponge) / −1.452 (wall sponge) with exterior reflections killed. B3 — cone slowdown confirmed, stronger than reported (corner ratio 5.91, interior 2.57). The "any holes help" baseline collapses to +0.02…+0.06 — mostly a closed-box effect. Zero causality violations in all 20 runs.

The B1 rescue rests on a longer (5·dmax) run of the carve arms only, registered after the full run and before the long run; even +0.123 is a lower bound — the registered verdict stands as registered, the correction is labeled.

Closing Q8's escape hatches

Hatch A closed: a two-decade fine memory scan (γ down to 0.002, memory ~250 splashes) finds no shell onset — max peak_frac 0.0645 vs the 0.10 bar, no limit cycle anywhere (revivals 0.17–0.28 vs 0.5). Q8's one live thread (D4) also dies: the confinement ratio wanders 0.77–1.06 with no trend — the earlier −28% was coarse-scan noise. Hatch B closed: every Ladder B droplet run freezes (stuck_frac 0.59–0.74, participation ratio 0.018–0.031 of the random-walk control) — excluded by the pre-registered moving-state bars, but a real substrate-specific secondary finding: the 49.5%-flat-band substrate parks the walker, it never orbits it. The minimal pilot-wave-on-the-carve mechanism is closed at graph-wave realism.

The frozen corner-origin droplets ring in a tiny period-14 cycle (autocorrelation revival 0.71/0.61 at lag 14) — excluded from all verdicts by the moving requirement, reported for the record.

Handoff tasks without ledger entries

The handoff document that registered T3 and T6 also registered T1 (generalized Menger fractions — search d-dimensional removal rules against the cosmic fractions), T2 (the log-ladder map — decade positions of fundamental scales against k-fold log-partitions), T4 (CMB discrete scale invariance — log-periodicity tests on public Planck maps), and T5 (the Dirac square-law check). Their results are not recorded in the ledger this page is built from, so no numbers are claimed for them here. Given the ledger's standing rule on constant-matching (search-before-registration is dead; the measured null rate is ~5/14 hits at 0.5% tolerance), T1/T2/T5-style tasks are admissible only as pre-registered single-rule tests.