31 October 2026 · working results, not peer reviewed · one supported, three partial, six not supported

Ten New Hypotheses — Tested

Ten hypotheses from the 31 October 2026 sets, operationalised and tested. Full reports, data and code are in the matching tests/ folders.

01 — H18: The Glass-Bead Water Map

Source. 29 Original Hypotheses (31 October 2026), H18. Verdict: PARTIAL SUPPORT.

Claim

The near/far-side difference in solar-wind water stored in lunar impact glass beads is controlled by glass composition — especially FeO and TiO₂ — rather than latitude. Among mare glasses, water should scale with FeO above 15 wt% with R² > 0.7; non-mare glasses at similar latitude should stay below 50 µg/g.

Test

We reanalysed the published source data of He et al. (2025): 58 Chang'e-6 impact-glass grains with paired water (Source Data 3) and major-element compositions (Source Data 6), merged on mount/grain. Water was log₁₀-transformed; FeO and TiO₂ were tested with Spearman rank correlation and OLS. The claimed threshold at FeO = 15 wt% was specified before the fit. Bootstrap intervals use 10,000 resamples.

Data

• 58 grains: 41 mare, 17 highlands; all are Chang'e-6 farside material.
• Water range 6.2–1,410 µg/g; FeO 5.0–23.4 wt%; TiO₂ 0.18–6.48 wt%.
• All 41 mare grains have FeO > 15 wt%, so the claimed threshold has no below-threshold mare control in this sample.
• Source: He, H. et al. (2025) Nature Communications 16, s41467-025-60388-y, Source Data 3 and 6.

Results

• Among mare grains with FeO > 15: R² = 0.120, slope = 0.109 log₁₀(µg/g) per wt% FeO (95% bootstrap 0.031–0.190), p = 0.026. The claimed R² > 0.7 fails by a wide margin.
• Spearman FeO–water: ρ = 0.198, p = 0.215 (n = 41).
• Spearman TiO₂–water: ρ = 0.333, p = 0.033 — a weak positive signal, not the claimed retention law.
• Rim-water sensitivity (the surface layer most relevant to solar-wind retention, n = 19): ρ = 0.640, p = 0.003; R² = 0.559, still below the 0.7 target but much stronger than the grain average.
• Mare glasses carry more water than highlands (median 51 vs 30 µg/g; Mann–Whitney p = 0.020), but that difference is confounded with composition and is not evidence for the FeO threshold.

Verdict

Partial support. Composition is not irrelevant — TiO₂ has a weak positive association with average water, and rim water has a stronger FeO relation (R² = 0.56) — but the specific R² > 0.7 prediction fails on both measures. The near/far test cannot be run on this table because every analysed grain is farside material.

Limitations

• No nearside grains with paired FeO/TiO₂ and water; the geographic half of the hypothesis is untested.
• Rim water and grain-average water differ; the primary analysis uses the grain average (58 paired grains), and the rim sensitivity is reported separately (n = 19). Both are in the source.
• Detection limits and terrestrial contamination are inherited from the published SIMS data.
• The 15 wt% threshold is not identifiable: the mare sample is entirely above it.

Reference

He, H., Hu, S., Gao, L. et al. (2025). Lunar dichotomy in surface water storage of impact glass beads. Nature Communications 16. https://doi.org/10.1038/s41467-025-60388-y

02 — H11: AMOC has an 18.6-year tidal pacemaker

Source. 30 Unconventional Hypotheses (31 October 2026), H11. Verdict: NOT SUPPORTED.

Claim

The 18.6-year lunar nodal cycle modulates tidal mixing over the Reykjanes Ridge and leaves a detectable signal in subpolar SST, overflow proxies and AMOC reconstructions, stronger over rough topography. Kill condition: no nodal-period signal in a long enough record.

Test

We built a monthly subpolar North Atlantic SST index from HadISST (45–60°N, 60–10°W, 1870–2024), removed the monthly climatology and a linear trend, and fitted a harmonic at 18.6 years. The amplitude was tested against a 5-year block bootstrap that preserves serial correlation. A 45–50°N box is a within-basin control; 40-year windows test stationarity.

Data

• HadISST 1° monthly SST, NOAA CoastWatch ERDDAP erdHadISSTDecomp, 1,860 months.
• The ERDDAP subset covers 45–60°N only; this is a North Atlantic test, not a global AMOC reconstruction.

Results

• Subpolar amplitude: 0.068 °C (SE 0.013), phase 11.3 years into the 18.6-year cycle; OLS p-values are small (p_sin = 1.7×10⁻⁵).
• Block-bootstrap p = 0.36. Once serial correlation is preserved, the amplitude is not distinguishable from a red-noise null.
• 45–50°N control amplitude: 0.056 °C (p_sin = 0.027), i.e. not weaker than the subpolar box.
• 40-year window amplitudes range from about 0.07 to 0.17 °C and the phase is not stable, which is not the signature of a persistent pacemaker.

Verdict

Not supported. The naive OLS fit is misleading; the autocorrelation-aware test finds no robust 18.6-year signal in this SST index. The claim's stronger, topography-dependent prediction was not tested because no overflow or AMOC reconstruction was used.

Limitations

• One proxy (SST), one basin, no RAPID or overflow time series.
• HadISST is a reconstruction with changing input coverage; early decades are sparse.
• A small nodal signal could be present but below the detection threshold of this design.
• The 18.6-year cycle is only eight cycles long in 150 years, so phase estimates are sensitive to trend removal.

Reference

HadISST: https://coastwatch.pfeg.noaa.gov/erddap/griddap/erdHadISSTDecomp.html. Hypothesis text: 30 Unconventional Hypotheses, H11.

03 — B05: Trees remember last year's drought

Source. 99 Original Hypotheses (31 October 2026), B05. Verdict: NOT SUPPORTED.

Claim

Vessel size in a given ring is set mainly by the previous year's late-season soil moisture, producing a one-year lag that allows hindcasting. Kill condition: vessel size is predicted best by current-year spring conditions with no lag.

Test

We assembled 57 ITRDB ring-width chronologies from the western United States, paired each with the nearest long GHCN-D precipitation station and CRU TS 4.10 potential evapotranspiration at the nearest 0.5° cell, and computed a monthly moisture index P − PET. For each site we regressed the standardized ring-width index on previous August–September moisture and current March–May moisture, then pooled the sites in a mixed model with a site random intercept.

Data

• 57 chronologies, 4,213 site-years, 20 GHCN stations (ring-width index; the hypothesis specifies vessel anatomy, which ITRDB does not measure).
• Chronologies span roughly 1700–2020; the common climate window is 1902–2024.
• GHCN-D daily PRCP; CRU TS 4.10 PET. Moisture = precipitation − PET.

Results

• Mean standardized coefficient: previous late-season 0.027 vs current spring 0.220.
• The previous late-season coefficient exceeds the spring coefficient at only 14% of sites (Wilcoxon p = 1.1×10⁻⁸).
• Mean R²: 0.013 (previous late) vs 0.072 (current spring).
• Mixed model: previous late 0.029 (p = 0.057), current spring 0.219 (p = 4.4×10⁻⁴⁸).
• The lag hypothesis predicts the opposite ordering.

Verdict

Not supported for ring width. Current spring moisture dominates; the previous late-season term is small and only marginal. This is a proxy test: it cannot rule out a vessel-specific lag, but it removes the strong growth-ring version of the claim.

Limitations

• Ring width is not vessel diameter; the anatomical prediction remains untested.
• Western US only; dry-site selection favors spring-limited growth.
• P − PET is a crude moisture index; it ignores snowpack, soil storage and species differences.
• ITRDB chronologies are detrended differently across sites; the analysis uses a common 51-year rolling-median standardization.

Data sources

NOAA ITRDB: https://www.ncei.noaa.gov/pub/data/paleo/treering/measurements/ · GHCN-D: https://www.ncei.noaa.gov/pub/data/ghcn/daily/ · CRU TS 4.10: https://crudata.uea.ac.uk/cru/data/hrg/cru_ts_4.10/

04 — G04: The fortnightly tide unlocks the fault

Source. 99 Original Hypotheses (31 October 2026), G04. Verdict: NOT SUPPORTED.

Claim

Microseismicity on locked subduction interfaces is modulated at the fortnightly tidal period, and the modulation amplitude tracks locking state. Kill condition: no phase preference anywhere, or amplitude unrelated to locking.

Test

We downloaded 30,667 USGS earthquakes (2000–2025, M ≥ 2.5, 20–60 km depth) in five subduction boxes: Japan, Cascadia, Chile, Tonga and Mexico. For each event we computed the fortnightly phase from the synodic month (spring at new/full) and applied a Rayleigh test. We repeated the test on M ≥ 4 events and after 1-day declustering; the latter removes aftershock sequences that can manufacture phase concentration.

Data

• USGS FDSN event service, five regional boxes; 11,368 Japan, 2,223 Cascadia, 11,185 Chile, 2,821 Tonga, 3,070 Mexico.
• Depth boxes are a proxy for the subduction interface; the catalogue does not classify interface versus intraslab events.

Results

• Japan: raw R = 0.097, p ≈ 1.6×10⁻⁴⁷ — but after 1-day declustering R = 0.005, p = 0.93.
• Chile: raw R = 0.033, p = 4.7×10⁻⁶; declustered R = 0.016, p = 0.51.
• Cascadia, Tonga and Mexico: no robust phase preference in any specification.
• The apparent Japanese and Chilean signals are carried by aftershock clustering, not by independent microseismicity.

Verdict

Not supported after the clustering control. The raw phase preference is real as a catalogue property but is not evidence that the tide unlocks the fault. Locking state was not tested, so the second half of the claim is unresolved rather than refuted.

Limitations

• No interface classification and no GNSS locking model; the regional labels are coarse.
• 1-day declustering is crude and may remove some independent events.
• USGS completeness varies by region and time.
• A weak tidal modulation could be hidden below the detection threshold.

Data source

USGS FDSN event service: https://earthquake.usgs.gov/fdsnws/event/1/

05 — C09: Surrogates learn the grid, not the physics

Source. 99 Original Hypotheses (31 October 2026), C09. Verdict: SUPPORTED.

Claim

Neural surrogates trained on physics simulations learn the solver's numerical artefacts, detectable by testing on refined grids where artefacts change but the physics does not. Kill condition: error on refined grids is no worse than on same-grid held-out data.

Test

We generated 1-D periodic linear advection fields with a first-order upwind solver at coarse (N = 64) and refined (N = 256) resolution, same CFL and final time. A small MLP surrogate was trained on 1,800 coarse pairs and tested on 300 held-out initial conditions against (a) the coarse solver and (b) the refined solver downsampled to 64 points. A mixed-grid model trained on 50% coarse and 50% refined targets is the control.

Data

• 1,800 training / 300 test fields, generated deterministically (seed 20261031).
• Coarse N = 64, refined N = 256, CFL = 0.5, T = 0.6.
• No external data; the experiment isolates the solver grid.

Results

• Same-grid MSE: 0.00019; refined-grid MSE: 0.122; ratio 648.
• Persistence (no change) refined MSE: 1.60 — the coarse-trained model is far better than persistence on its own grid, but its refined error is much larger than its coarse error.
• Mixed-grid control: same-grid 0.030, refined 0.034, ratio 1.12 — the control removes most of the failure.

Verdict

Supported. The surrogate is nearly exact on the coarse solver (MSE 0.00019) but 648× worse on refined-grid truth; mixed-grid training cuts the penalty to 1.12×. The transfer failure is grid-specific and the control behaves as the hypothesis predicts.

Limitations

• Synthetic 1-D advection, one MLP, one PDE; not a real simulator.
• The coarse and refined solvers differ by numerical diffusion, so the 648× ratio is a measure of that difference as much as of “learnt artefacts”.
• The refined solution is treated as truth; it is itself a numerical approximation.
• The model is a plain MLP, not a convolutional or graph surrogate.

Reference

Hypothesis text: 99 Original Hypotheses, C09. Code and generated data: code/analyze.py.

06 — C01: Quantisation error has a shape

Source. 99 Original Hypotheses (31 October 2026), C01. Verdict: NOT SUPPORTED.

Claim

Neural-network quantisation error concentrates along a small set of “brittle” directions identifiable from the Hessian, setting a hard floor on 4-bit accuracy that better rounding cannot cross. Kill condition: error predicted by bit-width and weight distribution with no curvature structure.

Test

We trained 10 MLPs (64-64-10) on sklearn's digits, computed Hessian-vector products by autograd, estimated the top eigenvalues by power iteration and the trace by Hutchinson, and quantised each weight tensor uniformly at 8, 5, 4 and 3 bits. We tested (i) whether a matched-norm perturbation along the top Hessian direction raises loss more than a random perturbation, and (ii) whether the 4-bit error lies in the top-3 curvature subspace.

Data

• sklearn digits: 1,797 8×8 images; 10 models, seeds 20261031–40.
• No external data; all models and quantisation are reproducible from code/analyze.py.

Results

• Mean test accuracy: fp32 0.972, 8-bit 0.972, 5-bit 0.972, 4-bit 0.970, 3-bit 0.955.
• Mean 4-bit drop: 0.0022 — there is no material 4-bit floor in this setting.
• Top-direction perturbation ratio: 1.45 (70% of models > 1), so curvature does identify a locally brittle direction.
• Fraction of 4-bit weight error in the top-3 Hessian subspace: 0.0001 — essentially none.
• Spearman(Hessian trace, 4-bit accuracy): ρ = −0.30, p = 0.41.

Verdict

Not supported. The Hessian finds a brittle direction, but the quantisation error does not concentrate there and 4-bit accuracy barely moves. The proposed curvature-based floor is not present in these small MLPs.

Limitations

• Small MLPs and a simple uniform quantiser; transformers and per-channel schemes may behave differently.
• Some Hessian eigenvalues are negative because the models are not at a strict local minimum.
• Only 10 models; the correlation test is underpowered.
• The hypothesis concerns 10 models and 3/4/5-bit dithering; only a subset of that protocol was implemented.

Reference

Hypothesis text: 99 Original Hypotheses, C01.

07 — H30: Grokking is a first-order transition with hysteresis

Source. 30 Unconventional Hypotheses (31 October 2026), H30. Verdict: PARTIAL SUPPORT.

Claim

Grokking is a first-order transition with hysteresis, not a smooth crossover.

Test

We trained a 1-layer transformer (d = 64, 4 heads) on modular addition mod 53 with 40% of all pairs, AdamW at lr = 10⁻³ and weight decay 1.0. After the model grokked, we stepped weight decay down from 1.0 to 0.01 and then back up, measuring test accuracy at each step. First-order behaviour requires an abrupt jump; hysteresis requires the descending and ascending paths to disagree at matched weight decay.

Data

• 2,809 possible pairs; 1,124 training pairs, 1,685 held-out pairs.
• Up to 2,500 epochs to grok, then 10 × 150 epochs descending and 10 × 150 epochs ascending.
• One seed (20261031); no replication across seeds.

Results

• Grokking at epoch 1,525; final train 0.931, test 0.820.
• Largest test-accuracy jump in a 25-epoch interval: 0.442 — consistent with a sharp transition.
• Mean absolute hysteresis gap: 0.072; the loop is weak and non-monotonic.
• At wd = 0.7 the descending path is 0.69 and the ascending path is 0.997 (gap 0.304), but at wd = 0.3 the gap reverses (−0.164).

Verdict

Partial support. The abrupt jump supports a first-order-like transition. The hysteresis loop is not stable or large enough to support the full claim; the one large gap at high weight decay is not reproduced across the path.

Limitations

• One task, one architecture, one seed; grokking is stochastic and seed-sensitive.
• The weight-decay path is only 150 epochs per step; the system may not equilibrate.
• Weight decay is not the only control parameter; learning rate and data fraction can produce different transitions.

Reference

Hypothesis text: 30 Unconventional Hypotheses, H30.

08 — #18: Erasure heat is protocol-dependent, not a physical constant

Source. 20 Original Hypotheses (31 October 2026), #18. Verdict: NOT SUPPORTED.

Claim

A logically reversible erasure protocol can show heat per erased bit falling below k_B T ln 2 toward zero, while the standard irreversible protocol always yields at least k_B T ln 2.

Test

We enumerated an n-bit memory plus an n-bit ancilla (n = 1–4), compared a standard reset (all bits to zero) with a unitary copy of the memory into the ancilla followed by tracing out the memory, and computed the Shannon entropy of the joint state and of the memory marginal.

Data

• Closed-form state enumeration; no external data.
• Entropies in nats; one bit of entropy equals k_B ln 2 of heat at temperature T.

Results

• Standard reset: joint entropy falls by ln 2 per bit, so the heat lower bound is k_B T ln 2 per bit.
• Copy protocol: the memory marginal has zero entropy (it looks erased), but the joint memory+ancilla state still carries ln 2 per bit; the joint entropy change is 0.
• The apparent sub-Landauer heat is therefore an accounting artifact of not counting the ancilla.

Verdict

Not supported as stated. The hypothesis conflates logical reversibility (a unitary copy) with thermodynamic erasure. A calorimeter that measures only the memory will see less heat, but the missing entropy is in the ancilla; no closed-system protocol violates the bound.

Limitations

• This is a bookkeeping proof, not a flight calorimeter experiment.
• Real hardware has finite-time dissipation and additional entropy export; the idealised count is a lower bound.
• The hypothesis could be reframed as a protocol-relative measurement claim, but the stated “approaching zero” prediction does not survive the joint accounting.

Reference

Lairez, D. (2024). The fundamental difference between logical and thermodynamic irreversibilities. Symmetry 16, 1594. arXiv:2409.15085.

09 — C04: Sums remember their order

Source. 99 Original Hypotheses (31 October 2026), C04. Verdict: PARTIAL SUPPORT.

Claim

Floating-point summation order leaves a reproducible fingerprint in the low bits of a numerical result, sufficient to watermark a computation without changing its high-order value. Kill condition: the fingerprint does not survive a compiler change or standard numerical noise.

Test

A C kernel generated 10,000 uniform doubles, applied one of 200 seeded Fisher–Yates permutations, summed sequentially, and printed the IEEE-754 bit pattern. We compiled the same source with clang at -O0, -O1, -O2, -O3 and -Ofast, and compared the low 8 bits and the high-order value for each permutation.

Data

• 200 permutations × 5 optimisation levels; one CPU (Apple arm64), one compiler (clang).
• No external data.

Results

• Low-8-bit agreement with -O0: 100% at -O1, -O2 and -O3; 0.5% at -Ofast.
• Distinct low-8 patterns: 72 at -O0 through -O3, 49 at -Ofast.
• High-order values are unchanged: maximum relative difference 2.2×10⁻¹⁷.
• The fingerprint is exact under normal optimisation but destroyed by fast-math reassociation.

Verdict

Partial support. The low-bit fingerprint is a real, reproducible watermark under conventional compilation, and it does not change the high-order result. It is not robust to aggressive re-association, so the “survives optimisation-level change” part of the claim fails.

Limitations

• One compiler and one CPU; no cross-hardware test.
• Only the low 8 bits were compared; other bit ranges may behave differently.
• -Ofast is an aggressive, non-conforming mode; a stricter reading of “optimisation level” might exclude it.
• The watermark is only as stable as the exact reduction order; library or hardware changes can override it.

Reference

Hypothesis text: 99 Original Hypotheses, C04.

10 — C02: Order teaches more than architecture

Source. 99 Original Hypotheses (31 October 2026), C02. Verdict: NOT SUPPORTED.

Claim

At small scale, training-data order determines a model's inductive bias more than architecture, and the effect persists after fine-tuning. Kill condition: order effects disappear after fine-tuning, or are smaller than architecture effects at every scale tested.

Test

We trained 30 models on the two-moons task: 5 data orders (random, easy-first, hard-first, label-block, alternating) × 2 architectures (shallow-wide 128; deep-narrow 32×4) × 3 seeds. Inductive bias was measured on a 45°-rotated out-of-distribution (OOD) test set; we then fine-tuned on 120 OOD examples and re-measured. Two-way ANOVA η² compares the order and architecture terms.

Data

• 840 training / 360 test points; OOD = test set rotated 45°.
• 30 models, 40 epochs each; fine-tune 15 epochs on 120 OOD points.
• No external data.

Results

• Mean in-distribution accuracy 0.953; OOD 0.680; after fine-tune 0.810.
• In-distribution η²: order 0.319, architecture 0.074 — order dominates ID fit.
• OOD η²: order 0.082, architecture 0.440 — architecture dominates transfer.
• After fine-tuning: order 0.100, architecture 0.729 — the order effect does not persist.
• Both comparative predictions fail.

Verdict

Not supported. Order shapes in-distribution fit, but architecture dominates the OOD inductive bias and the effect grows after fine-tuning. The “curriculum shadow” does not survive the shift.

Limitations

• Small 2-D task, one OOD rotation, one fine-tuning budget.
• Architecture is confounded with capacity; the shallow model has more parameters.
• The order manipulations are coarse; a curriculum defined by example difficulty may behave differently.
• Three seeds per cell is enough for a large effect, not for a narrow one.

Reference

Hypothesis text: 99 Original Hypotheses, C02.