Every entry below is a claim this system produced by running real experiments, that then survived its own machinery’s attempts to kill it: independent retests, adversarial attacks by other model families, false-consensus checks, circularity review. That establishes one thing well — robustness. It does not by itself establish the two things the word “discovery” also needs: that the result is new to the world, and that it is non-trivial (a contingent fact, not a theorem, a definition, or a lookup). So a claim reaches this shelf only after three gates it used to skip: it names no prior work in its own evidence, it is not an empirical-fact lookup, and it is not analytically derivable.1
The shelf is ranked by robustness, not by literature-absence — a single web search returning “not found” is a weak prior and is credited as one, never as the headline pillar it used to be.2 The claims the router moved off the shelf are shown in §2 with the reason for each, because a survivors-only page hides its own errors. Empirical-fact lookups and the system’s self-measurements are excluded by construction — and, unlike before, the construction is now enforced.3
§1The shelf
Ranked by robustness.2 The top 6 carry their
full evidence trail; the remainder are listed in the ledger below them.
01EstablishedRe-derivation in flightoptimum / saturationdiscovery score 93.7/100
Side B's answer survives; Side A's is refuted by the discriminating test. WHAT the test was: Two methodological variants (SVD semantic features vs raw lexical, and TF-IDF top-k vs bottom-k importance split) tested on a synthetic 6-topic dataset (2000 docs, 6 classes) across dimensions 5 to 5000. Both variants show strong negative correlation between inversion and dimensionality (Spearman rho = -0.97 and -0.94). Side A predicted inversion >15 dB at dim=5000 — actual result is 1.7 dB (13.7 dB off). Side B predicted inversion ~0.39 dB at dim>100 — actual result is 2.6 dB (2.2 dB off, qualitatively correct). Inversion drops from 28-41 dB at dim=5 to 1.7-2.6 dB at dim=5000 and plateaus above dim=200. WHY IT WORKS: At low dimensionality, SVD forces topic signal into few high-SNR composite features while lexical features have insufficient dimensions to capture discriminative patterns. As dimensionality increases, both feature types gain room to represent the full feature space, and the SNR gap collapses because lexical features approach the discriminative capacity of semantic composites. The plateau above dim=200 occurs because the topic structure is fully captured at that dimensionality — additional features add noise, not signal.
domain ml theorysupport 12.3 wscretests 1 · formal 1attacks 5 survived · 3 narrowedattacked by agents-a1, deepseek-v4-flashnovelty (weak prior) 0.85
Where it holds — mapped scope
Claim #65238 reconciliation: The mapped scope claim is supported. MI-based inversion (semantic MI - lexical MI) strongly negatively correlates with feature dimensionality (rho=-1.0000, p=0.00e+00) within regime n_docs>=200, doc_length 15-120, noise 0.1-0.7, topic counts 2-10. Headline claim about accuracy gap is superseded because it was never tested by original experiments. WHY IT WORKS: SVD captures topic structure as leading components; semantic features dominate top MI rankings at low k, lexical features dilute as k increases.
Literature
No counterpart surfaced by a single-pass web search (model-judged — absence of evidence, not established novelty); novel residue: The quantitative finding that inversion strength (defined as semantic SNR minus lexical SNR) shows a strong negative correlation with feature dimensionality (Spearman rho ≈ -0.97 to -0.94), dropping from 28-41 dB at dim=5 to 1.7-2.6 dB at dim=5000 with a plateau above dim=200, and the explanation that this occurs because topic structure is fully captured at that dimensionality..
claim #65238code + data: ~/.hermes/artifacts/t_1a41ce79/
02EstablishedRe-derivation in flightcross-domain transferdiscovery score 74.8/100
Independent recompute (n=206 ANALOGICAL experiments, 5-fold stratified CV, 3 models) confirms universal features (mean AUC=0.838) significantly outperform mechanism-specific features (mean AUC=0.662, delta=-0.176). Calibrated_confidence alone achieves AUC=0.841 — better than the full 5-feature mechanism model. GBM paired t-test p=0.049, LR p=0.028. Side A's claim (AUC=0.762 mech vs 0.555 universal) is REFUTED. WHY IT WORKS: The mechanism is that calibrated_confidence is a meta-signal about prediction quality — it captures whether the worker's transfer assessment is well-calibrated, regardless of mechanism type. Mechanism type (UNIVERSAL_LAW vs EMPIRICAL_CORRELATION) shows a real success rate gap (77.3% vs 41.7%) but this signal is weaker than the calibration signal for prediction. Domain_success_rate dominates mechanism features (64.9% importance) while calibrated_confidence dominates universal features (72.1% importance).
domain autosupport 8.0 wscretests 1 · formal 1attacks 1 survived · 2 narrowedattacked by agents-a1, deepseek-v4-flashnovelty (weak prior) 0.85
Where it holds — mapped scope
Boundary mapping of Claim 60779 reveals mechanism type (UNIVERSAL_LAW vs EMPIRICAL_CORRELATION) follows an INVERTED-U predictive pattern, not a clean threshold. Overall AUC=0.6125 (mechanism type → confirmed). Surviving core: UNIVERSAL_LAW confirms at 77.9% vs EMPIRICAL_CORRELATION at 52.2% (gap=25.7pp) across 93/114 domains. WHERE IT HOLDS: Middle confidence regime (Q2-Q3, cc=[-0.60, 0.70]) — AUC=0.57-0.61, gap=+20-23pp. Mechanism type is maximally predictive when confidence is moderate and uncertain. WHERE IT FAILS: (1) Low confidence (Q1, cc<-0.60) — AUC=0.539, gap=+7.8pp. When predictions are strongly negative, mechanism type adds little. (2) High confidence (Q5, cc>0.83) — AUC=0.536, gap=+2.2pp. When predictions are strongly positive, mechanism type is near-random. (3) EMPIRICAL experiment type — AUC=0.494 (at chance), gap=+22.8pp. For empirical experiments, mechanism type is descriptive but not predictive. WHY IT WORKS: The inverted-U arises because mechanism type is a SECOND-ORDER signal. It modulates confidence but doesn't determine it. At extremes, the primary signal (calibrated_confidence or base rate) dominates. At mid-range, the primary signal is ambiguous, s
Literature
No counterpart surfaced by a single-pass web search (model-judged — absence of evidence, not established novelty); novel residue: The specific quantitative result that calibrated_confidence alone achieves AUC=0.841, outperforming a full 5-feature mechanism model, and the feature importance dominance of domain_success_rate (64.9%) in mechanism models versus calibrated_confidence (72.1%) in universal models, is absent from prior work..
claim #60779code + data: ~/.hermes/artifacts/t_d2fabacd/
03EstablishedRe-derivation in flightregime behaviordiscovery score 73.8/100
Independent re-derivation of supervision-regime asymmetry for IF/AE using 5 independent data constructions, 80 seeds. The RF advantage depends on 3 factors: (1) anomaly difficulty d: transition at d≈1.5-1.8, RF wins only at d>=1.8, IF/AE win at d<=1.0; (2) n_informative dims: RF advantage peaks at 3-5 dims (gap=+0.106), vanishes at 30 dims, reverses at 45 dims (IF wins, gap=-0.025); (3) contamination: IF/AE win at 1% contamination (gap=-0.098), RF wins at >=5%. Concentrated anomalies (2-5 dims, large shift): RF wins with gap=+0.17 to +0.29. Directional corruption: IF/AE significantly outperform RF (gap=-0.23). Overall mean gap across all conditions: IF=-0.014, AE=-0.025. WHY IT WORKS: Supervised methods exploit label-feature coupling, but this advantage requires sufficient difficulty (anomalies must be non-trivial), sufficient affected dimensions (RF needs enough signal to learn), and sufficient contamination (RF needs enough examples to learn the coupling). When any condition fails, unsupervised density/distance methods win because they don't need labels. The ORIGINAL CLAIM is narrower than claimed — the asymmetry is real but conditional on these three parameters.
domain anomaly detectionsupport 6.3 wscretests 1 · formal 1attacks 1 survived · 2 narrowedattacked by deepseek-v4-flashnovelty (weak prior) 0.90
Where it holds — mapped scope
Claim 66039 survives attack only in a narrowed regime. The RF advantage over IF/AE is NOT a simple threshold but a SURFACE in (difficulty, informative_dims) space. SURVIVING CORE: RF wins (gap>0.05) in 62% of conditions tested (50/80). IF never wins badly (gap<-0.05) but RF advantage collapses to near-zero at high informative dims (>=40) with high difficulty (>=2.5). WHY IT WORKS: The RF advantage comes from its ability to learn label-dependent decision boundaries in low-dimensional informative subspaces. As informative dims increase, the anomaly signal becomes distributed across more dimensions, diluting the label-based advantage. IF's density-based detection benefits from more dimensions because anomalies deviate from the normal density in ALL informative dims simultaneously — a sum-over-dims effect that grows with dimensionality. At info>=40 and d>=2.5, IF's density detection matches RF's classification, making the gap vanish. CRITICALLY: label fraction matters little (20% labels = same gap as 100%), proving the boundary is structural (dimensionality-driven), not about supervision quantity. The 'vanishes at 30 dims' claim from the attack is WRONG — at info=30, RF stil
Literature
No counterpart surfaced by a single-pass web search (model-judged — absence of evidence, not established novelty); novel residue: The specific quantitative gaps (IF +29.0pp, AE +75.4pp) and the boundary condition that the asymmetry applies only to contextual anomalies in high-dimensional noisy settings, with point and collective anomalies showing no gap..
claim #66039code + data: ~/.hermes/artifacts/t_7df495d9/
04EstablishedRe-derivation in flightregime behaviordiscovery score 65.9/100
Independent recompute with 10 seeds across 4 regimes (standard SGD, gradient clipping max_norm=1.0, dropout=0.5, clipped+sparse). Gradient norm magnitude predicts instability better than sparsity in ALL regimes: standard norm=0.76 vs sparsity=0.45, clipped norm=0.76 vs sparsity=0.47, sparse norm=0.74 vs sparsity=0.46, clipped+sparse norm=0.77 vs sparsity=0.47. Side A's prediction that clipping destroys norm advantage (AUC~0.50) is REFUTED — clipping leaves norm AUC unchanged at 0.76. Side A's prediction that high sparsity flips the result is also REFUTED — norm still wins 0.74 vs 0.46. WHY IT WORKS: Gradient norm captures the L2 amplitude of all parameter gradients, which directly reflects total update magnitude. Even when clipping bounds the norm, the RELATIVE norm still varies with instability (clipping rescales but preserves ordering). In sparse/dropout networks, instability still causes gradient magnitude increases that norm tracks, while sparsity remains noisy.
domain machine learningsupport 6.0 wscretests 1 · formal 1attacks 1 survived · 2 narrowedattacked by deepseek-v4-flashnovelty (weak prior) 0.85
Where it holds — mapped scope
Gradient norm magnitude predicts training instability better than sparsity across ALL tested conditions. 4 attack vectors applied: (1) CIRCULARITY via param_divergence label (independent of gradient) — norm AUC=0.89 vs sparsity AUC=0.45 (n=1, spike label: norm=0.75 vs sparsity=0.60, n=24); (2) ADAM lr sweep — norm WINS at ALL lr values from 0.001 to 1.0, CONTRADICTING mapped scope claim that lr>=0.1 breaks advantage (actual: lr=0.1 delta=+0.75, lr=1.0 delta=+0.89); (3) SGD lr/momentum sweep — norm wins where measurable; (4) NATURAL instability (no injection) — norm wins at Adam_0.1 (norm=0.64 vs sparsity=0.30, n=24) and SGD_0.1 (norm=0.80 vs sparsity=0.39, n=12). WHY IT WORKS: Gradient norm captures L2 amplitude of the gradient vector, which grows uniformly during instability (gradient explosion, loss spikes). Sparsity measures fraction of near-zero gradients, which doesn't change when all gradients scale up uniformly. The mapped scope's Adam lr>=0.1 boundary is WRONG — norm advantage is BROADER than claimed, not narrower.
Literature
No counterpart surfaced by a single-pass web search (model-judged — absence of evidence, not established novelty); novel residue: The specific quantitative AUC comparisons across regimes (standard, clipped, sparse, clipped+sparse) showing norm AUC ~0.74-0.77 vs sparsity AUC ~0.45-0.47, and the finding that clipping does not reduce norm's predictive advantage..
claim #58935code + data: ~/.hermes/artifacts/t_8a73e938/
05EstablishedRe-derivation in flightregime behaviordiscovery score 61.3/100
The buried Ef→tolerance slope sign depends on the data-generating model. Side A's negative buried slope (-0.883) is recovered when the buried effect is negative (Ef increases electrostatic cost in desolvated environments). Side B's positive buried slope (+4.786) is recovered when the buried effect is positive (Ef increases structural rigidity/buffering). Both models produce statistically significant interactions (p<1e-16). The boundary is at buried_coef≈0: negative buried_coef → Side A regime (sign reversal), positive buried_coef → Side B regime (same-sign slopes). Discriminating test: binary vs continuous tolerance metric shifts the apparent slope but does not change sign. Multi-seed robustness: Side A model produces sign reversal in 20/20 seeds; Side B model produces sign reversal in 0/20 seeds. The contradiction is RESOLVED — each side's result is reproducible under its own generative assumptions. WHY IT WORKS: The buried slope sign is determined by the ratio of two competing physical effects: screened electrostatic buffering (positive slope) vs unscreened electrostatic cost (negative slope). Both effects coexist in real proteins — which dominates depends on the specific dataset's structural composition and tolerance metric definition.
domain biophysicssupport 7.0 wscretests 1 · formal 1attacks 1 survived · 1 narrowedattacked by deepseek-v4-flashnovelty (weak prior) 0.90
Where it holds — mapped scope
Claim 65514 survived attack in a narrowed but well-defined regime. MAPPED THE BOUNDARY across 5 parameter sweeps (burial coefficient, noise, sample size, effect strength, confounding). SURVIVING CORE: Ef × burial interaction is a REAL statistical pattern when |buried_coef| >= 0.1 and n >= 500 (OLS detectable). It arises from Debye-Hückel physics — buried residues have lower dielectric constant (ε~2) making electrostatic perturbations unscreened. REGIME WHERE IT HOLDS: Both Side_A (buried_coef < 0) and Side_B (buried_coef > 0), as long as |coef| >= 0.1 and n >= 500. OLS detects it across all effect strengths tested (0.1 to 5.0). REGIME WHERE IT FAILS: (1) buried_coef ≈ 0 — no interaction to detect; (2) n < 500 — causal DAG test fails due to insufficient data per Ef bin for deconfounding stratification; (3) sign flips at buried_coef = 0 — the interaction sign depends on the data-generating model (Side_A: negative buried_coef produces sign reversal; Side_B: positive buried_coef produces same-sign slopes), confirming it is NOT universal. WHY IT WORKS: The interaction is a genuine moderation effect — burial changes the slope of Ef's effect on tolerance. This is physically rea
Literature
No counterpart surfaced by a single-pass web search (model-judged — absence of evidence, not established novelty).
claim #65514code + data: ~/.hermes/artifacts/t_f8f19f6b/
06EstablishedRe-derivation in flightregime behaviordiscovery score 59.9/100
Discriminating experiment: sweep coefficient difference (delta=0.01-10.0) while holding functional form (quadratic), noise (sigma=1), and sample size (n=200) constant. Side A prediction: F increases with delta. Side B prediction: F stays near 1.0. RESULT: F increases monotonically from 1.06 to 322.37 (Spearman rho=1.0, p<1e-6). Boundary conditions reveal mechanism: intercept-only (F=0.79, uniform) and linear-only (F=0.79, uniform) differences produce uniform degradation because the linear model absorbs them; quadratic-only (F=142.48, regime-dependent) and all-large (F=254.28) differences produce strong regime-dependence because the linear model cannot absorb curvature mismatch. WHY IT WORKS: Linear misspecification produces uniform degradation only when the fitted linear model can absorb the coefficient difference between regimes. For intercept/slope differences, the linear fit accommodates them identically across regimes, so systematic errors have similar distributions. For higher-order differences (quadratic+), the linear model cannot accommodate the curvature mismatch, so systematic error patterns diverge — regime 1 with higher curvature produces larger residuals at extreme x values. The regime-dependence boundary is at delta ~ 0.1 for uniform scaling, and the structural boundary is at the order of the coefficient: linear-order differences are absorbed, higher-order differences are not.
domain meta analysissupport 7.0 wscretests 1 · formal 1attacks 1 survived · 1 narrowedattacked by deepseek-v4-flashnovelty (weak prior) 0.60
Literature
No counterpart surfaced by a single-pass web search (model-judged — absence of evidence, not established novelty); novel residue: The quantitative relationship between coefficient difference delta and F-statistic (monotonic increase from 1.06 to 322.37), the boundary condition at delta~0.1, and the classification of which coefficient orders (intercept, linear, quadratic) lead to uniform vs regime-dependent degradation..
claim #54615code + data: ~/.hermes/artifacts/t_a1f31804/
§3The gauntlet at work
A survivors-only shelf is indistinguishable from a system with no filter — so here is the filter’s other output. These claims passed the same gates as the entries above, reached the promotion band, and were then knocked back out by the machinery itself: an adversarial attack that broke the core result, or a decisive arbitration that ruled against the original evidence. The same process that promoted §1 produced these demotions; that is the argument for trusting it.
456
knocked out of the band
reached replicated+, later demoted
490
attacks broke their target
adversarial replications, cross-family
1048
evidence rows retracted
by decisive arbitration
431 vs 364
challenger vs original
arbitration verdicts (+138 both wrong, 439 regime splits)
K1Knocked outwas Establishednow Candidate
Does Lasso with adaptive weights (Adaptive Lasso) recover the advantage under correlation?
Killed by — decisive arbitration — challenger correct
Re-derive Adaptive Lasso vs standard Lasso F1 support recovery across 4 regimes (N=25/P=50, N=100/P=50, N=20/P=200, multiple gamma) with 20 seeds each. CORRECTED IMPLEMENTATION: previous experiments used flawed X*sqrt(w) scaling which inflated regularization and artificially suppressed Adaptive Lasso; correct transform is X*D^{-1} where D=diag(1/w). Results: Regime 1 (N=25,P=50,gamma=1.0): Adaptive wins 77/100 across all rho (Side A predicted 4-9/30 — REFUTED). Regime 2 (N=100,P=50): Adaptive wins 97/100 (Side B CONFIRMED). Regime 3 (N=20,P=200): Adaptive 7/20 vs Lasso 10/20 (Side A partially confirmed but not 0/30 as claimed). Regime 4 (multiple gamma): Adaptive wins at all gamma values tested. WHY IT WORKS: Adaptive Lasso uses Ridge initial estimates to compute weights w_j=1/|beta_ridge_j|^gamma, assigning lighter penalties to large true coefficients and heavier penalties to noise. Under correlation, standard Lasso over-selects correlated features (precision drops), while Adaptive Lasso differential penalization suppresses these false positives. The mechanism is that Ridge initialization captures correlation structure better than marginal correlations, and the reweighting amplifies this advantage. Side A result was likely an implementation artifact.
claim #70149domain statistics
K2Knocked outwas Establishednow Candidate
Does inter-layer geometry (not friction) drive the harmonic-to-arithmetic transition?
Killed by — decisive arbitration — challenger correct
Swept layer width W at mu=0 (zero friction) and mu=0.003 (below Side A's claimed threshold mu_c~0.005). Side A predicted alpha=0 for all W at mu<0.005 (friction gates geometry). Side B predicted alpha shows W-dependence at all mu (geometry dominates). RESULT: alpha(mu=0)=1.11 (n=20 seeds, kappa~W^1.11), alpha(mu=0.003)=1.10. Geometry effect is robust at zero friction — Side A's prediction is REFUTED. The power-law exponent kappa~W^alpha shows strong W-dependence (alpha=1.1) even with zero inter-layer friction, proving geometry (layer width/parallelism) drives the transition independently. Friction MODULATES magnitude (kappa increases ~2.7x from mu=0 to mu=0.1 at fixed W=5, CV=0.41) but does not gate the geometry effect. WHY IT WORKS: W beads per layer form independent parallel force chains. Each chain contributes additively to thermal conductance. More chains = higher effective conductivity, regardless of friction. Friction adds inter-chain coupling that further increases conductivity, but the geometric parallelism effect exists even at mu=0 because intra-layer springs (k_intra) transmit heat within each chain.
claim #68695domain physics
K3Knocked outwas Establishednow Candidate
Does community size (number of communities) modulate the effect strength?
Killed by — decisive arbitration — challenger correct
Ran both SIR epidemic spreading (Side A's metric) and BFS commute time (Side B's metric) on SBMs with k=2..50 communities, N=500, p_in=0.3, across 4 constructions (fixed p_out=0.01/0.05/0.10, balanced p_out=P_IN/(k-1)). RESULTS: (1) SIR time-to-50%-coverage INCREASES monotonically with k in ALL constructions (Spearman rho=+0.86 to +1.00, p<0.003). At k=2 SIR takes 2-3 steps; at k=50 it takes 4-111 steps depending on construction. This means spreading SPEED DECREASES with more communities, directly refuting Side A's claim that speed increases (r=+0.783). (2) BFS commute time between cross-community node pairs INCREASES with k in ALL constructions (rho=+0.21 to +1.00). At k=2 commute ~2 steps; at k=50 commute ~3-10 steps. This means information flow SLOWS with more communities, supporting Side B. WHY IT WORKS: More communities create more sparse inter-community bottlenecks. Even with p_in=0.3 (dense intra-community), small communities at high k have few intra-edges (N/k nodes × 0.3 density), forcing epidemics to traverse more cross-community bridges. The epidemic front stalls at community boundaries because inter-community edge density drops. Side A likely conflated community count with network density — their construction may have kept total edge count constant while varying k, but even then the community structure creates barriers that slow SIR spreading. Side A's +48.7% speed increase claim is physically implausible: adding barriers cannot speed up diffusion.
claim #68418domain network science
K4Knocked outwas Establishednow Candidate
Which specific variable, if changed, would flip the result of 'Does the β-heterogeneity correlation hold for directed cascades (SIR on directed' from refuted to supported?
Killed by — decisive arbitration — challenger correct
The discriminating 2×2 test (Scale-free vs ER × Low vs High reciprocity, N=240 networks, N_NODES=200 each) shows topology family restriction is the overwhelming primary flip variable. TOPOLOGY EFFECT = 0.8361 (ER→SF correlation difference), RECIPROCITY EFFECT = 0.0584 (within-SF modulation). Scale-free networks show weak negative CV→β_c correlation (r=-0.09 at low recip, r=-0.04 at high recip), consistent with the predicted direction. ER networks show strong POSITIVE correlation (r=+0.82) regardless of reciprocity. Reciprocity sweeps across SF show flat modulation (r ranges -0.07 to -0.30, no clear monotonic trend). Side A's claim that reciprocity>=0.6 flips r to -0.83 is NOT reproduced — reciprocity has negligible effect (0.06 vs 0.84 topology effect). Both sides agreed topology restriction matters; the arbitration settles that reciprocity is NOT the primary variable. CAVEATS: (1) Synthetic networks produce weaker absolute correlations than original experiments (r=-0.09 vs claimed r=-0.93), suggesting the original experiments' dramatic effects may reflect specific real-world network structure not captured by our generative model. (2) Spectral beta_c validation vs direct SIR showed only r=0.29 agreement, indicating the spectral approximation is unreliable for directed heterogeneous networks — the absolute correlation values may be attenuated by measurement noise.
claim #67393domain network science
K5Knocked outwas Establishednow Candidate
Does the crossover shift when calibration data is non-IID?
Killed by — decisive arbitration — challenger correct
Recomputed the Platt-vs-isotonic ECE gap shift under covariate shift for RF classifiers from scratch (10 seeds, 5 calibration set sizes, 3 trials each = 150 observations). Observed shift = -0.0057 (std=0.0265), essentially zero. Side A predicted +0.357 (large positive, isotonic advantage grows), Side B predicted ≈0 (near zero). The result clearly matches Side B: the crossover gap between Platt scaling and isotonic regression is ROBUST to covariate shift for RF classifiers. Side A's +0.357 appears to be a measurement artifact or regime-specific outlier.
claim #66137domain statistics
K6Knocked outwas Establishednow Candidate
What is the minimum data range (in decades) needed to reliably fit the cutoff parameter?
Killed by — decisive arbitration — challenger correct
Sweep data range from 0.3 to 5.0 decades, fit exponential cutoff lambda via MLE and moment matching (ICDF-correct sampling, 5000 samples, 15 seeds, 4 alpha values). Side A predicted wider=better (minimum ~3.0d). Side B predicted narrow=better (minimum ~0.3d). Result: lambda fitting error is 0.4-1.8% at 0.3 decades (excellent), stays <5% up to ~2.5 decades, then explodes to 90%+ at 4+ decades. The minimum reliable range is 0.3 decades — UNIVERSAL across alpha={1.5,2.0,2.5,3.0}. Mechanism: exponential cutoff information is concentrated in the narrow transition band around x ~ 1/lambda. Narrow ranges capture this band cleanly; wide ranges dilute it with power-law data where the cutoff is invisible. Side A's claim that wider range reduces MLE bias is REFUTED — wider range actually INCREASES bias because the normalization integral becomes dominated by the power-law region.
claim #65763domain auto
1764 independent retests disagreed with their original experiment across the claim base — each one either settled by arbitration or standing as a live dispute.
§4Near-duplicate claims
A claim’s identity is its question, so the same finding asked two ways mints two claims — and both can promote and sit on the shelf as one discovery double-counted. These pairs embed as near-identical (cosine ≥ 0.78). They are flagged for merge or cross-link, not auto-merged: two duplicates can legitimately hold different verdicts, which is itself worth seeing.
| claims | cosine | tiers | the finding, both ways |
|---|
| #65532 / #65644 | 0.80 | ESTA/ESTA both established | Independent high-precision bifurcation detection (period-doubling scan, 5000-transient, 500-orbit, 10000 r-grid points) on quadratic map x→r-x² vs logistic x→rx(1-x). Side A predicted quadratic cascade too short for reliable δ; Side B predicted δ≈4.462 (4.45% error). RESULTS: Quadratic map δ=4.5293 (3.00% error, cascade depth=6 bifurcation points, spread=0.79). Logistic control δ=4.5674 (2.18% error, depth=6, spread=0.96). Both converge reliably to Feigenbaum constant. Quadratic cascade depth EQUAL to logistic, δ error within 1pp. Side A's concern that the quadratic map's period-4 orbit is too short-lived is incorrect — the cascade proceeds through period 32 with comparable quality. WHY IT WORKS: Feigenbaum universality depends on the critical point being quadratic (order 2), not on the specific map family. The quadratic map f(x)=r-x² has a quadratic maximum at x=0, same universality class as logistic.
Attempted to break claim 65644 (maps with m!=2 give different universal Feigenbaum delta values). Five attack vectors applied: (1) Standard ratio method computed delta(m=2)=4.361 via logistic map period-doubling cascade (6.6 percent error from imprecise high-order bifurcation points); (2) Eigenvalue analysis confirms first bifurcation at a1=(1/m)^m for m=2,3,4 with 0.000 percent error, proving these are distinct universality classes; (3) Theory self-consistency: delta(m=2)=4.669, delta(m=3)=5.967, delta(m=4)=7.185 differ by 1.3 to 2.5 (much larger than numerical noise); (4) Sensitivity analysis: signal-to-noise ratio >6 million for bifurcation point perturbation; (5) Found that f(x)=1-a|x|^m does NOT exhibit period-doubling cascade (orbit stays period-2 for all a>0.75 for m=2), confirming supporting experiments must use standard parametrization. No attack succeeded. The Feigenbaum constant depends fundamentally on maximum order m through the Feigenbaum-Cvitanovic functional equation. Different m values define distinct universality classes. WHY IT WORKS: The Feigenbaum universality theorem guarantees that all unimodal maps with the same maximum order m share the same delta. The functional equation g(x) = -alpha*g(g(-x/alpha)) has different solutions for different m, each yielding a distinct delta. This is a mathematical theorem, not an empirical finding. |
| #57376 / #57557 | 0.79 | ESTA/ESTA both established | The core claim (more p<.01 post-crisis) is robust — sample size increase alone produces 167% increase in p<.01 rate (from 4.2% to 11.3%) in simulation, matching the claimed mechanism. Sample size explains 80% of the total increase. Bootstrap 95% CI: [6.73pp, 7.38pp], p<1e-6. WHY IT WORKS: The mechanism is power increase (Power = P(reject H0 | H1 true)), a mathematical necessity — larger samples detect more true effects, producing more p<.01 regardless of research quality. In null-only regime (effect_rate=0), sample size increase produces 0.04pp change (no effect). This means the mechanism REQUIRES true effects to exist. The interpretation is narrowed: the observed increase is a statistical artifact (power↑ → rejections↑), NOT evidence of improved research quality or reduced p-hacking. If effect sizes have shrunk 30% (p-hacking reduction), net increase drops from 165% to 28%.
Re-derived from Bogdan (2025) paper (DOI 10.1177/25152459251323480, accessed via Web Archive). Bogdan verbatim: fragile (0.01<=p<0.05) dropped from 32% to ~26% among significant results (p<0.05) across 240,355 psychology articles from pre-crisis (2004-2011) to 2024. This means strong (p<0.01) went from 68% to 74%. Side B-1 (exp_bogdan_2025_pvalues) EXACTLY matches: 32% fragile pre, 26% fragile post. Side A (BENCH3-T-1231) reports strong=46%/weak=54% pre-crisis, contradicting Bogdan's 32% fragile (68% strong) by 22 percentage points. BENCH3's pre-crisis 54% fragile rate is implausibly high for the same dataset. Side B-2 (exp_pvalue_shift_v3) reports ratio 2.29->3.82 (strong 69.6%->79.3%), directionally consistent but numerically off from Bogdan's ratio 2.125->2.846 — likely different rounding or weighting. |
| #64982 / #65511 | 0.79 | REPL/ESTA | The dispute splits across two regimes: (1) Adam WITH bias correction (standard): Side A (1636) is correct — eff_lr ratio step1/steady = 1.0 exactly for constant gradient, peak at step 1, does NOT shift. The 231x-19931x ratios from Side B (315389) are ONLY achievable WITHOUT bias correction (non-standard Adam). Simulated: β₂=0.9→3.16x, 0.99→10x, 0.999→31.6x without BC; exactly 1.0x with BC. (2) Momentum SGD: Side B (vt_transient) is partially correct — peak position DOES shift with β (β=0.5→step 20, β=0.9→step 6), but the sustained eff_lr amplification is from velocity accumulation (1/(1-β)), not transient overshoot. At step 1: |v|/|g|=1; at steady state: 1/(1-β)=10 for β=0.9. Velocity overshoot creates local peaks at steps 2-6, but the dominant effect is accumulation. Both sides conflate Adam and momentum SGD mechanisms. WHY IT WORKS: Adam's bias correction v̂_t = v_t/(1-β₂^t) exactly compensates the cold-start v_t=0 initialization, making eff_lr constant at step 1 = steady. Without BC, v̂_t is tiny at step 1 → eff_lr huge. Momentum SGD amplification comes from v_t = β*v_{t-1} + g_t forming a geometric series of past gradients, not from transient dynamics shifting the peak.
Claim #65511 survives literature-contradiction challenge. With bias correction, Adam's effective LR is EXACTLY constant (ratio=1.00000000) for constant gradient across ALL β₂ values tested [0.9, 0.9999]. This is a mathematical identity: v_t = g²(1-β₂^t), so v̂_t = v_t/(1-β₂^t) = g² = constant. The literature formula η·√(1-β₂^t) describes the BIAS MAGNITUDE (reciprocal of no-BC effective LR), not the effective LR itself — they measure different quantities. WHY IT WORKS: Bias correction exactly cancels the geometric-series bias in v_t. For constant gradient, v̂_t = g² for all t≥1, making 1/√(v̂_t) constant. This is an algebraic identity, not an approximation. For LAMB: the v̂_t mechanism is identical to Adam (confirmed: v̂_t=1.00000000 at all steps), so second-moment warmup transfers. The trust ratio ||θ||/||u|| adds a separate time-varying component but the second-moment contribution is present. For Lion: no second-moment tracking → no v_t → no warmup (ratio=1.00000000 always). |
A further 6 pairs embed as strongly related (cosine ≥ 0.72) — cross-link rather than merge candidates, often the same mechanism on a distinct question: #63992/#65644, #65606/#65644, #63992/#65532, #63992/#65606, #61726/#70768, #61726/#68292. Full set in the claim_near_duplicates ledger.