/- BaselineComparison.lean — BraidCore Predictions vs Standard Physics For every pre-registered prediction, this module states what standard, established physics predicts for the SAME observable, then classifies BraidCore's relationship to that baseline. Classification categories: - `agrees` — BraidCore and standard physics give the same value/range - `disagrees` — BraidCore contradicts established physics - `goesBeyond` — Standard physics has no prediction; BraidCore offers one - `noPrediction` — Neither BraidCore nor standard physics makes a prediction This addresses the adversarial review's implicit attack: "Does BraidCore add any predictive power beyond what is already known?" Conventions: PascalCase types, camelCase functions. theorem for every boundary claim. #eval! for executable receipt. Namespace: Semantics.BaselineComparison -/ import Semantics.Toolkit namespace Semantics.BaselineComparison open Semantics.Toolkit -- ═══════════════════════════════════════════════════════════════════════════ -- §0 Classification Type -- ═══════════════════════════════════════════════════════════════════════════ /-- Relationship of a BraidCore prediction to standard physics. -/ inductive BaselineRelation where | agrees -- Same value/range as established physics | disagrees -- Contradicts established physics | goesBeyond -- Standard physics silent; BraidCore offers prediction | noPrediction -- Neither side predicts deriving Repr, DecidableEq, BEq def BaselineRelation.toString : BaselineRelation → String | .agrees => "AGREES" | .disagrees => "DISAGREES" | .goesBeyond => "GOES_BEYOND" | .noPrediction => "NO_PREDICTION" -- ═══════════════════════════════════════════════════════════════════════════ -- §1 Standard Physics Baselines (one per prediction) -- ═══════════════════════════════════════════════════════════════════════════ /-- P1 Rydberg quantum defect δ₁. Standard physics (QDT / MQDT): odd-power terms in the quantum defect expansion vanish for hydrogenic systems due to parity. For non-hydrogenic systems, δ₁ is system-specific and must be fitted to spectroscopic data. There is NO universal theoretical prediction for δ₁. BraidCore predicts δ₁ = 2/137 ≈ 0.0146 universally. Relation: GOES_BEYOND (standard physics has no universal δ₁). -/ def p01StandardPhysics : String := "QDT/MQDT: no universal odd-power δ₁; system-specific fit required" def p01Relation : BaselineRelation := .goesBeyond /-- P2 Magnetic domain wall volume fraction. Standard physics (micromagnetics): wall fraction depends on material anisotropy, exchange stiffness, temperature, and geometry. No universal theory predicts f_wall ≈ 0.25 for all simple ferromagnets. BraidCore predicts f_wall = 931/3699 ≈ 0.252 universally. Relation: GOES_BEYOND. -/ def p02StandardPhysics : String := "Micromagnetics: material-specific, no universal wall fraction" def p02Relation : BaselineRelation := .goesBeyond /-- P3 Percolation threshold in 3D lattices. Standard physics: each lattice has its own threshold. BCC site: 0.246, FCC site: 0.198, diamond: 0.429, simple cubic: 0.311. BraidCore predicts p_c ≈ 7/27 ≈ 0.259 for ALL 3D lattices. Relation: DISAGREES (contradicts known lattice-specific values). -/ def p03StandardPhysics : String := "Percolation theory: lattice-specific thresholds (BCC 0.246, SC 0.311, etc.)" def p03Relation : BaselineRelation := .disagrees /-- P4 Ecological regime shift period. Standard physics / ecology: no theory predicts a universal ~61-year oscillation period across all populations. Individual populations (sardines, lynx-hare) have their own characteristic periods. BraidCore predicts P(5) ≈ 61.2 years universally. Relation: GOES_BEYOND. -/ def p04StandardPhysics : String := "WITHDRAWN — required fitted dimensional scale factor P0 = 1 year" def p04Relation : BaselineRelation := .noPrediction /-- P5 Mott metal-insulator transition criterion. Standard physics: Mott criterion n_c^(1/3)·a_B ≈ 0.26 for 3D disordered systems (Edwards, Mott, 1969–1995). Value is empirically established. BraidCore predicts 7/27 ≈ 0.259. Relation: AGREES (within 0.3%). -/ def p05StandardPhysics : String := "Mott-Edwards: n_c^(1/3)·a_B ≈ 0.26 for 3D disordered systems" def p05Relation : BaselineRelation := .agrees /-- P6 Weak value amplification limit. Standard physics (Aharonov-Vaidman weak measurement): maximum weak value is unbounded in principle; in practice limited by post-selection probability and technical noise. No universal theoretical limit A_w(max) ≈ 51,429. BraidCore predicts A_w(max) = 1/α_T ≈ 51,429. Relation: GOES_BEYOND. -/ def p06StandardPhysics : String := "Weak measurement: no universal A_w(max); platform-dependent" def p06Relation : BaselineRelation := .goesBeyond /-- P7 Species-area exponent. Standard ecology: Preston-MacArthur theory predicts z ≈ 0.20–0.35 depending on dispersal, speciation rate, and spatial heterogeneity. The canonical value is z ≈ 0.25 (quarter-power law). BraidCore predicts z = 931/3699 ≈ 0.252 (corrected) or 7/27 ≈ 0.259 (bare). Relation: AGREES (within canonical range). -/ def p07StandardPhysics : String := "Species-area law: z ≈ 0.20–0.35, canonical 0.25" def p07Relation : BaselineRelation := .agrees /-- P8 Random close packing void fraction. Standard physics (granular materials): RCP solid fraction φ_solid ≈ 0.64, so void fraction φ_void ≈ 0.36 (Bernal, 1960; Song et al., 2008). BraidCore predicts φ_void ≈ 7/27 ≈ 0.259. Relation: DISAGREES (off by 28%). -/ def p08StandardPhysics : String := "Granular packing: φ_void(RCP) ≈ 0.36, not 0.259" def p08Relation : BaselineRelation := .disagrees /-- P9 FQHE lowest filling factor. Standard physics: Laughlin theory predicts ν = 1/3, 1/5, 1/7, ... (odd-denominator fractions). Wigner crystal forms at ν < 1/7. BraidCore predicts ν_min ≈ 7/27 ≈ 0.259 (or exploratory 1/4 = 0.25). Relation: DISAGREES (7/27 is not a Laughlin fraction). -/ def p09StandardPhysics : String := "FQHE: Laughlin ν = 1/3, 1/5, 1/7, ...; Wigner crystal below 1/7" def p09Relation : BaselineRelation := .disagrees /-- P10 Jupiter-Europa Laplace resonance deviation. Standard celestial mechanics (Laplace, 1805; modern JPL ephemerides): the Io-Europa-Ganymede resonance is dynamically stable over billion-year timescales. No detectable deviation above ~10⁻¹² is expected. BraidCore predicts no deviation above α_T ≈ 2×10⁻⁵. Relation: AGREES (both predict no measurable effect, but BraidCore's bound is much weaker than standard mechanics). -/ def p10StandardPhysics : String := "Celestial mechanics: Laplace resonance stable; no deviation above ~10⁻¹²" def p10Relation : BaselineRelation := .agrees /-- P11 Menger period ratio P(k+1)/P(k) = 3. Standard ecology: no theory predicts a universal period ratio of 3 across ecological systems. Individual populations have their own characteristic period ratios (often non-integer, e.g., lynx-hare ~10). BraidCore predicts P(k+1)/P(k) = 3 for any system showing multiple oscillation periods. Relation: GOES_BEYOND. -/ def p11StandardPhysics : String := "Population ecology: no universal period-ratio theory; species-specific" def p11Relation : BaselineRelation := .goesBeyond -- ═══════════════════════════════════════════════════════════════════════════ -- §2 Summary Table -- ═══════════════════════════════════════════════════════════════════════════ /-- Count predictions by their relationship to standard physics. Note: P4 is withdrawn, so only 10 active + 1 withdrawn = 11 total. The count here includes all 11 for completeness. -/ def countByRelation (target : BaselineRelation) : Nat := let all := [p01Relation, p02Relation, p03Relation, p04Relation, p05Relation, p06Relation, p07Relation, p08Relation, p09Relation, p10Relation, p11Relation] (all.filter (fun r => r = target)).length -- ═══════════════════════════════════════════════════════════════════════════ -- §3 Theorems — Classification Correctness (executable via native_decide) -- ═══════════════════════════════════════════════════════════════════════════ /-- P1 is classified as goesBeyond. -/ theorem p01Relation_correct : p01Relation = BaselineRelation.goesBeyond := by native_decide /-- P2 is classified as goesBeyond. -/ theorem p02Relation_correct : p02Relation = BaselineRelation.goesBeyond := by native_decide /-- P3 is classified as disagrees. -/ theorem p03Relation_correct : p03Relation = BaselineRelation.disagrees := by native_decide /-- P5 is classified as agrees. -/ theorem p05Relation_correct : p05Relation = BaselineRelation.agrees := by native_decide /-- P7 is classified as agrees. -/ theorem p07Relation_correct : p07Relation = BaselineRelation.agrees := by native_decide /-- P8 is classified as disagrees. -/ theorem p08Relation_correct : p08Relation = BaselineRelation.disagrees := by native_decide /-- P10 is classified as agrees. -/ theorem p10Relation_correct : p10Relation = BaselineRelation.agrees := by native_decide /-- P11 is classified as goesBeyond. -/ theorem p11Relation_correct : p11Relation = BaselineRelation.goesBeyond := by native_decide /-- P4 (withdrawn) is classified as noPrediction. -/ theorem p04Relation_withdrawn : p04Relation = BaselineRelation.noPrediction := by native_decide /-- Count of active predictions that go beyond standard physics: 4. -/ theorem countGoesBeyond : countByRelation BaselineRelation.goesBeyond = 4 := by native_decide /-- Count of predictions that agree with standard physics: 3. -/ theorem countAgrees : countByRelation BaselineRelation.agrees = 3 := by native_decide /-- Count of predictions that disagree with standard physics: 3. -/ theorem countDisagrees : countByRelation BaselineRelation.disagrees = 3 := by native_decide /-- Count of withdrawn predictions: 1. -/ theorem countNoPrediction : countByRelation BaselineRelation.noPrediction = 1 := by native_decide /-- Honest breakdown: 4 novel, 3 agreeing, 3 contradictory, 1 withdrawn. -/ theorem totalClassified : countByRelation BaselineRelation.goesBeyond + countByRelation BaselineRelation.agrees + countByRelation BaselineRelation.disagrees + countByRelation BaselineRelation.noPrediction = 11 := by native_decide -- ═══════════════════════════════════════════════════════════════════════════ -- §4 Honest Assessment -- ═══════════════════════════════════════════════════════════════════════════ /- Summary of BraidCore vs Standard Physics: Prediction Standard Physics BraidCore Relation ───────────────────────────────────────────────────────────────────────────────── P1 Rydberg δ₁ No universal δ₁ δ₁ = 2/137 GOES_BEYOND P2 Magnetic walls No universal f_wall 0.252 GOES_BEYOND P3 Percolation p_c Lattice-specific 0.259 universal DISAGREES P4 Ecological period WITHDRAWN (fitted P0) 61.2 yr WITHDRAWN P5 Mott criterion n_c^(1/3)*a_B ~ 0.26 7/27 ~ 0.259 AGREES P6 Weak value limit No universal limit 51,429 GOES_BEYOND P7 Species-area z z ~ 0.20--0.35 0.252 AGREES P8 RCP void fraction phi_void ~ 0.36 0.259 DISAGREES P9 FQHE nu_min Laughlin 1/3, 1/5, ... 7/27 DISAGREES P10 Jupiter resonance Stable; no deviation < 2e-5 AGREES (weak) P11 Period ratio No universal ratio 3 GOES_BEYOND FIX APPLIED: P4 withdrawn due to dimensional inconsistency (fitted P0). Replaced by P11: dimensionless period ratio P(k+1)/P(k) = 3. The adversarial assessment: BraidCore makes 4 genuinely novel predictions (P1, P2, P6, P11), 3 that agree with established physics (P5, P7, P10), and 3 that contradict it (P3, P8, P9). The 3 contradictory predictions are the strongest falsification targets. If all 3 are falsified, BraidCore loses 30% of its active predictive claims. The honest A-rate for novel predictions is currently 0/4 (all pending). -/ -- ═══════════════════════════════════════════════════════════════════════════ -- §5 Executable Receipts -- ═══════════════════════════════════════════════════════════════════════════ #eval! countByRelation BaselineRelation.goesBeyond #eval! countByRelation BaselineRelation.agrees #eval! countByRelation BaselineRelation.disagrees end Semantics.BaselineComparison