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