Research-Stack/0-Core-Formalism/lean/Semantics/Semantics/BaselineComparison.lean
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/-
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, 19691995). 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 ≈ 0.200.35
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 ≈ 0.200.35, 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