/-
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
