docs(physics): break points — where the model falsifies, ranked

The 5 knife edges:
  1. w_a gap (HIGH): SM gives -0.06, DESI sees -0.59. Factor 10.
  2. w0 formula (HIGH): heuristic, 2.1s from DESI. Needs proper QFT.
  3. LISA null (MODERATE): 0.13 rad predicted. Launch ~2035.
  4. SH0ES H0 (MODERATE): model says 68.0, SH0ES says 73.04. 4.8s.
  5. alpha = beta/(4*pi) (LOW): within 0.3% at 2-loop. g-2 is hedge.

Model breaks FIRST on w_a if DESI DR3 confirms w_a ≈ -0.6.

0-Core-Formalism/lean/Semantics/Semantics/Physics/BreakPoints.lean

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+-- BreakPoints.lean
+--
+-- Where the model breaks — ranked by likelihood.
+-- Every testable model needs clear falsification criteria.
+-- These are the knife edges.
+
+namespace Semantics.Physics.BreakPoints
+
+-- ═════════════════════════════════════════════════════════════════════════════
+-- KNIFE EDGE 1: w_a (HIGH — factor 10 gap)
+-- ═════════════════════════════════════════════════════════════════════════════
+
+-- SM Higgs running gives w_a = -0.06
+-- DESI DR2 sees w_a = -0.59 +- 0.25
+-- Factor 10 gap. If DESI DR3 tightens to +-0.10 and confirms -0.6,
+-- the Higgs sector alone cannot produce this. The model needs a
+-- non-Higgs coupling source (top quark? neutrino? axion?).
+--
+-- Current tension: 2.1 sigma (DESI DR2 w_a error is still large).
+-- If DR3 halves the error and the central value stays: TENSION > 4 sigma.
+
+-- ═════════════════════════════════════════════════════════════════════════════
+-- KNIFE EDGE 2: w0 projection formula (HIGH — heuristic, 2.1s off)
+-- ═════════════════════════════════════════════════════════════════════════════
+
+-- Predicted: w0 = -0.953 from heuristic projection formula
+-- DESI DR2:  w0 = -0.838 +- 0.055
+-- Residual: 2.1 sigma. The formula w0 = -1 + 2*f_lam*omega*P is heuristic.
+-- Needs a proper QFT derivation.
+--
+-- If DESI DR3 tightens w0 to +-0.03 and the central value stays:
+-- residual becomes > 3 sigma. The model is ruled out unless the
+-- projection formula can be fixed with a proper derivation.
+
+-- ═════════════════════════════════════════════════════════════════════════════
+-- KNIFE EDGE 3: LISA null result (MODERATE — cleanest test, 10 years out)
+-- ═════════════════════════════════════════════════════════════════════════════
+
+-- The model predicts 0.13 rad of integrated torsion phase shift at mHz
+-- frequencies for high-z gravitational wave sources. LISA (launch ~2035)
+-- will have sensitivity to detect this at > 1000 sigma.
+--
+-- If LISA sees NO shift at 0.01 rad precision: FALSIFIED.
+-- If LISA sees exactly 0.13 rad: CONFIRMED.
+-- If LISA sees 0.01-0.12 rad: torsion coupling weaker than predicted.
+
+-- ═════════════════════════════════════════════════════════════════════════════
+-- KNIFE EDGE 4: SH0ES H0 (MODERATE — 4.8s exclusion could reverse)
+-- ═════════════════════════════════════════════════════════════════════════════
+
+-- The model predicts H0 = 68.0 km/s/Mpc. SH0ES measures H0 = 73.04.
+-- The model rules out SH0ES at 4.8 sigma. If systematic errors in
+-- the SH0ES measurement are small (< 1 km/s/Mpc), the model is correct.
+-- If SH0ES is right and Planck/DESI have systematics, the model is wrong.
+
+-- ═════════════════════════════════════════════════════════════════════════════
+-- KNIFE EDGE 5: alpha = max|beta|/(4*pi) (LOW — already within 0.3% at 2-loop)
+-- ═════════════════════════════════════════════════════════════════════════════
+
+-- If a BSM particle is discovered that changes the SM beta function,
+-- the predicted alpha would shift. Fermilab muon g-2 is the most
+-- likely source. Current tension with SM: 5 sigma.
+-- If g-2 proves BSM, alpha is not from SM beta alone.
+-- If g-2 resolves with lattice QCD, alpha from beta stands.
+
+-- ═════════════════════════════════════════════════════════════════════════════
+-- SUMMARY
+-- ═════════════════════════════════════════════════════════════════════════════
+
+-- The model has 5 knife edges. 2 are high-probability (w_a, w0 formula).
+-- 2 are moderate (LISA, SH0ES). 1 is low (alpha).
+--
+-- The FIRST break will be w_a. If DESI DR3 (2026-2027) confirms
+-- w_a ≈ -0.6 with tight error bars, the SM Higgs running alone
+-- cannot explain it. The model needs either:
+--   1. A non-Higgs coupling source (top quark, neutrino, axion)
+--   2. DESI w_a is wrong (systematic in SN data)
+--
+-- Either way: w_a is the knife edge. Everything else holds together.
+
+end Semantics.Physics.BreakPoints