From 40202cfdb604604f1feef9e7e7457d044489433c Mon Sep 17 00:00:00 2001 From: Brandon Schneider Date: Wed, 13 May 2026 21:25:52 -0500 Subject: [PATCH] =?UTF-8?q?docs(physics):=20break=20points=20=E2=80=94=20w?= =?UTF-8?q?here=20the=20model=20falsifies,=20ranked?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit 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. --- .../Semantics/Physics/BreakPoints.lean | 81 +++++++++++++++++++ 1 file changed, 81 insertions(+) create mode 100644 0-Core-Formalism/lean/Semantics/Semantics/Physics/BreakPoints.lean diff --git a/0-Core-Formalism/lean/Semantics/Semantics/Physics/BreakPoints.lean b/0-Core-Formalism/lean/Semantics/Semantics/Physics/BreakPoints.lean new file mode 100644 index 00000000..1a3fec69 --- /dev/null +++ b/0-Core-Formalism/lean/Semantics/Semantics/Physics/BreakPoints.lean @@ -0,0 +1,81 @@ +-- 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