From c42bd6b7db4579eedfd26f4f6f4268dfc44d3dbe Mon Sep 17 00:00:00 2001 From: Steve Moraco Date: Thu, 20 Aug 2026 03:34:04 -0600 Subject: [PATCH 1/2] Verify YM C328 parabolic-cone harmonic bootstrap --- ...lShabirParabolicConeHarmonicBootstrap.lean | 66 +++++++++++++++++++ 1 file changed, 66 insertions(+) create mode 100644 verification/ym-c328-parabolic-cone-harmonic-bootstrap/FaizalShabirParabolicConeHarmonicBootstrap.lean diff --git a/verification/ym-c328-parabolic-cone-harmonic-bootstrap/FaizalShabirParabolicConeHarmonicBootstrap.lean b/verification/ym-c328-parabolic-cone-harmonic-bootstrap/FaizalShabirParabolicConeHarmonicBootstrap.lean new file mode 100644 index 000000000..0e7ec8748 --- /dev/null +++ b/verification/ym-c328-parabolic-cone-harmonic-bootstrap/FaizalShabirParabolicConeHarmonicBootstrap.lean @@ -0,0 +1,66 @@ +import Mathlib + +/-! +# C328: parabolic center/stable cone finite firewall + +Finite real-algebra consumers for the repaired Faizal--Shabir weak-RG architecture. + +The file proves only: +* a cubic center step with remainder `|R| <= rho * g^3` lies between two + cubic comparison steps; +* `rho < beta` leaves a positive effective cubic decrement; +* on the parabolic boundary `K = A g^2`, the mixed `g K` channel is exactly + cubic order and therefore can shift the one-loop coefficient unless a + stronger cancellation/subquadratic theorem is supplied. + +It does not formalize the Yang--Mills Banach RG, an invariant cone, asymptotic +freedom, AF/IR identification, continuum OS reconstruction, a mass gap, or the +Clay theorem. +-/ + +namespace Millennium.YangMills.FaizalShabirParabolicConeHarmonicBootstrap + +/-- A center step with an absolute cubic remainder lies between the two +comparison cubic steps. -/ +theorem center_step_two_sided + (g g' beta rho R : ℝ) + (hstep : g' = g - beta * g ^ 3 + R) + (hR : |R| ≤ rho * g ^ 3) + (hg : 0 ≤ g) : + g - (beta + rho) * g ^ 3 ≤ g' ∧ + g' ≤ g - (beta - rho) * g ^ 3 := by + have hpow : 0 ≤ g ^ 3 := by positivity + have hRlo : -(rho * g ^ 3) ≤ R := (abs_le.mp hR).1 + have hRhi : R ≤ rho * g ^ 3 := (abs_le.mp hR).2 + constructor + · rw [hstep] + nlinarith + · rw [hstep] + nlinarith + +/-- A strict cubic remainder margin leaves a positive effective decrement. -/ +theorem effective_cubic_margin_pos + (beta rho : ℝ) + (hmargin : rho < beta) : + 0 < beta - rho := by + linarith + +/-- On the parabolic boundary `K = A g^2`, the allowed mixed center channel +`g*K` is exactly cubic order. -/ +theorem mixed_channel_is_cubic_on_parabolic_boundary + (g A : ℝ) : + g * (A * g ^ 2) = A * g ^ 3 := by + ring + +/-- The quadratic stable channel on the same boundary is fourth order. -/ +theorem stable_square_is_quartic_on_parabolic_boundary + (g A : ℝ) : + (A * g ^ 2) ^ 2 = A ^ 2 * g ^ 4 := by + ring + +#print axioms center_step_two_sided +#print axioms effective_cubic_margin_pos +#print axioms mixed_channel_is_cubic_on_parabolic_boundary +#print axioms stable_square_is_quartic_on_parabolic_boundary + +end Millennium.YangMills.FaizalShabirParabolicConeHarmonicBootstrap From 96847983b2671a7918b1fa9590b3fea0e362682b Mon Sep 17 00:00:00 2001 From: Steve Moraco Date: Thu, 20 Aug 2026 03:34:18 -0600 Subject: [PATCH 2/2] Add guarded verifier for YM C328 --- ...c328-parabolic-cone-harmonic-bootstrap.yml | 52 +++++++++++++++++++ 1 file changed, 52 insertions(+) create mode 100644 .github/workflows/ym-c328-parabolic-cone-harmonic-bootstrap.yml diff --git a/.github/workflows/ym-c328-parabolic-cone-harmonic-bootstrap.yml b/.github/workflows/ym-c328-parabolic-cone-harmonic-bootstrap.yml new file mode 100644 index 000000000..201b4bc7f --- /dev/null +++ b/.github/workflows/ym-c328-parabolic-cone-harmonic-bootstrap.yml @@ -0,0 +1,52 @@ +name: YM C328 parabolic-cone harmonic bootstrap + +on: + push: + branches: + - verification/ym-c328-parabolic-cone-harmonic-bootstrap-20260820 + paths: + - verification/ym-c328-parabolic-cone-harmonic-bootstrap/*.lean + - .github/workflows/ym-c328-parabolic-cone-harmonic-bootstrap.yml + pull_request: + paths: + - verification/ym-c328-parabolic-cone-harmonic-bootstrap/*.lean + - .github/workflows/ym-c328-parabolic-cone-harmonic-bootstrap.yml + workflow_dispatch: + +permissions: + contents: read + +jobs: + verify: + runs-on: ubuntu-22.04 + timeout-minutes: 20 + steps: + - uses: actions/checkout@v4 + - name: Verify flattened Lean theorem source + shell: bash + run: | + set -euo pipefail + SRC=verification/ym-c328-parabolic-cone-harmonic-bootstrap/FaizalShabirParabolicConeHarmonicBootstrap.lean + if grep -nE '\b(sorry|admit|sorryAx|axiom|opaque|unsafe|native_decide|Lean\.ofReduceBool)\b' "$SRC"; then exit 1; fi + SRC="$SRC" python3 - <<'PY' + import hashlib, json, os, pathlib, urllib.request + path = pathlib.Path(os.environ['SRC']) + source = path.read_text() + payload = json.dumps({'content': source,'environment':'lean-4.30.0','ignore_imports':True,'mathlib_options':False,'timeout_seconds':900}).encode() + req = urllib.request.Request('https://axle.axiommath.ai/api/v1/check', data=payload, headers={'Content-Type':'application/json'}, method='POST') + with urllib.request.urlopen(req, timeout=960) as response: + result = json.load(response) + receipt={'source_path':str(path),'source_sha256':hashlib.sha256(source.encode()).hexdigest(),'axle_environment':'lean-4.30.0','axle_result':result} + pathlib.Path('/tmp/ym-c328-axle-receipt.json').write_text(json.dumps(receipt,indent=2)) + print(json.dumps(receipt,indent=2)) + lean=result.get('lean_messages',{}); tool=result.get('tool_messages',{}) + bad=(not result.get('okay') or bool(result.get('failed_declarations',[])) or bool(lean.get('errors',[])) or bool(lean.get('warnings',[])) or bool(tool.get('errors',[])) or bool(tool.get('warnings',[])) or 'sorryAx' in json.dumps(result)) + if bad: raise SystemExit(1) + PY + - uses: actions/upload-artifact@v4 + if: always() + with: + name: ym-c328-parabolic-cone-harmonic-bootstrap-axle-receipt + if-no-files-found: warn + retention-days: 30 + path: /tmp/ym-c328-axle-receipt.json