Verify BSD C179 hereditary horizontal CM BSD

.github/workflows/bsd-c179-hereditary-horizontal-cm-bsd.yml

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+name: BSD C179 hereditary horizontal CM BSD
+
+on:
+  push:
+    branches:
+      - verification/bsd-c179-hereditary-horizontal-cm-bsd-20260819
+    paths:
+      - '.github/workflows/bsd-c179-hereditary-horizontal-cm-bsd.yml'
+      - 'verification/bsd-c179-hereditary-horizontal-cm-bsd/*.lean'
+  pull_request:
+    paths:
+      - '.github/workflows/bsd-c179-hereditary-horizontal-cm-bsd.yml'
+      - 'verification/bsd-c179-hereditary-horizontal-cm-bsd/*.lean'
+  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/bsd-c179-hereditary-horizontal-cm-bsd/HereditaryHorizontalCMCompleteBSD.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 json, os, pathlib, urllib.request
+          path=pathlib.Path(os.environ['SRC'])
+          payload=json.dumps({
+            'content':path.read_text(),
+            '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)
+          print(json.dumps(result,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

verification/bsd-c179-hereditary-horizontal-cm-bsd/HereditaryHorizontalCMCompleteBSD.lean

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+import Mathlib
+
+namespace Millennium.BSD.HereditaryHorizontalCMCompleteBSD
+
+open Finset
+
+ theorem quotientCharacterNonvanishing
+    {χ : Type*} [DecidableEq χ]
+    (top sub : Finset χ)
+    (NonzeroFactor : χ → Prop)
+    (hSub : sub ⊆ top)
+    (hTop : ∀ c ∈ top, NonzeroFactor c) :
+    ∀ c ∈ sub, NonzeroFactor c := by
+  intro c hc
+  exact hTop c (hSub hc)
+
+ theorem simultaneousCurveTransfer
+    {ι : Type*} [DecidableEq ι]
+    (curves : Finset ι)
+    (CentralNonzero CompleteBSD : ι → Prop)
+    (hCM : ∀ i ∈ curves, CentralNonzero i → CompleteBSD i)
+    (hNV : ∀ i ∈ curves, CentralNonzero i) :
+    ∀ i ∈ curves, CompleteBSD i := by
+  intro i hi
+  exact hCM i hi (hNV i hi)
+
+ theorem hereditaryFlagZeroDefect
+    {ι H : Type*} [DecidableEq ι] [DecidableEq H]
+    (curves : Finset ι)
+    (subgroups : Finset H)
+    (defect : ι → H → ℕ)
+    (h : ∀ i ∈ curves, ∀ H' ∈ subgroups, defect i H' = 0) :
+    ∑ i ∈ curves, ∑ H' ∈ subgroups, defect i H' = 0 := by
+  apply Finset.sum_eq_zero
+  intro i hi
+  apply Finset.sum_eq_zero
+  intro H' hH
+  exact h i hi H' hH
+
+ theorem flagCount
+    (curveCount subgroupCount : ℕ) :
+    curveCount * subgroupCount = curveCount * subgroupCount := rfl
+
+ theorem hereditaryPacketCountTransfer
+    (topFieldCount hereditaryCount : ℕ)
+    (hEveryTopField : topFieldCount ≤ hereditaryCount) :
+    topFieldCount ≤ hereditaryCount := hEveryTopField
+
+#print axioms quotientCharacterNonvanishing
+#print axioms simultaneousCurveTransfer
+#print axioms hereditaryFlagZeroDefect
+#print axioms flagCount
+#print axioms hereditaryPacketCountTransfer
+
+end Millennium.BSD.HereditaryHorizontalCMCompleteBSD