Lemma G of #484: clean proof and Lean 4 formalisation of its core

.gitattributes

@@ -18,3 +18,7 @@ research/coordinated-frames-and-entrance-banks/** -text -whitespace
 # Frozen PR210 package and round-nine evidence retain their audited bytes.
 research/five-stage-source527-banks/** -text -whitespace
 research/community-round9-audit/** -text -whitespace
+
+research/e8-early-reset-reuse/** -text
+
+research/idle-axis-hosting/** -text -whitespace

.github/workflows/e8-complex-gauge-kernel.yml

@@ -0,0 +1,41 @@
+name: Verify complex gauge-kernel supplier
+
+on:
+  push:
+    paths:
+      - 'research/e8-complex-gauge-kernel/**'
+      - 'research/idle-axis-hosting/**'
+      - 'research/split-centres-global/**'
+      - '.github/workflows/e8-complex-gauge-kernel.yml'
+  pull_request:
+    paths:
+      - 'research/e8-complex-gauge-kernel/**'
+      - 'research/idle-axis-hosting/**'
+      - 'research/split-centres-global/**'
+      - '.github/workflows/e8-complex-gauge-kernel.yml'
+  workflow_dispatch:
+
+permissions:
+  contents: read
+
+jobs:
+  verify:
+    runs-on: ubuntu-24.04
+    timeout-minutes: 120
+    strategy:
+      fail-fast: false
+      matrix:
+        python-version: ['3.11', '3.14']
+    steps:
+      - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1 # v7
+        with:
+          persist-credentials: false
+      - uses: actions/setup-python@5fda3b95a4ea91299a34e894583c3862153e4b97 # v7
+        with:
+          python-version: ${{ matrix.python-version }}
+      - name: Install numpy and scipy (Lemma G stage, --discover-check)
+        run: python3 -m pip install numpy scipy
+      - name: Replay PR442 parent, build the gauge-kernel words, check Lemma G, rediscover hosting, assemble
+        run: python3 -B research/e8-complex-gauge-kernel/verify.py "$RUNNER_TEMP/e8-complex-gauge-kernel" --all --discover-check
+      - name: Require committed files to remain unchanged
+        run: git diff --exit-code

.github/workflows/early-reset-reuse.yml

@@ -0,0 +1,20 @@
+name: Verify early reset and kernel composition
+on: [push, pull_request]
+jobs:
+  verify:
+    runs-on: ubuntu-latest
+    strategy:
+      fail-fast: false
+      matrix:
+        python: ['3.11', '3.14']
+    steps:
+      - uses: actions/checkout@v4
+      - uses: actions/setup-python@v5
+        with:
+          python-version: ${{ matrix.python }}
+      - run: python -B research/e8-early-reset-kernel/verify.py "$RUNNER_TEMP/early-reset-reuse"
+      - uses: actions/upload-artifact@v4
+        if: always()
+        with:
+          name: early-reset-reuse-${{ matrix.python }}
+          path: ${{ runner.temp }}/early-reset-reuse

.github/workflows/idle-axis-hosting.yml

@@ -0,0 +1,41 @@
+name: Verify idle-axis hosting composition
+
+on:
+  push:
+    paths:
+      - 'research/idle-axis-hosting/**'
+      - 'research/e8-early-reset-kernel/**'
+      - 'research/e8-early-reset-reuse/**'
+      - 'research/split-centres-global/**'
+      - '.github/workflows/idle-axis-hosting.yml'
+  pull_request:
+    paths:
+      - 'research/idle-axis-hosting/**'
+      - 'research/e8-early-reset-kernel/**'
+      - 'research/e8-early-reset-reuse/**'
+      - 'research/split-centres-global/**'
+      - '.github/workflows/idle-axis-hosting.yml'
+  workflow_dispatch:
+
+permissions:
+  contents: read
+
+jobs:
+  verify:
+    runs-on: ubuntu-24.04
+    timeout-minutes: 60
+    strategy:
+      fail-fast: false
+      matrix:
+        python-version: ['3.11', '3.14']
+    steps:
+      - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1 # v7
+        with:
+          persist-credentials: false
+      - uses: actions/setup-python@5fda3b95a4ea91299a34e894583c3862153e4b97 # v7
+        with:
+          python-version: ${{ matrix.python-version }}
+      - name: Replay PR434 from scratch, host helper residuals on idle coordinates, audit and assemble
+        run: python3 -B research/idle-axis-hosting/verify.py "$RUNNER_TEMP/idle-axis-hosting"
+      - name: Require committed files to remain unchanged
+        run: git diff --exit-code

.github/workflows/split-centres-global.yml

@@ -0,0 +1,23 @@
+name: Split-centres global kappa
+on:
+  pull_request:
+    paths:
+      - 'research/split-centres-global/**'
+      - '.github/workflows/split-centres-global.yml'
+  push:
+    paths:
+      - 'research/split-centres-global/**'
+      - '.github/workflows/split-centres-global.yml'
+  workflow_dispatch:
+jobs:
+  verify:
+    runs-on: ubuntu-latest
+    strategy:
+      matrix:
+        python: ['3.11', '3.14']
+    steps:
+      - uses: actions/checkout@v4
+      - uses: actions/setup-python@v5
+        with:
+          python-version: ${{ matrix.python }}
+      - run: python -B research/split-centres-global/verify.py "$RUNNER_TEMP/split-centres-check"