diff --git a/.github/workflows/beal_global_audit.yml b/.github/workflows/beal_global_audit.yml
new file mode 100644
index 0000000..f92bf5d
--- /dev/null
+++ b/.github/workflows/beal_global_audit.yml
@@ -0,0 +1,47 @@
+name: Beal global audit mirror
+
+on:
+  push:
+    branches:
+      - research/beal-signature357-probe
+  workflow_dispatch:
+
+permissions:
+  contents: read
+
+jobs:
+  replay:
+    runs-on: ubuntu-latest
+    timeout-minutes: 20
+    steps:
+      - uses: actions/checkout@v5
+        with:
+          repository: Th0rgal/beal-conjecture-lean
+          ref: 97b776a728b66942912a564d47b09e84078e2b1e
+      - name: Replay corrected global certificates
+        run: |
+          python3 scripts/check_global_beal_prime_exponent_reduction.py --self-test
+          python3 scripts/check_global_beal_prime_exponent_reduction.py
+          python3 scripts/check_global_beal_repeated_exponent_audit.py --self-test
+          python3 scripts/check_global_beal_repeated_exponent_audit.py
+          python3 scripts/check_global_beal_one_four_core.py --self-test
+          python3 scripts/check_global_beal_one_four_core.py
+          python3 scripts/check_global_beal_signature457_power_residue.py --self-test
+          python3 scripts/check_global_beal_signature457_power_residue.py
+
+  lean:
+    runs-on: ubuntu-latest
+    timeout-minutes: 30
+    steps:
+      - uses: actions/checkout@v5
+        with:
+          repository: Th0rgal/beal-conjecture-lean
+          ref: 97b776a728b66942912a564d47b09e84078e2b1e
+      - uses: leanprover/lean-action@v1
+      - name: Compile new global modules
+        run: |
+          lake env lean BealUnified/ExponentReduction.lean
+          lake env lean BealUnified/Research/CyclotomicAudit.lean
+          lake env lean BealUnified/Research/Signature457.lean
+
+# This mirror is intentionally pinned to one research commit.
diff --git a/.github/workflows/beal_signature357_decisive.yml b/.github/workflows/beal_signature357_decisive.yml
new file mode 100644
index 0000000..dcb4e31
--- /dev/null
+++ b/.github/workflows/beal_signature357_decisive.yml
@@ -0,0 +1,58 @@
+name: Beal global canonical audit
+
+on:
+  push:
+    branches:
+      - research/beal-signature357-probe
+  pull_request:
+    paths:
+      - ".github/workflows/beal_signature357_decisive.yml"
+  workflow_dispatch:
+
+permissions:
+  contents: read
+
+concurrency:
+  group: beal-global-canonical-audit-${{ github.ref }}
+  cancel-in-progress: true
+
+jobs:
+  replay:
+    runs-on: ubuntu-latest
+    timeout-minutes: 20
+    steps:
+      - uses: actions/checkout@v5
+        with:
+          repository: Th0rgal/beal-conjecture-lean
+          ref: 97b776a728b66942912a564d47b09e84078e2b1e
+          path: beal
+      - name: Replay corrected global certificates
+        working-directory: beal
+        run: |
+          python3 scripts/check_global_beal_prime_exponent_reduction.py --self-test
+          python3 scripts/check_global_beal_prime_exponent_reduction.py
+          python3 scripts/check_global_beal_repeated_exponent_audit.py --self-test
+          python3 scripts/check_global_beal_repeated_exponent_audit.py
+          python3 scripts/check_global_beal_one_four_core.py --self-test
+          python3 scripts/check_global_beal_one_four_core.py
+          python3 scripts/check_global_beal_signature457_power_residue.py --self-test
+          python3 scripts/check_global_beal_signature457_power_residue.py
+
+  lean:
+    runs-on: ubuntu-latest
+    timeout-minutes: 30
+    steps:
+      - uses: actions/checkout@v5
+        with:
+          repository: Th0rgal/beal-conjecture-lean
+          ref: 97b776a728b66942912a564d47b09e84078e2b1e
+          path: beal
+      - uses: leanprover/lean-action@v1
+        with:
+          lake-package-directory: beal
+      - name: Compile global research modules
+        working-directory: beal
+        run: |
+          lake env lean BealUnified/ExponentReduction.lean
+          lake env lean BealUnified/Research/CyclotomicAudit.lean
+          lake env lean BealUnified/Research/Signature457.lean
diff --git a/.github/workflows/beal_signature357_mod5_137781_prime13.yml b/.github/workflows/beal_signature357_mod5_137781_prime13.yml
new file mode 100644
index 0000000..49360ba
--- /dev/null
+++ b/.github/workflows/beal_signature357_mod5_137781_prime13.yml
@@ -0,0 +1,36 @@
+name: Beal signature 357 level 137781 prime 13 filter
+
+on:
+  push:
+    branches:
+      - research/beal-signature357-probe
+    paths:
+      - ".github/workflows/beal_signature357_mod5_137781_prime13.yml"
+  workflow_dispatch:
+
+permissions:
+  contents: read
+
+concurrency:
+  group: beal-signature357-mod5-137781-prime13
+  cancel-in-progress: false
+
+jobs:
+  prime13:
+    runs-on: ubuntu-latest
+    timeout-minutes: 20
+    steps:
+      - uses: actions/checkout@v5
+        with:
+          repository: Th0rgal/beal-conjecture-lean
+          ref: 76cec47d35dfc38bda15b2370844bc3534af8a13
+          path: beal
+      - name: Apply the complete prime-13 local union to both parity spaces
+        run: >-
+          python3 beal/scripts/run_signature_357_magma_mod5_137781_prime13_parity.py
+          > mod5-137781-prime13-parity.json
+      - uses: actions/upload-artifact@v4
+        with:
+          name: signature357-mod5-137781-prime13-parity
+          path: mod5-137781-prime13-parity.json
+          if-no-files-found: error
diff --git a/.github/workflows/beal_signature357_mod5_19683_raw.yml b/.github/workflows/beal_signature357_mod5_19683_raw.yml
new file mode 100644
index 0000000..e2504b9
--- /dev/null
+++ b/.github/workflows/beal_signature357_mod5_19683_raw.yml
@@ -0,0 +1,36 @@
+name: Beal signature 357 level 19683 raw Brandt filter
+
+on:
+  push:
+    branches:
+      - research/beal-signature357-probe
+    paths:
+      - ".github/workflows/beal_signature357_mod5_19683_raw.yml"
+  workflow_dispatch:
+
+permissions:
+  contents: read
+
+concurrency:
+  group: beal-signature357-mod5-19683-raw
+  cancel-in-progress: false
+
+jobs:
+  raw:
+    runs-on: ubuntu-latest
+    timeout-minutes: 20
+    steps:
+      - uses: actions/checkout@v5
+        with:
+          repository: Th0rgal/beal-conjecture-lean
+          ref: 72b19b2e27141c2cfe94bf2727a8c18a0392ea3c
+          path: beal
+      - name: Apply parity and removed-prime filters on the raw Brandt module
+        run: >-
+          python3 beal/scripts/run_signature_357_magma_mod5_19683_raw.py
+          > mod5-19683-raw.json
+      - uses: actions/upload-artifact@v4
+        with:
+          name: signature357-mod5-19683-raw
+          path: mod5-19683-raw.json
+          if-no-files-found: error
diff --git a/.github/workflows/beal_signature357_raw_restriction_probe.yml b/.github/workflows/beal_signature357_raw_restriction_probe.yml
new file mode 100644
index 0000000..8bf0bd4
--- /dev/null
+++ b/.github/workflows/beal_signature357_raw_restriction_probe.yml
@@ -0,0 +1,36 @@
+name: Beal signature 357 raw Hecke restriction probe
+
+on:
+  push:
+    branches:
+      - research/beal-signature357-probe
+    paths:
+      - ".github/workflows/beal_signature357_raw_restriction_probe.yml"
+  workflow_dispatch:
+
+permissions:
+  contents: read
+
+concurrency:
+  group: beal-signature357-raw-restriction
+  cancel-in-progress: false
+
+jobs:
+  probe:
+    runs-on: ubuntu-latest
+    timeout-minutes: 10
+    steps:
+      - uses: actions/checkout@v5
+        with:
+          repository: Th0rgal/beal-conjecture-lean
+          ref: 767d4aadc25eac4dd4493c53c1accd30f8e7503e
+          path: beal
+      - name: Compare raw and ordinary Hecke restrictions
+        run: >-
+          python3 beal/scripts/run_signature_357_magma_hecke_raw_restriction_probe.py
+          > magma-hecke-raw-restriction.json
+      - uses: actions/upload-artifact@v4
+        with:
+          name: signature357-magma-hecke-raw-restriction
+          path: magma-hecke-raw-restriction.json
+          if-no-files-found: error