Native Clifford realization of the P104 low-rank channel (no new kappa)

.github/workflows/p104-native-channel.yml

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+name: P104 exact native low-rank channel
+
+on:
+  pull_request:
+    paths:
+      - research/p104-native-channel/**
+      - .github/workflows/p104-native-channel.yml
+  push:
+    branches:
+      - codex/p104-native-channel-20261014
+    paths:
+      - research/p104-native-channel/**
+      - .github/workflows/p104-native-channel.yml
+  workflow_dispatch:
+
+permissions:
+  contents: read
+
+jobs:
+  verify:
+    runs-on: ubuntu-latest
+    timeout-minutes: 8
+    strategy:
+      fail-fast: false
+      matrix:
+        python: ['3.11', '3.12', '3.14']
+    steps:
+      - uses: actions/checkout@v4
+        with:
+          fetch-depth: 0
+      - uses: actions/setup-python@v5
+        with:
+          python-version: ${{ matrix.python }}
+      - name: Validate registered package metadata
+        run: python scripts/research_package.py --package research/p104-native-channel --check-only
+      - name: Independent native replay and complete regeneration
+        run: python -I -O -B research/p104-native-channel/verify.py --regenerate --out "$RUNNER_TEMP/native-channel.json"
+      - uses: actions/upload-artifact@v4
+        with:
+          name: p104-native-channel-${{ matrix.python }}
+          path: ${{ runner.temp }}/native-channel.json
+          if-no-files-found: error

research/p104-native-channel/EXPECTED.json

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+{
+  "all_physical_pairings": 14400,
+  "all_private_copy_gaussian_columns": 4096,
+  "controls": {
+    "global_phase": true,
+    "missing_final_query_cleanup": true,
+    "missing_initial_query_compensation": true,
+    "missing_transport": true,
+    "physical_label": true
+  },
+  "formal_boundary_columns": 280,
+  "intrinsic_endpoint_adapters": 208,
+  "paid_profile": {
+    "1": 1074,
+    "2": 58,
+    "3": 86,
+    "4": 104,
+    "5": 48,
+    "6": 24,
+    "7": 8,
+    "8": 8
+  },
+  "rank_mass": 2368,
+  "recipes_raw_sha256": "0aa152945ffe3797e8295cd17d4ec6646ba24a93372ec35b16c0b164d9858529",
+  "scalar_events": {
+    "add": 2624,
+    "copy": 8,
+    "erase": 8,
+    "zero": 8
+  },
+  "scope": "Concrete finite Clifford primitives plus a complete framed induction over all 280 arbitrary channel inputs, source gathering and 72 dirty helper restorations. No I-G/2 side correction, global helper assignment, precision, all-size admission or new kappa.",
+  "source_witness_sha256": "0f541bef7f19fdeffd67157684e9f03d785f42c89973632f508fc1a0452b580e",
+  "status": "PASS_CONCRETE_NATIVE_P104_LOW_RANK_CHANNEL",
+  "transports": 740
+}

research/p104-native-channel/PROOF.md

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+# Finite native realization and its boundary
+
+## 1. Physical labels
+
+Reconstruct the 120 root lines from doubled integer E8 coordinates. Write
+`B[i,j] = (<r_i,r_j>+1) mod 2`. Its rank is nine. Select nine independent
+principal coordinates as recorded in `label_isometry`. The compressed labels
+`l_i` do **not** use the ordinary dot product: their pairing matrix is `J`,
+the inverse of the recorded nonsingular compressed Gram matrix.
+
+Find a `J`-orthonormal basis `v_0,...,v_8` and set
+`q(l)_a = l^t J v_a`. The independent checker reconstructs the roots and Gram
+matrix without producer imports, checks the inverse and orthonormality, and
+verifies every one of the 120^2 identities
+`q(l_i) dot q(l_j) = B[i,j]`.
+The map is a linear isometry on the whole nine-dimensional binary space, so
+it applies to every intermediate frame, including labels outside the 120 roots.
+Each root label is odd because `B[i,i]=1`.
+
+This is a concrete finite choice of physical labels. It is not an all-size
+admission proof for an extended label alphabet.
+
+## 2. Complete primitive identities
+
+Use the retained canonical chart `Gamma_W` for a binary frame `W`. A literal
+transport from `A` to `B` is `Gamma_B Gamma_A^-1`. Every transport is nested.
+The exact compiler emits a Gaussian monomial, one positive child of rank
+`|dim B-dim A|`, and another Gaussian monomial. No rank is inferred merely
+from scalar event counts. There are 740 distinct recipes and 1410 paid uses;
+the checker binds every use to its literal source-witness event and rank.
+
+The independent interpreter imports no Clifford compiler. It compares signed
+Pauli conjugations and an exact Gaussian state column. Equal signed Pauli
+actions determine a Clifford up to scalar phase; equality on the nonzero state
+column fixes that phase. Thus this checks the complete operator, not only its
+unsigned symplectic matrix. In addition, all 512 Gaussian columns of each of
+the eight rank-seven private drops are compared directly: 4096 columns total.
+
+Let `C_q = ((1+i)I+(1-i)X_q)/2` and `F9 = product_a C_ea`.
+For each source root the intrinsic input chart is `C_q`; its recorded adapter
+is `Gamma_<q> C_q^-1`. For each target the intrinsic output chart is
+`F9 C_q^-1`; its adapter is `F9 C_q^-1 Gamma_(q-perp)^-1`.
+All 208 operators independently check as rank-zero Gaussian monomials,
+including their phases. The final source and dirty-helper full charts are
+already `F9`. Monomial endpoints add no positive child to this finite invoice.
+
+## 3. Full channel induction
+
+For each live register maintain a rational row `a_r` over the 280 independent
+logical inputs. Its physical value is `Gamma_(W_r) a_r z`.
+The entry adapters establish this invariant for the 104 intrinsic source
+inputs. All other inputs start in the zero frame.
+
+- A verified native transport changes only `W_r`, retaining `a_r`.
+- A literal scalar addition is allowed only in a common physical chart; it
+  changes `a_r` by the stated exact rational row addition.
+- Owned private initialization creates the zero row, copying requires that
+  zero row and the same chart, and discard requires the prescribed owned
+  private register and chart. These are the inherited private-copy semantics,
+  not a claim that a live copy was reversibly uncomputed to zero.
+
+Inducting through every event proves the complete physical composition. The
+checker reconstructs the expected ordinary Gram matrix directly from root
+coordinates. At the end each source and each of the 72 dirty helper rows is
+its original logical input; each target row is
+`y_t + sum_s <r_t,r_s> x_s/2`.
+Every endpoint frame also matches. Applying the target exit adapters gives
+the stated intrinsic output charts. This covers arbitrary address functions,
+not only scalar samples: the rows are identities of operators under the
+verified common-chart invariant.
+
+The source witness is hash-pinned to PR1972. None of its gather, dirty
+compensation, delivery or query-cleanup algorithms is newly claimed here.
+The new step proves that its abstract chart cancellations have this particular
+exact native realization.
+
+## 4. Accounting and controls
+
+The independent occurrence recount gives
+`{1:1074,2:58,3:86,4:104,5:48,6:24,7:8,8:8}`.
+Rank mass is `2368`; the monotone boundary coverage is
+`104*8 + 104*8 + 72*9 = 2312`, leaving eight rank-seven private descents.
+There are 2624 scalar additions and eight each of private initialization,
+copy and discard, for 4058 total events. No additional rank-zero endpoint
+child is inserted.
+
+Five actual faults reject: change a native recipe's global phase; remove a
+transport recipe; corrupt a physical root image; set the first initial-query
+compensation coefficient to zero; set the last query-cleanup coefficient to
+zero. The last two preserve every transport index and are rejected by the
+complete endpoint induction, not merely by an event-index mismatch.
+
+## 5. Unresolved supplier obligations
+
+This channel implements `G/2`, not `I`. A compatible `I-G/2` correction must
+be integrated and priced. The 72 dirty width-nine roles are a local inventory,
+not a chronological global owner map. The finite native identities do not
+establish recursive precision, arbitrary-size lifting, all global residual
+children or an improved recursive moment. No new kappa follows from this
+certificate alone.

research/p104-native-channel/README.md

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+# Native P104 low-rank channel
+
+Concrete finite Clifford recipes for the complete low-rank channel in
+[Rohan Arun's PR1972](https://github.com/CrocSwap/integer-mult-bounds/pull/1972),
+head `fd82d172f46933fd253c2c6de4bd5eaff5429cfd`. Its scalar/frame construction
+is retained, not claimed new. This package replaces its conditional free-chart
+realization with exact Gaussian-dyadic primitive recipes and intrinsic data
+endpoint adapters.
+
+**No complete P104 supplier or new kappa.** The `I-G/2` side correction,
+chronological global hosting, precision and all-size admission remain open.
+The selected frontier is unchanged.
+
+## Result
+
+For the frozen 104 root ports, source logical values `x`, target values `y`
+and 72 independent arbitrary dirty helpers, the channel implements
+`y <- y + (G/2)x`, with the prescribed source/target transports. All 72 helper
+logical values are restored at the full frame. A separate owned private copy
+has eight explicit allocate/copy/descend/discard lifetimes under the inherited
+private-copy contract; it is not one of the 72 dirty inputs.
+
+[EXPECTED.json](EXPECTED.json) records:
+
+- 740 distinct native transport recipes covering all 1410 paid occurrences;
+- 208 monomial data endpoint adapters: 104 source entries and 104 target exits;
+- all 280 arbitrary register input columns in a complete framed induction;
+- 14,400 physical root-pairing checks and 4096 exact Gaussian private-drop columns;
+- five rejecting controls, including global phase and missing query compensation/cleanup.
+
+The exact profile remains
+`1074 H1 + 58 H2 + 86 H3 + 104 H4 + 48 H5 + 24 H6 + 8 H7 + 8 H8`.
+Its rank mass is **2368 = 2312 boundary coverage + COPY56**. This is the same
+local boundary invoice as PR1972, not a globally hosted recursive price.
+
+The compressed root labels require a nontrivial Gram isometry before using
+ordinary physical binary dot products. [PROOF.md](PROOF.md) gives that binding,
+the native operator check and the full-word induction.
+
+## Reproduce
+
+Standard-library Python. Default replay is read-only, needs no network or Git,
+and imports neither the channel producer nor the Clifford compiler:
+
+```sh
+python3 -I -O -B research/p104-native-channel/verify.py
+```
+
+Also rebuild every recipe in temporary storage and compare the complete
+decompressed payload:
+
+```sh
+python3 -I -O -B research/p104-native-channel/verify.py --regenerate
+```
+
+The registered hook runs both checks with a 300-second limit:
+
+```sh
+python3 scripts/research_package.py --package research/p104-native-channel --check-only
+python3 scripts/research_package.py --package research/p104-native-channel
+```
+
+The generic metadata check needs Git provenance. The direct command also works
+from a read-only source export. `--out PATH` writes a receipt exclusively to a
+new caller-selected file. Source hashes and exact origins are in
+[SOURCES.json](SOURCES.json); [TASK.json](TASK.json) records the changed audit scope.
+Compression bytes are not used to compare regenerated mathematics.
+
+## Open next questions
+
+Integrate a fully charged `I-G/2` side word while the required source/target
+frames remain available. Appending it after source completion is not justified.
+Then assign actual chronological owners to the completed word, count all idle
+and residual children, and compare the exact recursive moment. Those steps,
+plus precision and all-size lifting, are required before a supplier or kappa
+claim. Concrete first steps and blockers are in `TASK.json`.
+
+## Credit
+
+Rohan Arun / PR1972 supplies the complete scalar/frame channel; Adam Gall /
+PR1940 supplies the schedule. The P104 fixture and decoder derive from Josie
+Elliston / PR1071, with Ali Romman / PR1125 and the PR968/717/446/595/620 lineage.
+The exact compiler is retained through icekylinx's frame-sa504 package; the
+independent Gaussian interpreter comes from Ali Romman's PR1862, also retained
+in PR1931. Exact predecessor notices are under `notices/`.
+
+Native lowering, the independent physical binding and framed induction were
+prepared for Chafik Boukhalfa with substantial OpenAI Codex assistance.
+Apache-2.0. No independent human review, proof assistant or literature-priority
+guarantee is claimed. The fresh overlap screen covered 470 open PRs and 614
+discussions; its limits are recorded in `SOURCES.json`.

research/p104-native-channel/SOURCES.json

@@ -0,0 +1,87 @@
+{
+  "schema_version": 1,
+  "base_commit": "25c80aa5345afa3867ff4bc81108a8e182669abd",
+  "files": [
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "ae6a99f28aa468649eb66a361e764d769363bf11",
+      "sha256": "10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "06c96f5579bb67ed1b86d334e78fbed7da6945f1",
+      "sha256": "6686ad58f1fbdbc87134a78901b60fd53a20d3984355e91defbbebc9e9fa8075"
+    }
+  ],
+  "vendored_inputs": [
+    {
+      "path": "inputs/LOWRANK-WITNESS.json",
+      "sha256": "0f541bef7f19fdeffd67157684e9f03d785f42c89973632f508fc1a0452b580e",
+      "head": "fd82d172f46933fd253c2c6de4bd5eaff5429cfd",
+      "upstream_path": "research/p104-restored-dirty-delivery/LOWRANK-WITNESS.json",
+      "role": "Rohan Arun / PR1972: complete frame-model low-rank channel"
+    },
+    {
+      "path": "inputs/LOWRANK-RESULT.json",
+      "sha256": "7143ec7780f6f38a8c294df8009c3621936b281d05ae79946ce22f581b73d1b1",
+      "head": "fd82d172f46933fd253c2c6de4bd5eaff5429cfd",
+      "upstream_path": "research/p104-restored-dirty-delivery/LOWRANK-RESULT.json",
+      "role": "PR1972 exact invoice; independently recounted"
+    },
+    {
+      "path": "inputs/P104-FIXTURE.json",
+      "sha256": "516c06f6ec3cb84be588c546108de897650288576dd5fbf5fe44b9c5546ad8a4",
+      "head": "fd82d172f46933fd253c2c6de4bd5eaff5429cfd",
+      "upstream_path": "research/p104-restored-dirty-delivery/source/research/biframe-decoder-ladder/RESULTS.json",
+      "role": "Josie Elliston / PR1071 fixture through PR1940 and PR1972"
+    },
+    {
+      "path": "vendor/clifford_exact.py",
+      "sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962",
+      "head": "25c80aa5345afa3867ff4bc81108a8e182669abd",
+      "upstream_path": "research/frame-sa504/vendor/clifford/clifford_exact.py",
+      "role": "Exact compiler through icekylinx PR531; PR523/514/507/425/433 ancestry"
+    },
+    {
+      "path": "vendor/native_verify.py",
+      "sha256": "3049471905b47b385c88378a1a3be7a18b8858aadd035b8a6da2f4a03b470f38",
+      "head": "bb29ea73ad9be9a0c3d53cdcb1d22b2ee9ffe42f",
+      "upstream_path": "research/native-source-codes/native_verify.py",
+      "role": "PR1862 independent exact Gaussian interpreter, also retained through PR1931"
+    }
+  ],
+  "predecessors": [
+    {
+      "pr": 1972,
+      "head": "fd82d172f46933fd253c2c6de4bd5eaff5429cfd",
+      "role": "Entire scalar/frame low-rank construction and dirty-helper cancellation; not invented here"
+    },
+    {
+      "pr": 1940,
+      "head": "a9b7dfe2809092a9a4c90784d12bb60061e995e8",
+      "role": "Adam Gall: 32-chain target-order schedule"
+    },
+    {
+      "pr": 1931,
+      "head": "7c9b37812b6803fe64bf4427dee7ab82c0155513",
+      "role": "Retained exact Gaussian interpreter distribution; not the reflection construction"
+    }
+  ],
+  "disclosure": "Native lowering, independent physical binding and framed induction prepared for Chafik Boukhalfa with substantial OpenAI Codex assistance. No independent human review or formal proof assistant.",
+  "overlap": {
+    "checked_utc": "2026-10-14T16:12:30Z",
+    "open_prs": 470,
+    "discussions": 614,
+    "pagination_complete": true,
+    "terms": [
+      "P104",
+      "Clifford",
+      "dirty-restored"
+    ],
+    "closest_predecessor": 1972,
+    "difference": "Replace free-chart conditional replay by concrete Gaussian-dyadic primitive recipes and intrinsic endpoint adapters. No scalar construction or kappa improvement claimed.",
+    "limits": "Open PR bodies, discussion bodies/comments and local metadata; no complete code or literature novelty search."
+  }
+}

research/p104-native-channel/SUMMARY.json

@@ -0,0 +1,23 @@
+{
+  "status": "COMPILED_EXACT_P104_LOW_RANK_CHANNEL",
+  "source_pr": 1972,
+  "source_head": "fd82d172f46933fd253c2c6de4bd5eaff5429cfd",
+  "upstream_schedule_pr": 1940,
+  "upstream_schedule_head": "a9b7dfe2809092a9a4c90784d12bb60061e995e8",
+  "source_witness_sha256": "0f541bef7f19fdeffd67157684e9f03d785f42c89973632f508fc1a0452b580e",
+  "source_compiler_sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962",
+  "source_native_checker_sha256": "3049471905b47b385c88378a1a3be7a18b8858aadd035b8a6da2f4a03b470f38",
+  "paid_profile": {
+    "3": 86,
+    "1": 1074,
+    "4": 104,
+    "8": 8,
+    "2": 58,
+    "5": 48,
+    "6": 24,
+    "7": 8
+  },
+  "rank_mass": 2368,
+  "private_drop_basis_columns": 4096,
+  "scope": "Concrete finite Clifford transport and endpoint adapters for the complete low-rank G/2 channel, including gathering and all 72 dirty helper restorations. Not I-G/2 side correction, chronological global hosting, all-size compilation, precision or a new supplier/kappa."
+}