Prove the selected P104 all-column caller algebra (no new κ)

research/selected-native-tensor-closure/README.md

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+# Exact native traces and the selected all-column caller
+
+This package proves and independently checks the **algebraic** assertion
+`native_all_columns` for the pinned selected #6030 P104 native layer and its
+assembled caller, at every positive column width and with arbitrary spectator
+factors. It joins every signed native recipe,
+the complete local word, all 18 forward calls and 16 wrappers, and every
+whole-job helper/main/idle adapter. It does **not** implement the selected-rate
+physical dispatcher or discharge the complete five-assumption framework.
+The all-column operator assertion is proved; physical realization and the
+source's ideal owned-reset semantics remain distinct obligations.
+**No new κ.**
+
+The accepted source remains canonical main
+`7c49fe32c55de02c2c873655c804b16e4c3fef0a`, with conditional
+κ = `781451/250000000`. No prior source, selected record, tariff or bill is
+modified. [PROOF.md](PROOF.md) states the exact quantified theorem, proves the
+trace algorithm and tensor interpretation, and gives the complete composition.
+
+## Result and evidence
+
+The new native acceptance mechanism computes the exact closed overlap
+`tr(V*U)` as a constrained quadratic Gauss sum over binary variables. Checked
+unitarity makes the value `2^9` equivalent to full operator equality. The
+checker retains constant phases and Gaussian normalizations; it uses neither
+a Pauli tableau, a distinguished input column, floating point, nor a dense
+512-by-512 operator matrix. Quadratic elimination is polynomial in the finite
+circuit description. This is a certificate-verification bound, not a
+multiplication-runtime improvement.
+
+The caller verification keeps two different types of objects distinct:
+native products are lifted columnwise, while rational coefficients of
+register ADD/COPY/SCALE and signed swaps stay outside the tensor power. A
+native constant phase becomes `i^(p*f)`; a register coefficient remains the
+same coefficient. The proof does not infer an all-width identity by tensoring
+a width-one sum of different native group elements.
+
+| Verified object | Complete coverage |
+|---|---:|
+| Distinct signed native/helper pairs | 2,922 |
+| Distinct MOVE pairs within that union | 2,886 |
+| Intrinsic main adapters | 208 |
+| Complete local main paths | 312 |
+| Distinct complete helper boundary types | 69 |
+| Arbitrary helpers per local call | 562 |
+| Local endpoint coefficients | 799 × 799 |
+| Literal local events | 22,803 |
+| Actual raw contacts | 7,488 |
+| Composed contact/native/contact paths | 5,616 |
+| Complete free-Laurent caller entries | 32 × 32 |
+| Arbitrary main productive fields | 3,328 |
+| Arbitrary helper productive fields | 10,116 |
+| Whole-idle paid fields | 3,120 |
+
+The source-bound reverse-functional Laurent replay checks all 218 physical
+controller events and both literal rational boundary programs. It uses the
+free Laurent ring, with no `Q^4=1` quotient. The geometry check composes the
+actual entry/native/exit maps, matches the selected raw-contact payload hash,
+and explicitly fixes the 120 omitted spectator rows of the 265-row source.
+Each main/idle positive basis is completed on all 145 retained rows. The
+all-width proof then applies to every complete occurrence embedding, including
+the embeddings supplied by #6878.
+
+The exact selected bill is unchanged: **13,444 productive fields, 66,834 paid
+calls, paid rank mass 240,152 and productive rank mass 240,912**. The checker
+reconstructs both complete profiles from the literal source events rather
+than inferring a bound from this positive rank margin. Ordinary adapters,
+source access, staging, physical erasure and restoration still require their
+own implementation and charging theorems.
+
+## What is new, and what is already proved
+
+This is not a new local common-chart lemma or another dense native census.
+The contribution is a different exact native acceptance mechanism together
+with the **complete selected-source join** from those native equalities to
+the assembled all-forward caller, including the exterior-scalar typing and
+whole-job boundaries.
+
+| Predecessor or concurrent work | Already established; relationship here |
+|---|---|
+| #5442, `research/allwidth-caller-certificate/` | Group-algebra and tensor framework for the older #5413 caller. The product-lifting principle is credited. |
+| #5974, `research/p104-allwidth-native-certificate/` | Full exact native verification for #5599 and the factorwise lift. Its native census is not repeated as a claimed new theorem. |
+| #6043, `research/p104-6030-independent-audit/` | Independent dense verification of the current #6030 native inventory. The present trace method shares neither its dense mechanism nor its candidate compiler's tableau/anchor acceptance. |
+| #6635 | Complete selected scalar common-chart census. The present typed induction uses that established mechanism and checks its composition with every MOVE. |
+| #6293 and #6331 | The `i^(p*f)` phase convention and the obstruction to deleting native phases. The current width-two controls explicitly enforce those distinctions. |
+| #6546, `research/selected-absolute-stochastic-caller/` | Concurrent direct stochastic local execution and a fixed-local all-width lift; its stated limitation is identification with complete recursive callers. The present package closes the algebraic assembled-caller join, without importing its unmerged code. |
+| #6878, `research/selected-compiler-occurrence-layout/` | Complete occurrence-specific coordinate embeddings and retained-row geometry. This package supplies their native algebraic endpoint premise; it does not reprice or redevelop the embeddings. |
+
+At the frozen reconnaissance, #6546 was an open contribution at
+`ff038070b8d122a43993f2b2524154323cc6b4d7`, and #6878 was an open contribution
+at `41febf890fbbb852c6059d4c0cc8c593ae9dfa5c`. They are credited comparisons and
+applications, **not runtime or source-import dependencies** of this package.
+The proved tensor/naturality statement quantifies over any complete embedding;
+the exact accepted inputs below all come from the pinned canonical main.
+
+The native/caller identities and raw phase construction in
+`research/p104-productive-controller/` and the independent caller audit remain
+credited source results. Existing physical compact, Gaussian-monomial and old
+controller work #3055, #3087 and #3385 was checked during scope selection and
+was not reimplemented. Its older tariffs do not automatically price the
+current selected dispatcher.
+
+## Reproduction
+
+From the repository root, using only Python's standard library:
+
+```sh
+python3 -I -B research/selected-native-tensor-closure/verify.py
+```
+
+Expected final marker:
+
+```text
+PASS_SELECTED_NATIVE_TENSOR_CLOSURE {"kappa_changed": false, "native_pairs": 2922, "paid_calls": 66834, "productive_fields": 13444, "raw_contacts": 7488, "rejecting_controls": 20}
+```
+
+The registered replay also checks the generic trace engine in normal and
+optimized Python and rebuilds the full native recipe artifact with the
+credited source compiler:
+
+```sh
+python3 -B scripts/research_package.py --package research/selected-native-tensor-closure
+```
+
+`SOURCES.json` records exact Git blob and SHA256 pins. Every live source input
+is declared in `VERIFY.json`. The independent verifier authenticates the
+selected word, result, controller, port data and mathematical source files
+before parsing them; it imports no predecessor verifier or compiler.
+`emit_recipes.py` alone imports the credited compiler to regenerate the
+candidate artifact. Its complete recipe payload must reproduce the already
+registered selected digest
+`e22642923d5437c49e2d1dc79dd6b795503499d6f33615a1df3568f0b96164c1`.
+The independent checker then accepts every complete emitted product by the
+trace method. This producer/acceptor separation is deliberate.
+
+`RESULT.json` is deterministic and records the exact coverage, profile and
+endpoint digests and every rejecting control. `--write` regenerates only this
+new package's receipt. `emit_recipes.py --write` regenerates only this package's
+small compressed candidate artifact; ordinary replay compares its full
+decompressed contents instead.
+
+## Verification and negative controls
+
+The trace engine's independent dense-column oracle uses exact rational
+arithmetic on 120 deterministic random small circuits. Additional checks
+enumerate all 16,933 quadratic forms through four variables with zero constant
+term, 480 affine systems, 480 affine substitutions, nonzero constant phases,
+unitary inverses and a 300-variable symbolic trace. Fixed seeds are `7606030`
+and `7606546`; these are bounded verifier tests, not an open-ended supplier
+search. Ten trace grammar/operator controls reject malformed expected gates,
+wrong phases and invalid gates, including cases that agree on the zero column.
+
+The source package has 20 separate controls. They reject source-byte and
+registered-payload drift; a global `i` invisible to conjugation action; reversed
+native factors; an omitted positive child; confusing a canonical rank-one
+chart with the translation Gaussian on that vector; `i^p` used where `i^(p*f)` is
+required; tensor-powering an exterior minus sign; tensoring a Gaussian sum
+termwise; a wrong whole-helper normalizer; a scalar chart mismatch; reversed
+MOVE orientation; aliased public roles; a missing wrapper translation or swap
+sign; a wrong raw final exponent; a corruption on an arbitrary spectator
+coordinate; and an omitted whole-job final translation. Mathematical fault
+controls call the comparison mechanisms directly, so their rejection is not
+merely an earlier source-hash failure.
+
+Both normal and `-O` execution are required by the registered manifest. The
+package uses explicit checks rather than optimization-disabled assertions.
+The finite tests support the checker implementation; the all-f and arbitrary
+spectator conclusions come from the written theorem, not from sampling
+column widths. This is not a proof-kernel formalization or independent human
+acceptance.
+
+## Open next questions
+
+The structured versions are in [TASK.json](TASK.json).
+
+1. Bind this exact typed algebraic word to the selected-rate physical
+   dispatcher. Start with one full compiled occurrence, preserving the
+   distinction between native column phases and exterior scalar field
+   coefficients, and account for every adapter, complete field, recursive
+   child and return operation. This is blocked by the remaining physical
+   implementation and charging obligations, not by a missing local chart
+   identity.
+2. Compose the resulting implementation with the owned-stream and precision
+   contracts. Start with a complete source-owned call/return that realizes
+   the 29-label local owned bank and separate thin scratch field, without
+   treating the ideal CLEAR in this algebraic proof as a physical erasure
+   algorithm. The required ownership and rounding premises remain explicit.
+
+## Attribution and license
+
+Prepared for **@CubeJerry**, with substantial **OpenAI Codex** assistance in
+research, derivation, implementation and adversarial checks. The lead research
+reviewer checked the Gauss-sum derivation and the complete typed composition;
+that is an AI-assisted mathematical review, not a separate formal proof.
+
+Credit DreamingOfClouds for the selected #6030 change; David Arias for the
+coalesced source word, Cinna Davis for private reuse, the native representations
+and the Laurent controller,
+Gareth Davidson for their composition, and Ali Romman for the P104 caller and
+independent source audits. The native compiler, source constructions and
+proof framework retain their existing contributors' credit. Relevant earlier
+and concurrent mechanisms are identified above rather than claimed anew.
+Apache-2.0, following the repository license. No predecessor source is copied
+or modified; the compressed artifact contains deterministically emitted
+recipe data authenticated against the selected registration.

research/selected-native-tensor-closure/RESULT.json

@@ -0,0 +1,154 @@
+{
+  "all_size_status": "PROOF.md proves the typed algebraic implication for every positive f and arbitrary spectator factors; finite replay is the exact selected-source premise",
+  "base_commit": "7c49fe32c55de02c2c873655c804b16e4c3fef0a",
+  "complete_caller": {
+    "all_1024_laurent_entries_checked": true,
+    "controller_events": 218,
+    "endpoint_sha256": "4ba0b7b54172171102343f81f03f2dac7753ffd184cdffcbe62c8b9d6b1dc0bf",
+    "five_step_forward_wrappers": 16,
+    "forward_local_calls": 18,
+    "literal_boundary_events": 145,
+    "method": "reverse linear-functional substitution; no finite-order quotient of Q",
+    "thin_queries_per_port": 15
+  },
+  "limitations": [
+    "ideal owned reset semantics remain assumed",
+    "physical selected-rate dispatcher not implemented",
+    "compiler, precision_tape and analytic_recovery not discharged",
+    "No new kappa"
+  ],
+  "local_gauge": {
+    "arbitrary_public_columns": 770,
+    "events": 22803,
+    "full_endpoint_coefficients": 638401,
+    "gauge_endpoint_sha256": "3a9a39e842438b4575689b5233c0d9237b4863b71f8f1939c757607fe4d35325",
+    "opcode_counts": {
+      "ADD": 18404,
+      "CLEAR": 31,
+      "COPY": 23,
+      "INIT": 31,
+      "MOVE": 3453,
+      "SCALE": 861
+    },
+    "owned_entrance_columns_erased": 29,
+    "owned_lifetimes": 31,
+    "paid_profile": {
+      "1": 2219,
+      "2": 457,
+      "3": 496,
+      "4": 100,
+      "5": 163,
+      "6": 11,
+      "7": 6,
+      "8": 1
+    },
+    "peak_owned": 13,
+    "rows": 799,
+    "rule": "chart coefficients are formal inverse/forward products; every scalar remains exterior"
+  },
+  "native_trace": {
+    "arbitrary_helpers": 562,
+    "central_squares": 104,
+    "complete_main_paths": 312,
+    "complete_trace_digest": "dcb7308d7925b139d4547247eae4955b58445155bda7ac93d7c3b18d479078a5",
+    "distinct_move_pairs": 2886,
+    "distinct_native_pairs": 2922,
+    "helper_normalized_pairs": 69,
+    "helper_profile": {
+      "1": 14,
+      "2": 8,
+      "3": 4,
+      "4": 107,
+      "5": 14,
+      "6": 2,
+      "7": 9,
+      "8": 19,
+      "9": 385
+    },
+    "main_adapters": 208,
+    "maximum_closed_trace_branches": 18,
+    "method": "exact constrained quadratic Gauss sum; no tableau or distinguished column",
+    "selected_recipe_payload_sha256": "e22642923d5437c49e2d1dc79dd6b795503499d6f33615a1df3568f0b96164c1"
+  },
+  "negative_controls": {
+    "MOVE_reversed_source_and_target": "current native source and ownership at 9896",
+    "aliased_local_public_role": "all productive owners",
+    "caller_exterior_swap_sign_lost": "full free-Laurent reverse output 8",
+    "caller_missing_central_translation": "full free-Laurent reverse output 8",
+    "caller_wrong_raw_diagonal_Q_exponent": "full free-Laurent reverse output 0",
+    "canonical_rank_one_chart_mistaken_for_C_q": "omitted nontrivial intrinsic main adapter: exact unitary overlap trace (256, 0, 0)",
+    "contact_corrupts_arbitrary_spectator_row": "nonidentity spectator action",
+    "exterior_minus_incorrectly_tensor_powered": "exterior sign squared: exact unitary overlap trace (-262144, 0, 0)",
+    "main_whole_job_final_translation_omitted": "omitted X_q final raw endpoint correction",
+    "native_constant_i_not_raised_to_column_width": "wrong i^(p*f): exact unitary overlap trace (0, -262144, 0)",
+    "native_global_i_preserving_conjugation_action": "lost absolute phase: exact unitary overlap trace (0, 512, 0)",
+    "native_left_right_order": "reversed native factors: exact unitary overlap trace (128, 0, 0)",
+    "native_missing_positive_child": "omitted native Gaussian: exact unitary overlap trace (256, -256, 0)",
+    "registered_recipe_payload_drift": "full selected recipe payload hash",
+    "scalar_chart_mismatch": "scalar current chart",
+    "source_drift:research/p104-helper470-twin-rung-removal/WORD.json.gz": "Rejected before parsing or execution",
+    "source_drift:research/p104-productive-controller/caller.py": "Rejected before parsing or execution",
+    "tensor_of_sum_replaced_by_sum_of_tensors": "tensoring a Gaussian expansion termwise: exact unitary overlap trace (2, 0, 0)",
+    "whole_helper_pre_normalizer_not_inverted": "wrong whole-helper entry: exact unitary overlap trace (16, 0, 0)",
+    "zero_column_agrees_but_quadratic_operator_differs": "missing controlled sign: exact unitary overlap trace (2, 0, 0)"
+  },
+  "ownership_and_invoice": {
+    "field_maps_sha256": "0cc409ad6083dedf325df5bd452ed58f84d579f5664e48a519a86ab2e15bdd33",
+    "fresh_helper_inputs": 10116,
+    "limits": "ideal source ownership only; allocation, physical erasure and retained backing remain premises",
+    "local_owned_labels": 29,
+    "main_arbitrary_inputs": 3328,
+    "paid_calls": 66834,
+    "paid_rank_mass": 240152,
+    "productive_inputs": 13444,
+    "separate_thin_owned_label": 13473,
+    "target_rank_mass": 240912
+  },
+  "schema": "selected-native-tensor-closure-result/1",
+  "source_sha256": {
+    "research/p104-caller-independent-audit/capsule/outputs/p104-caller-route-audit-v2-20261025/sources/DATA-PHASES.json": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa",
+    "research/p104-helper470-twin-rung-removal/RESULT.json": "84fcbe2a0b64307b5703c363408042bdd91555b0419509aa50daa43b3b1924ad",
+    "research/p104-helper470-twin-rung-removal/WORD.json.gz": "7834725d9e34ee846a9ccc615221ea81e0201613938afa185d2eda0c9a6c232f",
+    "research/p104-native-channel/vendor/clifford_exact.py": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962",
+    "research/p104-productive-controller/CONTROLLER.json": "a84f6bbd547379597464e56c420cc665f96bc43a9a1351eed4b7cd0fce3cc4b9",
+    "research/p104-productive-controller/caller.py": "300d40043953e4f6aecfde8f2d1004b8ad6dc5a79ec3c7666c9908c2466c91c8",
+    "research/p104-productive-controller/local.py": "878734dfd64c4b9d362d0ae476cc5c2a19fe93e48b7378763b23f3e0dd0a5a71"
+  },
+  "status": "PASS_SELECTED_NATIVE_TENSOR_CLOSURE",
+  "whole_job_algebra": {
+    "complete_idle_endpoints": 3120,
+    "complete_main_endpoints": 3328,
+    "complete_raw_contacts": 7488,
+    "composed_native_paths": 5616,
+    "full_coordinate_bijections": 4888,
+    "idle_boundary_sha256": "3b493ec6281025ba31b1a66b682d33292b58f99c982461f68018f340c8bbb677",
+    "idle_profile": {
+      "16": 416,
+      "24": 416,
+      "32": 416,
+      "40": 416,
+      "48": 416,
+      "56": 416,
+      "64": 416,
+      "72": 208
+    },
+    "limits": "algebraic whole-field bijections; physical scheduling and charged realization remain separate",
+    "main_boundary_sha256": "57d64f0cbbd7430e780837e64f8bd7336df73c88de52adbe91f8204b62770afd",
+    "main_profile": {
+      "17": 416,
+      "25": 416,
+      "33": 416,
+      "41": 416,
+      "49": 416,
+      "57": 416,
+      "65": 416,
+      "73": 208,
+      "145": 208
+    },
+    "omitted_identity_spectator_rows": 120,
+    "retained_source_rows": 145,
+    "source_dimension": 265,
+    "source_route_payload_sha256": "7f4f0ca768ffbc4f93dcff575592c4c67411f46b4289e45b73f715a2ad47b142",
+    "thin_query_boundaries": 104
+  }
+}