Add selected centre decoder demand floor audit

research/centre-selected-provider-demand-floor/README.md

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+# Exact information floor for the selected gauge44 centre decoder
+
+## Question and result
+
+For one invocation of the currently selected `gauge44` local provider, how many
+independent scalar channels must an exact linear replacement deliver to
+preserve the centre phase's updates to consumer rows 112 through 223?
+
+The answer is exactly eight. The selected provider copies eight distinct source
+rows into private centres, and its 112-by-8 consumer-demand matrix has rational
+rank eight in both forward and backward orientations. Any exact linear
+factorization through `m` scalar channels has rank at most `m`; therefore
+`m >= 8`. The selected provider attains this information bound with eight
+totals. Each total is carried by a rank-8 centre macro, so the selected profile
+spends 64 rank units per invocation.
+
+In matrix form, if a replacement uses an encoder `E` with `m` scalar outputs
+and a linear decoder `F` to preserve this endpoint, then `D = F E`, whence
+`8 = rank(D) <= rank(E) <= m`.
+
+The 64-unit statement is an observed profile and a conditional floor for
+replacements that retain the selected rank-8-per-channel carrier contract. The
+rank computation alone does not prove that every changed decoder graph or
+outside-code factorization must pay 64. The P112 copy-rank theorem has an
+explicit root-code factorization interface; applying it to a changed decoder
+requires proving that decoder meets that interface. This package claims the
+unconditional information floor of eight channels for the stated linear
+contract.
+
+## Contract and source binding
+
+The contract is the `centers` phase in
+`research/gauge44-slots-t16/evidence/local/LOCAL-PROGRAMS.json.gz`, dispatched
+by all calls in the selected global template to provider `gauge44`. The source
+manifest named by `certificates/selected-result.json` hashes both the global
+template and local program. The verifier checks those hashes, checks that the
+inline provider program equals the separately pinned local program, and checks
+each call's provider and orientation hash.
+
+Forward totals use source rows `(92, 57, 81, 224, 11, 240, 9, 256)` and private
+centres `C_0` through `C_7`, mapped by the selected global template to the
+physical private range `[7168, 7176)`. The eight rank-8 centre events have
+frames 413 through 420. Each total contributes to 28 distinct consumer rows with
+coefficient `+1/4` or `-1/4`; the union of the consumer rows is exactly 112
+through 223. The backward gather matrix is entrywise equal to the forward
+fanout matrix and restores the same eight source rows.
+
+An exact nonzero minor uses rows `(112, 117, 118, 120, 113, 116, 115, 123)`;
+its determinant is `-1/16384`, so the matrix has rank eight. Multiplying that
+determinant by `4^8` gives `-4`.
+
+This is source-current work complementary to PR #3120 (head
+`6e36982ccc888bdb4dc15982322d8fe1aed392b4`): that PR computed the same kind of
+demand rank from a frozen archived template. Its archived local program is a
+different input from the local program bound by the current selected source, so
+this verifier re-derives the claim from the current provider rather than
+importing that archive's binding.
+
+## Verification
+
+From the repository root:
+
+~~~sh
+python3 -B research/centre-selected-provider-demand-floor/verify.py
+python3 scripts/research_package.py --package research/centre-selected-provider-demand-floor --check-only
+~~~
+
+The verifier uses only the Python standard library and exact rational
+arithmetic. It checks the selected-record and source-manifest pins, provider
+dispatch, source and restore rows, all 224 fanout/gather terms, the exact rank
+and minor, and two rank-dropping mutations. It does not run the selected cold
+replay or any k-call cost calculation.
+
+## Scope and limitations
+
+- The lower bound is for linear scalar-copy interfaces that preserve this
+  exact 112-row endpoint and allow the eight named source-row values as
+  independent inputs.
+- It proves at least eight independent channels. A 64-unit lower bound for a
+  changed implementation additionally needs a proof that its factors satisfy
+  the fixed rank-8 root-code charge model.
+- No physical cross-call sharing eligibility, restoration bill, hosting,
+  precision, tape cost, supplier admission, or new kappa is established.
+- The selected-source local check records 716 columns; this package does not
+  independently rerun that source check or the full selected replay.
+
+## Open next questions
+
+Can the exact selected 112-by-8 demand be represented by a changed decoder whose
+copy channels fall outside the fixed rank-8 root-code factor model while
+preserving the endpoint and all source/restoration obligations? This decides
+whether the observed 64-unit charge extends beyond the retained carrier
+contract. First derive the full factor interface for one concrete replacement
+and price its exact matrix. The blocker is that no changed decoder is supplied
+by this per-call audit.
+
+## Credit
+
+Selected construction and source line: PR #1094 and the review bound by the
+selected record. Demand-rank predecessor: Aaron Wang's PR #3120, which this
+package rebinds to the current selected provider. The conditional root-code
+cost model is from `research/p112-batch-centre-floor/PROOF.md`; its credit chain
+remains with PR #845, PR #1098, PR #968, and PR #1180. Prepared by OpenAI Codex
+laptop-07 for Cinna Davis; substantial AI assistance, no human or proof-assistant
+review claimed. Apache-2.0.

research/centre-selected-provider-demand-floor/RESULT.json

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+{
+ "centre_path": {
+  "centre_frames_forward": [
+   413,
+   414,
+   415,
+   416,
+   417,
+   418,
+   419,
+   420
+  ],
+  "centre_ranks": [
+   8,
+   8,
+   8,
+   8,
+   8,
+   8,
+   8,
+   8
+  ],
+  "coefficients": [
+   "-1/4",
+   "1/4"
+  ],
+  "consumer_rows": [
+   112,
+   223
+  ],
+  "consumers_per_total": [
+   28,
+   28,
+   28,
+   28,
+   28,
+   28,
+   28,
+   28
+  ],
+  "physical_private_scratch_range": [
+   7168,
+   7176
+  ],
+  "private_scratch": [
+   "C0",
+   "C1",
+   "C2",
+   "C3",
+   "C4",
+   "C5",
+   "C6",
+   "C7"
+  ],
+  "source_rows_forward": [
+   92,
+   57,
+   81,
+   224,
+   11,
+   240,
+   9,
+   256
+  ],
+  "source_rows_restored_backward": [
+   92,
+   57,
+   81,
+   224,
+   11,
+   240,
+   9,
+   256
+  ],
+  "totals_per_invocation": 8
+ },
+ "controls": {
+  "merge_two_demand_columns_rank": 7,
+  "zero_one_demand_column_rank": 7
+ },
+ "decoder": {
+  "calls": 72,
+  "checked_input_columns": 716,
+  "events_per_orientation": {
+   "backward": 46772,
+   "forward": 46772
+  },
+  "global_template_version": "round20-R492-asynchronous-whole-owner-v1",
+  "orientations": {
+   "backward": 32,
+   "forward": 40
+  },
+  "provider_id": "gauge44"
+ },
+ "demand": {
+  "backward_equals_forward": true,
+  "independent_rows": [
+   112,
+   117,
+   118,
+   120,
+   113,
+   116,
+   115,
+   123
+  ],
+  "minor_determinant": "-1/16384",
+  "minor_determinant_times_4_pow_8": -4,
+  "rank_backward": 8,
+  "rank_forward": 8,
+  "shape": [
+   112,
+   8
+  ]
+ },
+ "lower_bound": {
+  "charged_floor_scope": "64 only under the retained rank-8-per-channel carrier restriction; arbitrary changed decoder factors are not covered",
+  "exact_linear_scalar_channels_per_invocation": 8,
+  "selected_rank_8_centre_charge_per_invocation": 64
+ },
+ "scope": "Exact linear-information floor for the selected gauge44 provider's pinned 112-row centre endpoint. No cross-call physical eligibility or universal cost bound for changed decoder graphs.",
+ "source_binding": {
+  "assembly_sha256": "1122cb3a575f8c788345fc1bf4c108ac7c3250fb81a5988671f5eb04b3ab3045",
+  "base_commit": "20ecf2891d80b5acf18d980b2164fb44ea7faa90",
+  "global_template_sha256": "f713f8e66aaeaebb8202fe72bf36c7d23497152497342c27892e0fda3092f95b",
+  "local_programs_sha256": "172dc3d23e437909ddc01d07b12ede735afbb5bb6145f1ddf5c2e03097dfebe2",
+  "selected_kappa": "836330098538459/500000000000000000",
+  "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129",
+  "selected_source_manifest_sha256": "79b3de5db3dbcb9829789ba58e9e45758926031e2a7d80667a08429d369be53b"
+ },
+ "status": "PASS_SELECTED_PROVIDER_CENTRE_DEMAND_RANK"
+}

research/centre-selected-provider-demand-floor/SOURCES.json

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+{
+  "schema_version": 1,
+  "base_commit": "20ecf2891d80b5acf18d980b2164fb44ea7faa90",
+  "files": [
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "input",
+      "git_blob": "b1fea0c94436b236cc2b7d41a7be032811b94c81",
+      "sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "67f085acd86acd7d4e03922d9cf4b26bca66fed5",
+      "sha256": "47b42433f5a85809a3aadd29c2c339da2c6ed728e4f7762df6b88bccb7874cf0"
+    },
+    {
+      "path": "research/community-frontier1094-audit/ASSEMBLY.json",
+      "usage": "input",
+      "git_blob": "5fd676df060f3b450782fdf5ff5f6beb63a5eeb0",
+      "sha256": "1122cb3a575f8c788345fc1bf4c108ac7c3250fb81a5988671f5eb04b3ab3045"
+    },
+    {
+      "path": "research/community-frontier1094-audit/SELECTED-SOURCE.json",
+      "usage": "input",
+      "git_blob": "6a75493790b4eff9c4a98051ef8b01d6aad0d5a8",
+      "sha256": "79b3de5db3dbcb9829789ba58e9e45758926031e2a7d80667a08429d369be53b"
+    },
+    {
+      "path": "research/gauge44-slots-t16/evidence/global/GLOBAL-TEMPLATE.json.gz",
+      "usage": "input",
+      "git_blob": "424c2df489364ea5b29e0df9841e6fe91a517df4",
+      "sha256": "f713f8e66aaeaebb8202fe72bf36c7d23497152497342c27892e0fda3092f95b"
+    },
+    {
+      "path": "research/gauge44-slots-t16/evidence/local/LOCAL-PROGRAMS.json.gz",
+      "usage": "input",
+      "git_blob": "d511f2afa49f9eed010e91eed590a15252506470",
+      "sha256": "172dc3d23e437909ddc01d07b12ede735afbb5bb6145f1ddf5c2e03097dfebe2"
+    }
+  ]
+}

research/centre-selected-provider-demand-floor/TASK.json

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+{
+  "schema_version": 1,
+  "task_id": "centre-path-sharing",
+  "priority_revision": 6,
+  "base_commit": "20ecf2891d80b5acf18d980b2164fb44ea7faa90",
+  "original_card": {
+    "id": "centre-path-sharing",
+    "question": "Can the 64-per-call centre path (eight rank-8 COPY/ERASE totals through the private temporary) be shared across calls or shrunk?",
+    "starting_points": [
+      "docs/research/research-family-status.md",
+      "research/complex-local-word-ceiling/README.md",
+      "research/split-centres-global/proofs/PR386-BIT-GEOMETRY.txt",
+      "certificates/selected-result.json"
+    ],
+    "methods": [
+      "Derive a fully charged favorable relaxation for sharing one centre path across k calls, including restoration, hosting and precision.",
+      "Prove a lower bound on copied information per call for the selected decoder contract."
+    ],
+    "acceptance_gate": "Show the changed centre charge and copy profile per call with every added restoration or hosting cost charged, and its ceiling via ceiling.ceiling(centre=...). A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.",
+    "first_step": {
+      "command": [
+        "python3",
+        "-B",
+        "research/complex-local-word-ceiling/verify.py"
+      ],
+      "expected": "PASS_COMPLEX_LOCAL_WORD_CEILING",
+      "inspect": "Read the selected word's per-call local profile, its packing ceiling and the lever table; run levers.py for the ideal budget of the lever you target.",
+      "scope": "Positive control and planning budget only; this is not a new construction or full cold replay."
+    },
+    "first_experiment": "Write the per-call centre charge and copy children for sharing across k = 2 calls, charge the sharing overhead, and screen it; stop this route if even the ideal sharing gains under 10%. Ideal budgets: free 2.80x, shared by two 1.90x (levers.py).",
+    "bottleneck_link": "The centre path consumes 64 of about 99.6 unpaid coordinates per call, i.e. about 64% of the raw deficit.",
+    "allowed_variations": [
+      "One sharing pattern across a fixed number of calls.",
+      "One reduced copied-total contract for the existing decoder.",
+      "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope."
+    ],
+    "scope_change_triggers": [
+      "Removing copies without a replacement contract for the decoder's copied totals.",
+      "Continuing a partial cost improvement while leaving the same unpriced consumer, restoration or central-readout obligation unresolved; refresh the family expansion decision first. Local product-retiming evidence has a narrow scope and is not a ban on changed graphs or contracts."
+    ],
+    "overlap_terms": [
+      "centre path",
+      "copied totals",
+      "private temporary",
+      "shared centre",
+      "batching"
+    ]
+  },
+  "scope_status": "refined",
+  "actual_scope": "For one invocation of the current selected gauge44 provider, derive the exact linear information rank of the centre phase from its source-bound 112-row consumer endpoint, and state the resulting lower bound on copied scalar channels.",
+  "scope_change_reason": "The assigned complementary scope is method 2 at one explicit decoder contract. I pinned the current selected provider and its input/output map; k-call sharing prices are left to the separately assigned worker.",
+  "bottleneck_link": "The selected local profile pays eight rank-8 centre macros (64 rank units) per invocation. The demand rank decides whether that decoder can use fewer independent copied totals.",
+  "budget_minutes": 60,
+  "stop_rule": "Stop after the selected record, source manifest, provider dispatch and local program are hash-bound and the exact forward/backward demand rank and nonzero minor are reproduced. Do not extend into cross-call pricing or changed decoder graphs.",
+  "outcome": "completed",
+  "evidence": "README.md and RESULT.json; verify.py recomputes the exact current-provider demand rank, source rows, consumer rows and nonzero minor from the two source-manifest-bound files. Direct verification passed on Python 3.14.8 and the package metadata/pin check passed; registered Python 3.12 replay was unavailable on this host.",
+  "author": "OpenAI Codex laptop-07 for Cinna Davis",
+  "ai_assistance": "Substantial OpenAI Codex assistance in source audit, derivation, exact arithmetic, verification and packaging.",
+  "open_questions": [
+    {
+      "question": "Can a changed exact decoder for this 112-by-8 demand use copy factors outside the fixed rank-8 root-code charge model while preserving the endpoint and source/restoration obligations?",
+      "why_it_matters": "The demand-rank result forces eight independent scalar channels, while the selected 64-unit profile uses eight rank-8 carriers. A changed factor class could alter the charged rank without reducing information rank.",
+      "first_step": "Specify one concrete alternative factor interface and derive its complete exact matrix and per-term support charges.",
+      "blocked_by": "No alternative decoder or proof that every admissible replacement falls under the P112 root-code model is supplied by this per-call audit."
+    }
+  ]
+}

research/centre-selected-provider-demand-floor/VERIFY.json

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+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [
+    "certificates/selected-result.json",
+    "research/community-frontier1094-audit/ASSEMBLY.json",
+    "research/community-frontier1094-audit/SELECTED-SOURCE.json",
+    "research/gauge44-slots-t16/evidence/global/GLOBAL-TEMPLATE.json.gz",
+    "research/gauge44-slots-t16/evidence/local/LOCAL-PROGRAMS.json.gz"
+  ],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 120,
+      "checks": "Selected-result/source-manifest binding; current gauge44 dispatch and embedded local-program equality; exact forward/backward demand rank, minor, source restoration, and rank-dropping controls."
+    }
+  ]
+}