Rule out fixed rank-one active repair with a 101-channel bound

research/active-rank1-controller/README.md

@@ -0,0 +1,90 @@
+# Fixed rank-one channels cannot cheaply repair the retained modes
+
+This source-bound necessary-quotient result restricts the rank-one-only part of
+[Ali Romman's PR5745](https://github.com/CrocSwap/integer-mult-bounds/pull/5745)
+open question about nine or more jointly noisy channels. It builds on
+[flyingviper's PR5720](https://github.com/CrocSwap/integer-mult-bounds/pull/5720).
+No new multiplication bound or physical construction is claimed.
+
+## Contract
+
+Keep the frozen F9-SOURCE-DAG-ALL8 backward word and omit its unimplemented
+physical_add tail. Each channel carries a fixed scalar combination of the eight
+original captured modes, prepared in one fixed rank-one chart. It may scatter
+at any number of chronological contacts in that chart. Arbitrarily many
+channels and joint cancellation of their nuisance outputs are allowed. Each
+channel must pay its preparation; gathering, storage and ordinary scatter costs
+are optimistically ignored. Ground-helper cleanup is granted. Y must return
+correctly through the stated controls: extra delivery to its final charts is
+not granted for free.
+
+Changing the native word, recomputing a payload from changed live data,
+inter-chart transport or reframing, and extra paid cleanup are outside this
+contract. Native address operators use the retained common-fixed-vector
+specialization. A negative necessary test is not a general feedback theorem.
+
+## Certificate and proof
+
+The retained endpoint is X-CY, Y, H, with C=I-R^T R/4. For every control form
+Z=deltaX+C deltaY. If all Y outputs are restored, the desired X correction must
+be supplied by Z. This allows cancellations between different channels rather
+than requiring each channel to be clean independently.
+
+The exact census covers every response-changing interval in each actual
+rank-one chart. For each chart, retain the union of possible nonzero Z output
+coordinates. Assign nonnegative weights to required output coordinates such
+that every chart's union has total weight at most one. Any successful set of
+charts must cover every required coordinate, so its size is at least the total
+weight. This argument permits arbitrary rational coefficients and cancellation;
+it is not a bounded coefficient search.
+
+The retained certificate establishes a weight of 50 for mode5. For the full
+eight-mode correction, all 112 X rows are required. The only chart reaching
+multiple Z coordinates reaches twelve; give those coordinates weight 1/12 and
+the other hundred weight one. Every chart has load at most one, giving a bound
+of 101 distinct fixed rank-one charts and hence at least 101 channels.
+For the recursive power tariff H_r=r^q H_1, 0<q<=1, the removed allowance
+8H_8 is at most 64H_1. Thus this rank-one-only family cannot repay the removed
+centers. This does not decide mixed-rank or changed-feedback constructions.
+
+`rank1-controller.json` retains the exact chart supports, weights, source pins,
+coverage counts and rejection controls. `rank1_controller.py` regenerates them
+with rational arithmetic. [Y-CLEANUP.md](Y-CLEANUP.md) explains why treating
+final Y cleanup as a free ground-frame ADD is invalid: its affected fields
+finish in 56 distinct rank-eight charts. The rational 1/13 correction also
+needs an actual arithmetic/precision contract.
+
+## Reproduce
+
+Python 3.12 standard library only, from the repository root:
+
+```sh
+python3 -B scripts/research_package.py --package research/active-rank1-controller
+python3 -B scripts/check_research_commit.py --package research/active-rank1-controller --check-source-history
+```
+
+The registered normal and optimized commands authenticate the unchanged source
+archive, read two data members into a temporary directory, and compare complete
+semantic receipts. No archived Python code is imported. Direct exported replay
+uses `python3 -B research/active-rank1-controller/verify.py`; inputs remain
+read-only and no Git or network access is needed.
+
+## Open next questions
+
+See TASK.json for concrete first steps: test a mixed-rank noisy-channel family,
+or change one source dependency/address map and charge its complete restoration.
+The higher-rank and general feedback questions in PR5745 remain open.
+
+## Provenance and credit
+
+Prepared on canonical main de5ec2e7a6074068452f45b1a191b5c72832df4a, priority
+revision 8. SOURCE pins preserve the current task card and the two predecessor
+proofs. The selected frontier is unchanged. Ali Romman's PR5745 provides the
+canonical channel contract, clean-channel tariff and at-most-eight noisy-channel
+argument; this package adds a resource bound for arbitrarily many rank-one-only
+channels. The frozen source retains Cao Yifan, Cinna Davis, Dugongue and the
+native/mode/controller authors and notices.
+
+Prepared for flyingviper with substantial OpenAI Codex assistance and separate
+agent checks. This is not independent human peer review or formal verification
+of the multiplication theorem. New work is Apache-2.0.

research/active-rank1-controller/SOURCES.json

@@ -0,0 +1,36 @@
+{
+  "schema_version": 1,
+  "base_commit": "de5ec2e7a6074068452f45b1a191b5c72832df4a",
+  "files": [
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "581f8d87008354eb5b869f7ed9de1317ad837ce8",
+      "sha256": "2a0220e866417774606e0f991e41b9c1d26b1f43b97857238cf478dbc7d330b5"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "3404fbdd5e7529a0674eef26114b5071e4586cec",
+      "sha256": "ead6cdc9d0af6d58e8a49744d8ec8c7c15e13d2ba93c276c434bcf9b51b93a81"
+    },
+    {
+      "path": "research/filtered-native-kappa004/inputs/original-packet.tar.gz",
+      "usage": "input",
+      "git_blob": "7f904307bd99f2d778bc7b64e98e353715cbc041",
+      "sha256": "595f988e748b1f3b25e7525a226da173966e4278a70f511b2919245cec1b45f7"
+    },
+    {
+      "path": "research/active-mode-delivery-frontier/PROOF.md",
+      "usage": "provenance",
+      "git_blob": "54ce2c79bbcfbe722d15c87bc2634e582284903d",
+      "sha256": "fd16bfbf4279f3988add6c2a1ffb5bee134b6ec838e7a084f0f92d34244aeaa3"
+    },
+    {
+      "path": "research/active-mode-restoration/PROOF.md",
+      "usage": "provenance",
+      "git_blob": "97f9eded0c5909b12806b20f244159f7e0cc6de3",
+      "sha256": "2d305e1a5cd1b467c792940b0bc932b67c20609e3caf7cdb93c6d4e64c16dc53"
+    }
+  ]
+}

research/active-rank1-controller/TASK.json

@@ -0,0 +1,90 @@
+{
+  "schema_version": 1,
+  "task_id": "joint-query-controller",
+  "priority_revision": 8,
+  "base_commit": "de5ec2e7a6074068452f45b1a191b5c72832df4a",
+  "original_card": {
+    "id": "joint-query-controller",
+    "question": "Can a changed query demand or caller remove real work while satisfying native chronology and restoration?",
+    "starting_points": [
+      "docs/research/current-priorities.md",
+      "docs/research/research-family-status.md",
+      "certificates/selected-result.json",
+      "docs/research/pr-intake-evidence/pr5599-completion/PROOF-REVIEW.md"
+    ],
+    "methods": [
+      "Construct and independently check one source-bound instance of the stated first experiment.",
+      "Seek an exact counterexample or target-specific complete-budget obstruction to that same proposed change."
+    ],
+    "acceptance_gate": "A source-bound arbitrary-input identity and legal producer/consumer boundary with the complete paid and productive target invoice, including restoration, ownership, native alignment and extra charges. Price under the actual current model; historical ceiling.py assumptions must be established before use. A favorable optimistic relaxation keeps a route open but is not a completed supplier. A scoped local result remains useful; expansion requires the family-level budget gate.",
+    "first_step": {
+      "command": [
+        "python3",
+        "-B",
+        "scripts/research_selected_baseline.py"
+      ],
+      "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+      "inspect": "Read revision 8, the selected review and live exact-source handoffs. Then follow this card's bounded first_experiment.",
+      "scope": "Source-bound orientation only, not a supplier replay or theorem proof."
+    },
+    "first_experiment": "Choose an exact caller and a new demand/interface hypothesis. Read the scoped #5617/#5631/#5649/#5747 and #5720/#5745 objections before rebuilding an excluded schedule. Compare the complete matched source/consumer protocols including all retained helper outputs. For an active-mode injection, first check #5745: its canonical delivery claim repays the eight removed centre jobs. Audit that exact claim or change its channel/feedback hypothesis; do not repeat the same free-injection search. Stop if the full favorable budget fails or the required restored output is unobservable.",
+    "bottleneck_link": "Judge the actual current supplier contract and complete signed target/paid bill; frozen-profile ceilings require an applicability proof.",
+    "allowed_variations": [
+      "One exact source head, helper/cut region or quantified proposition and changed hypothesis; check live handoffs first. Different seeds are not different scopes."
+    ],
+    "scope_change_triggers": [
+      "Changing source head, helper/cut domain, operation alphabet or caller boundary without recording the new scope.",
+      "Treating an archived proposal or local numerical pass as complete supplier admission."
+    ],
+    "overlap_terms": [
+      "query demand",
+      "active mode",
+      "5720",
+      "5745",
+      "5747",
+      "caller"
+    ],
+    "existing_checks": [
+      {
+        "scope": "PR #4166: author-checked installed producer/service/return/bridge connection; native-component comparison loses.",
+        "evidence": "research/qq16-caller-install/README.md",
+        "remaining": "Complete matched physical protocol bill, or changed source-compatible demand/circuit; no affordable supplier yet.",
+        "status": "author-checked",
+        "source_commit": "0b082d22a0e9a442d264ab0633e35ef26c790630",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      },
+      {
+        "scope": "Selected PR5599: complete helper-subspace construction and independent caller replay; five framework assumptions remain.",
+        "evidence": "docs/research/pr-intake-evidence/pr5599-completion/PROOF-REVIEW.md",
+        "remaining": "The next experiment must identify uncovered source-specific work. Successor archive intake does not transfer this admission.",
+        "status": "reviewed",
+        "source_commit": "09dd0965711ca7eeb169057a420abab1c9052137",
+        "selected_record_sha256": "2a0220e866417774606e0f991e41b9c1d26b1f43b97857238cf478dbc7d330b5"
+      }
+    ]
+  },
+  "scope_status": "refined",
+  "actual_scope": "Exact fixed-rank-one channel resource bounds for the retained active-mode repair, allowing arbitrary channel count and jointly cancelling nuisance outputs.",
+  "scope_change_reason": "Follow up PR5720 and complement PR5745 by bounding the rank-one-only slice of its nine-or-more jointly noisy channel question.",
+  "bottleneck_link": "The source deletes eight rank-eight centers; any replacement must restore Y and helpers and beat their complete paid allowance.",
+  "budget_minutes": 60,
+  "stop_rule": "Finish exact source-bound weighted-support certificate and independent review; no coefficient grid or higher-rank search.",
+  "outcome": "partial",
+  "evidence": "rank1-controller.json; y-cleanup.json; verify.py",
+  "author": "flyingviper",
+  "ai_assistance": "Substantial OpenAI Codex assistance with separate construction and review agents; not independent human review.",
+  "open_questions": [
+    {
+      "question": "Can higher-rank jointly noisy channels beat the removed-center allowance?",
+      "why_it_matters": "The rank-one-only resource bound does not decide the general open model in PR5745.",
+      "first_step": "Give a complete output response and payload matrix for one mixed-rank family, including every nuisance coordinate and paid transport.",
+      "blocked_by": "No physical construction or favorable complete bill is supplied."
+    },
+    {
+      "question": "Can changed feedback dependencies or inter-chart transport evade the fixed-channel premise?",
+      "why_it_matters": "These operations are explicitly outside the proved family.",
+      "first_step": "Specify one literal phase-aware map and retain all original inputs through its cleanup.",
+      "blocked_by": "Moving a payload changes its address action; arbitrary reframing is not free."
+    }
+  ]
+}

research/active-rank1-controller/VERIFY.json

@@ -0,0 +1,30 @@
+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [
+    "research/filtered-native-kappa004/inputs/original-packet.tar.gz"
+  ],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 120,
+      "checks": "Authenticate the frozen archive and two members; replay all chronological rank-one contacts, exact weighted-cover certificates and rejection controls; check rational cleanup and frame geometry."
+    },
+    {
+      "argv": [
+        "{python}",
+        "-O",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 120,
+      "checks": "Authenticate the frozen archive and two members; replay all chronological rank-one contacts, exact weighted-cover certificates and rejection controls; check rational cleanup and frame geometry."
+    }
+  ]
+}

research/active-rank1-controller/Y-CLEANUP.md

@@ -0,0 +1,38 @@
+# A conditional Y-feedback route and its restoration obligation
+
+This note concerns the exact scalar specialization of the retained native
+word. It does not certify a physical feedback construction or a new bound.
+`y_cleanup.py` checks the following facts against the two source members
+already declared in `SOURCES.json`; `y-cleanup.json` records its result.
+
+Write `r = R[5]^T`, using zero-based mode numbering. The retained matrix has
+
+    R R^T = 56 I8,
+    C = I112 - R^T R/4,
+    R C = -13 R,
+    C^-1 = I112 - R^T R/52.
+
+The inverse follows from `(R^T R)^2 = 56 R^T R`. Consequently, if a proposed
+pure Y-feedback route has endpoint response `deltaX = -C deltaY`, then the
+unique residue producing the desired `deltaX = -r m` is
+
+    deltaY = -r m/13.
+
+The checker verifies this identity on all112 entries. It establishes a
+possible scalar mechanism, conditional on such a route and on subsequent
+legal restoration of Y. The denominator13 is not a dyadic scale and must be
+handled by the actual arithmetic and precision contract.
+
+All112 Y fields start at ground and finish at rank8. The56 nonzero entries
+of this particular residue occupy56 distinct final rank8 hyperplanes;
+every pair joins to the full rank9 space. Rank1 frame72 is contained in28 of
+these destinations, while frames114 and115 are each contained in24.
+
+Thus a ground or rank1 provider does not grant an ordinary tail cleanup.
+A direct monotone lift from a rank1 provider to a containing rank8
+destination traverses seven additional ranks; for the other destinations,
+that direct monotone route is unavailable. Already-paid native paths,
+shared relays, or a coupled change to the program could behave differently
+and are not excluded by these facts. Any such proposal must supply the
+actual payload at the destination's frame, restore every original field,
+and include the complete routing and arithmetic cost.