Lower the seven-source full ternary connector upper bound to 6600 calls (no new κ)

research/f3-ternary-seven-source/README.md

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+# A 6600-call seven-source full ternary connector
+
+The unsigned dirty connector with seven immutable sources and all 2186
+nonzero coefficient rows over F3 has a **6600-call construction**, improving
+[#4256](https://github.com/CrocSwap/integer-mult-bounds/pull/4256)'s upper
+bound of 6603 by three complete calls. This answers its open question 2 with
+a small improvement. The claim type is a **finite construction certificate**,
+with the prefix identity explaining why the certified word works in every
+compatible dimension. No exact optimum, new kappa or supplier admission is
+claimed. The cited lower bound from
+[#4244](https://github.com/CrocSwap/integer-mult-bounds/pull/4244) remains
+6588, so the current cited interval is 6588 <= OPT_3(7) <= 6600.
+
+## Exact interface
+
+For each j = 0..6, x_j is immutable. The connector z and all distinct outputs
+y_v are arbitrarily dirty. For every nonzero v in F3^7 the required action is
+
+```text
+y_v += sum_j v_j A_v B_j x_j;     z and every x_j are unchanged.
+```
+
+The maps are arbitrary compatible F3-linear maps, including singular and
+noncommuting maps. Only unsigned complete calls are permitted:
+
+```text
+B_j: z += B_j x_j
+A_v: y_v += A_v z
+```
+
+Every call restores its private scratch and heads. Outputs are observed only
+after the batch and cannot be borrowed. There are no inverses, direct A_v B_j
+calls, extra connectors, frames, source mutation or free copies. The word is
+independent of data and map entries. This is the full-demand interface of
+Nick Petalas's #4238/#4244, building on the credited connector lineage below.
+The number priced here is complete calls at unit prices. Physical costs that
+are not part of those complete primitive implementations remain additional.
+
+## Certificate and argument
+
+Use this 42-event source word, with one digit denoting the source index:
+
+```text
+260536506545241601014125215430234634321306
+```
+
+Each of the seven source labels occurs six times, so the connector is
+restored in characteristic three. Let q_t be the vector of source counts
+modulo three before event t, for t = 0..41. The closing boundary is q_42 = 0
+and duplicates q_0. The verifier enumerates all
+binomial(44, 3) = 13244 boundary triples with repetition and checks
+
+```text
+{q_a + q_b + q_c : 0 <= a <= b <= c < 42} = F3^7.
+```
+
+For each nonzero row v, take its lexicographically first such triple and
+place its three A_v calls at those boundaries. Several readouts at the same
+boundary mean consecutive calls. Readouts do not change z, so all chosen
+triples can be scheduled together, in boundary order. At boundary t,
+
+```text
+z = z_initial + sum_j (q_t)_j B_j x_j.
+```
+
+The three readouts add three copies of A_v z_initial, which vanish, and
+sum_j v_j A_v B_j x_j. This uses only linearity and never interchanges A_v
+and B_j. Each target receives exactly its required increment. The total is
+
+```text
+42 source calls + 3 * (3^7 - 1) readouts = 42 + 6558 = 6600.
+```
+
+The predecessor #4256 has 45 source calls and the same 6558 readouts, giving
+6603. Both totals and the shared row/readout counts are checked numerically
+by the arithmetic above. No predecessor census or theorem is reverified.
+
+The source path was found by a bounded swap search starting with six uses of
+every source. Search stopped at the first covering path. Discovery is not
+part of the certificate: the explicit word and exhaustive triple check are
+sufficient, and no search-failure or optimality claim is made.
+
+## Evidence and reproduction
+
+The standard-library verifier writes no files and imports no predecessor
+code. It checks all 2187 rows including zero using both packed base-three
+arithmetic and a separately written tuple computation. It then emits and
+replays all 6600 calls using a generic coefficient ledger. That ledger tracks
+incoming dirt and each B_j x_j separately, with A_v acting on the left.
+
+Eight dense executions use dimensions 1..4, two fixtures per dimension, dirty
+connectors and outputs, and explicit singular noncommuting maps in dimensions
+at least two. Six mutations must fail: a dropped source call, a dropped
+readout, a misrouted output, relabelled source calls, an appended source call,
+and execution in characteristic six. The last control detects the unpaid
+assumption that three readouts always cancel incoming dirt.
+
+From the repository root, with CPython 3.12:
+
+```sh
+~/git/integer-mult-bounds/.venv/bin/python3.12 -W error -B research/f3-ternary-seven-source/verify.py
+~/git/integer-mult-bounds/.venv/bin/python3.12 -W error -O -B research/f3-ternary-seven-source/verify.py
+~/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/research_package.py --package research/f3-ternary-seven-source
+~/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/check_research_commit.py --package research/f3-ternary-seven-source --check-source-history
+```
+
+Expected marker: `PASS_F3_TERNARY_SEVEN_SOURCE`, with `calls=6600`,
+`rows=2186`, `source_calls=42`, `dense_cases=8` and `rejected_controls=6`.
+The generated stdout receipt binds the counts to SHA256 hashes of all five
+package files. No hand-written receipt or generated replay output is stored.
+[SOURCES.json](SOURCES.json) pins historical provenance at the public base.
+The pending predecessors are citations rather than executable dependencies.
+
+The code is nonrecursive, and every loop is bounded by fixed certificate
+sizes, at most 64 source events, 2186 rows and dense dimension four. Each
+function is shorter than 60 physical lines. Python-managed allocation is an
+explicit Power of Ten deviation: dynamic objects are required by the runtime;
+live verification storage is bounded by these fixed domains. There is no
+unbounded input, background process or generated file. Warnings are errors
+in both registered modes; checks use explicit exceptions and remain enabled
+under optimization.
+
+## Limits and family decision
+
+This finite certificate supplies an upper bound. It does not exclude shorter
+words or improve #4256's asymptotic exponent. The interval's lower endpoint
+is the cited result of #4244 and is not a new proof here. A proof-kernel build,
+independent human review and the selected cold replay are unclaimed and unrun.
+
+The call count is proved for the abstract interface. A concrete consumer for
+full ternary demand is unknown. Coefficient preparation, physical dispatch,
+stock, hosting, precision, tape costs and complete supplier admission remain
+unknown. Unknown costs are not zero. No selected source, frontier, shared
+code or predecessor package changes.
+
+The catalogue card asks for an alphabet extension. This is explicitly a
+changed scope: the alphabet is retained and a full-demand finite upper bound
+is improved. The family decision is to finish this small result and stop.
+There is no downstream implementation campaign or claim that the complete
+consumer fits a supplier budget.
+
+## Open next questions
+
+Structured questions are in [TASK.json](TASK.json).
+
+1. Is the cited lower bound 6588 attained? Start with a restored 30-event
+   source path covering all ternary rows by triples, or a word that trades
+   source calls for extra readouts. An unsuccessful search is not exclusion.
+2. Can the 42-event path yield a smaller leading constant in an all-n
+   construction? A lifting argument must preserve all triple decompositions
+   and charge every source event, rather than merely multiplying palette
+   sizes. No such lifting is supplied here.
+3. Does a concrete caller need every ternary row? Identify its complete maps,
+   dirty-state contract and physical invoice before extending this family.
+
+## Credit
+
+This contribution was produced by Nick Petalas. Nick Petalas's #4256 posed
+the seven-source upper-bound question and supplied the 6603-call torus-block
+baseline; #4238/#4244 introduced full ternary demand and its cited lower
+bounds. Credit #4231 for the unsigned ring interface, Riquelme Soares's
+#4189 for the unsigned F3 predecessor, Ross Richardson's #943/#934 for the
+prefix-connector and Gray-block lineage, conorholds's #2208 for block palettes
+and all-word counting in different alphabets, and ywz65 for the five-source
+contract map. No priority is claimed for elementary prefix sums or dirty
+cancellation. Predecessor credit is unchanged. Independent human and formal
+proof-kernel review are unclaimed. Apache-2.0.

research/f3-ternary-seven-source/SOURCES.json

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+{
+  "schema_version": 1,
+  "base_commit": "12fa8c5c844be21bfefb38a19503fbd867a11244",
+  "files": [
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "b1fea0c94436b236cc2b7d41a7be032811b94c81",
+      "sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "64bfc5af6709ed9811171e0a2108f05e1219cb65",
+      "sha256": "352a6184713b8843d96fd2c2071eb7aeaa655906b7c51d45ad444912666c8a96"
+    },
+    {
+      "path": "research/universal-connector-boundary/README.md",
+      "usage": "provenance",
+      "git_blob": "d277f7c5830b1f2bc42e1ff41ab86e7d7564929f",
+      "sha256": "23415f7829ab8d80a783142f10f7d31abbce84579362769984680af3df954476"
+    },
+    {
+      "path": "docs/research/five-source-connector-scope-map.md",
+      "usage": "provenance",
+      "git_blob": "c4b56250e35eb52f07987f7e96c7dba18fac75d1",
+      "sha256": "5b541588a5ddb38b4dbbf5dca91cc9e6684f67462d515e25f838d833ec30f62f"
+    }
+  ]
+}

research/f3-ternary-seven-source/TASK.json

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+{
+  "schema_version": 1,
+  "task_id": "connector-alphabet-change",
+  "priority_revision": 7,
+  "base_commit": "12fa8c5c844be21bfefb38a19503fbd867a11244",
+  "original_card": {
+    "id": "connector-alphabet-change",
+    "question": "Does one explicit extension of the connector alphabet offer a favorable completed budget?",
+    "starting_points": [
+      "docs/research/research-family-status.md",
+      "research/universal-connector-boundary/README.md",
+      "certificates/selected-result.json"
+    ],
+    "methods": [
+      "Construct and charge a legal extra operation on a minimal instance.",
+      "Prove a target-specific bound after adding one specified operation family."
+    ],
+    "acceptance_gate": "State which fixed-alphabet premise changes and charge its implementation; do not declare it free. 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/universal-connector-boundary/verify.py"
+      ],
+      "expected": "PASS_UNIVERSAL_CONNECTOR_BOUNDARY",
+      "inspect": "Reproduce the 945-pairing control, then read Exact interface to list the allowed calls.",
+      "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay."
+    },
+    "first_experiment": "Add exactly one legally priced operation and test a tiny dirty-input instance before enumerating larger cases.",
+    "bottleneck_link": "A new legal connector operation could change recursive interface cost; a larger census in the same alphabet is a separate side result.",
+    "allowed_variations": [
+      "Choose one additional operation and a small source count for its first counterexample."
+    ],
+    "scope_change_triggers": [
+      "Keeping the alphabet and only increasing the source count; record this as a changed assignment.",
+      "Extending a source-count census without naming a supplier/interface decision it could change; audit #2973 pruning concerns before relying on the affected predecessor exclusions."
+    ],
+    "overlap_terms": [
+      "universal connector",
+      "source-toggle",
+      "connector alphabet"
+    ]
+  },
+  "scope_status": "changed",
+  "actual_scope": "A 6600-call upper bound for the seven-source unsigned F3 dirty connector with all 2186 nonzero ternary rows.",
+  "scope_change_reason": "Retains the alphabet and improves a full-demand finite construction, answering PR4256 open question 2 rather than extending the operation alphabet.",
+  "bottleneck_link": "Side result on a recursive connector interface. A concrete full-demand consumer and complete supplier invoice are unknown; no kappa claim.",
+  "budget_minutes": 60,
+  "stop_rule": "Stop research at the first verified upper-bound improvement, then package it. No shorter-word search after the 42-event witness.",
+  "outcome": "completed",
+  "evidence": "All 13244 boundary triples cover all 2187 rows; packed and tuple arithmetic agree. Literal 6600-call replay, eight dense dirty executions and six rejection controls pass.",
+  "author": "Nick Petalas",
+  "ai_assistance": "Independent human and formal proof-kernel review are unclaimed.",
+  "open_questions": [
+    {
+      "question": "Is the cited lower bound 6588 attained?",
+      "why_it_matters": "Would settle the seven-source full ternary optimum.",
+      "first_step": "Seek a restored 30-event path covering every row by triples, or a legal source/readout tradeoff.",
+      "blocked_by": "No covering shorter word or stronger all-word lower bound is supplied."
+    },
+    {
+      "question": "Can this finite palette reduce the leading constant of an all-n construction?",
+      "why_it_matters": "PR4256 matches the exponent but leaves a constant gap.",
+      "first_step": "Prove a lifting rule preserving triple decompositions and count every positive source step.",
+      "blocked_by": "No such lifting rule is known here."
+    },
+    {
+      "question": "Which concrete caller requires full ternary demand?",
+      "why_it_matters": "A local call saving needs a consumer before it can affect a supplier.",
+      "first_step": "Pin a caller and price maps, dispatch and dirty return.",
+      "blocked_by": "Caller, stock, precision and physical implementation are unknown."
+    }
+  ],
+  "predecessors": [
+    {
+      "pr": 4256,
+      "head": "6a95ef419f94e7b5c2fff710e34081520cc6aba2",
+      "role": "6603 upper bound and open question 2; citation only"
+    },
+    {
+      "pr": 4244,
+      "head": "f436d2911351e5be2842208fe96b0b66442323a4",
+      "role": "full-demand interface and cited 6588 lower bound; citation only"
+    },
+    {
+      "pr": 4238,
+      "head": "191a905d7adba6695b079f744140a73e832787a8",
+      "role": "full ternary demand predecessor; citation only"
+    }
+  ],
+  "result": "Finite construction certificate: 42 source calls and 6558 readouts, total 6600, three fewer than the cited 6603 upper bound."
+}

research/f3-ternary-seven-source/VERIFY.json

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+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-W",
+        "error",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 120,
+      "checks": "Independent complete triple coverage, literal dirty coefficient replay, eight dense noncommuting fixtures and six rejection controls."
+    },
+    {
+      "argv": [
+        "{python}",
+        "-W",
+        "error",
+        "-O",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 120,
+      "checks": "The same scientific checks with Python optimization enabled; all contracts remain active."
+    }
+  ]
+}