Save 22 historical disjoint-triple roles through a descendant tie (no κ)

research/disjoint-descendant-traversal/PROOF.md

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+# Exact finite map and complete historical charges
+
+For ordered ground points P, let D_(a,b)(P) send each a-subset input to the
+sum of inputs disjoint from each b-subset target. Splitting P into L and R,
+the channel with source-left cardinality i and target-left cardinality j
+is `D_(i,j)(L) tensor D_(a-i,b-j)(R)`. Applying these two tensor factors in
+either order gives the same integer map. This equality holds on arbitrary
+inputs and needs no cancellation or approximation.
+
+The constructor changes only subproblems of shape `(n,a,b)=(11,2,2)`.
+The pinned planner splits them into five and six ground points. In channel
+`(i,j)=(1,1)`, the left-first and right-first unshared costs are both 146;
+the constructor checks this equality explicitly. It takes the opposite order
+from the planner. All other channels and all root choices stay as in #981.
+The argument above proves that every changed subproblem still computes
+D_(2,2)(11), and hence the full circuit computes D_(3,3)(22).
+
+Every addition combines disjoint source families. Retaining the first
+binary decomposition of an already existing support leaves its integer
+coefficient vector unchanged. Pruning unreachable nodes also leaves all
+output vectors unchanged. Different factor orders can expose different
+previously interned supports, so their equal unshared costs need not give
+equal final DAG sizes. The finite checker derives the 30,676 retained
+additions from this new DAG. It derives every output vector independently
+from the set-theoretic predicate `S intersect T is empty`. This establishes
+all 1,540 by 1,540 coefficients, with both zero and nonzero coefficients
+included. The count is a certificate of this construction, not a lower bound
+on other possible circuits.
+
+The retained compiler gives c+v roles for c additions and v outputs. Here
+c=30,676 and v=1,540, giving 32,216 roles. Every compiled operation first adds
+its other input roles into its pivot, then adds the pivot into its distinct
+fanout roles. It is an invertible integer linear map. Subtract the pivot
+from the fanout roles first, then subtract the other input roles from the
+pivot to invert it. The slot-alias checks ensure these instructions have
+the stated meaning. Thus arbitrary dirty values are permitted in the mixer
+and returned by its literal inverse. The clean source-to-output block is
+checked separately by full symbolic support replay. The retained twelve-step
+signed invocation can therefore reuse this block while cancelling every
+initial side value, exactly under its existing boundary contract.
+
+For any active node, let A be the union of ground points of ancestor source
+triples, and B the union of reachable target triples. Every such source
+triple is disjoint from every such target triple, since coefficients are
+positive and every output row has exactly the required support. Thus A and
+B are disjoint. The phase enclosure in the pinned
+`notes/disjoint-tensor-compression.tex` applies to any such DAG, rather than
+only its original factor choices. Source lines, coordinate spaces and target
+complements remain nested with the same norm-one residual witnesses.
+The retained checker traverses both actual physical orientations of the new
+compiled circuit. It checks the case conditions for every transition; it
+does not explicitly construct the 104,897 residual bases.
+
+For the complete historical invoice, retain h=22, v=binomial(h,3)=1,540,
+intersection-two roles `R2=binomial(h,2)*(4*(h-2)-6)=17094` and h+1 centres.
+The source proof gives
+
+```text
+R0 = c+v
+M = 2c+2*binomial(h,2)*(3*(h-2)-6)
+C = J = 4v
+S_inv = 4M+2C+4J+18v
+S_all = 3v^2*S_inv
+W = 2v^3+2v^2*(R0+R2+h+1)
+m = h^3
+L = 3v^2*h*(h+1)
+s = W*m-2v^3+2L
+E = 64*(W+m+1)^3
+```
+
+These formulas keep every mixer or inverse, source access, injection,
+restoration, centre, intersection-two role, join and recursive child in the
+same historical contract. The checker evaluates them at the new c, obtaining
+`S_inv=409880`, `S_all=2916214224000`, `W=241300813600` and
+`s=2569370958862400`. It also checks `2<=s<m^5` and
+`4*S_all+8*s+8*W+8*m<E`. Against #981's cited c=30,698, the 22 fewer additions
+save 22 roles, 176 steps per signed invocation and
+`24*v^2*22=1252204800` steps in the full scalar bound. No new fee is introduced
+because the boundary map, frame-enclosure rule and number of calls are the
+same. This statement does not transfer the old contract into the selected
+P104 supplier or prove its all-size assumptions.

research/disjoint-descendant-traversal/README.md

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+# Twenty-two fewer historical disjoint-triple helper roles
+
+This finite certificate constructs the h=22 disjoint-triple sum map with
+**30,676 additions and 32,216 reversible roles**, saving 22 of each against
+the 30,698-addition construction in ToikY's [PR #981](https://github.com/CrocSwap/integer-mult-bounds/pull/981).
+The complete historical three-stage scalar bound falls by **1,252,204,800**.
+There is no new kappa or selected-frontier change.
+
+The new step changes a proper descendant, a domain #981 explicitly excluded.
+It preserves #981's root split 11+11, root target-cardinality order
+`(1,2,3,0)`, reversed root channel `(1,1)`, point order, summation trees and
+first-decomposition support interning. Inside every encountered
+`D_(2,2)(11)` subproblem, keep its 5+6 split but reverse the factor order
+in channel `(1,1)`. Both orders have the same unshared cost 146.
+Different intermediate supports change which decompositions survive global
+interning and pruning. [PROOF.md](PROOF.md) gives the exact map and accounting
+argument. This is an improvement to this cited historical construction;
+no global circuit optimum or broader literature-priority claim is made.
+
+## Evidence and reproduction
+
+From the repository root, with CPython 3.12 and its standard library:
+
+```sh
+/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -W error -I -B research/disjoint-descendant-traversal/verify.py
+/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -W error -I -O -B research/disjoint-descendant-traversal/verify.py
+/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/research_package.py --package research/disjoint-descendant-traversal
+/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/check_research_commit.py --package research/disjoint-descendant-traversal --check-source-history
+```
+
+Other machines may replace the absolute interpreter path with their CPython
+3.12 executable. The final marker is
+`PASS_DISJOINT_DESCENDANT_TRAVERSAL additions=30676 roles=32216 no_new_kappa`.
+Default replay writes no files. Its computed stdout receipt includes all
+package and live-input SHA256 hashes, the environment and elapsed time.
+There is no handwritten receipt.
+
+The new checker reconstructs every active integer support from the literal
+addition DAG, separately constructs every desired disjointness row and checks
+all **2,371,600 coefficient positions**, including zeros. It independently
+replays the compiled embedding and checks its source, output, freshness and
+slot-alias conditions. The retained frame checker checks both physical
+orientations, with 104,897 distinct nontrivial transitions. One dense integer
+roundtrip uses deterministic dirty initial values in all 32,216 roles; its
+universal justification is the elementary inverse in PROOF.md, not sampling.
+Six rejecting controls cover a wrong output, duplicate summand, cycle,
+corrupt cached support, missing paid role and aliased fanout. All mutations
+are restored before a final successful map and embedding replay.
+
+Predecessor values are cited from #981, not re-established here. Its census
+and verifier are not replayed. This package constructs and checks only the
+new circuit. The first strict improvement ended the search; no optimality
+claim or complete negative census is attached to earlier unsuccessful probes.
+
+## Complete historical bill
+
+The unchanged historical contract retains the intersection-two circuit,
+23 centres, joins, source access, weighted injection, all four mixers or
+inverses, dirty restoration and all three tensor stages.
+
+| Quantity | Cited #981 | New circuit |
+| --- | ---: | ---: |
+| Disjoint additions | 30,698 | 30,676 |
+| Disjoint reversible roles | 32,238 | 32,216 |
+| Total side roles | 49,332 | 49,310 |
+| Mixer additions | 86,344 | 86,300 |
+| Complete signed invocation steps | 410,056 | 409,880 |
+| Complete three-stage scalar bound | 2,917,466,428,800 | 2,916,214,224,000 |
+| W | 241,405,164,000 | 241,300,813,600 |
+| s | 2,570,482,081,921,600 | 2,569,370,958,862,400 |
+
+Here `v=1540`, `m=10648`, `L=3600088800` and `W*m-s=104350400`.
+The verifier computes the new bill and the retained `E=64(W+m+1)^3` guard.
+It does not calculate a new logarithmic saving or compose a supplier with
+current BIT or outer budgets.
+
+## Scope and limits
+
+Scientific base is canonical main
+`de5ec2e7a6074068452f45b1a191b5c72832df4a`, priority revision 8.
+The selected binding-only orientation passed. This is a declared change
+from `complex-rank-shape-decoder` to a historical circuit side result.
+The selected P104 supplier is a different construction. Improving this old
+finite invoice does not discharge its compiler, ownership, all-column native,
+precision/tape or analytic recovery assumptions. No selected cold replay,
+full multiplication theorem, new native kernel, exact h22 residual-basis
+construction, all-size compiler or physical rounded multiplier is supplied.
+Independent human and formal proof-kernel review are unclaimed.
+
+Only this package is new. [SOURCES.json](SOURCES.json) pins the imported
+constructor, its executable dependency closure and the proof and comparison
+sources. Frozen predecessors and their credit lines are unchanged.
+[VALIDATION.md](VALIDATION.md) records local checks and implementation limits.
+
+## Open next questions
+
+1. Does an explicit physical caller benefit from this descendant sharing
+   mechanism in a competitive current supplier? Start with one named
+   disjoint-subset component and its complete boundary invoice. No such
+   component or compatibility with selected P104 is established here.
+2. Can one prove a bound on the benefit of changing a single proper
+   descendant's factor order under first-decomposition interning? Start with
+   the two 146-cost factorizations and the supports they create. This package
+   certifies one example and supplies no universal sharing bound.
+
+These questions are unreserved. TASK.json records the same questions and
+remaining blockers.
+
+## Credit
+
+This contribution was produced by Nick Petalas. Apache-2.0.
+ToikY's #981 supplies the root recipe and root-traversal improvement;
+Curtis Dransfield's #863 supplies the preceding tied-root construction.
+Douglas R. Colkitt supplies the disjoint-subset recurrence, support interning,
+reversible compiler, phase enclosure and historical signed-invocation and
+stopped-recurrence accounting. Their retained notices and predecessor
+attribution continue to apply. The new result is the descendant factor-order
+change, its 22-role improvement and the accompanying finite certificate.

research/disjoint-descendant-traversal/SOURCES.json

@@ -0,0 +1,60 @@
+{
+  "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": "notes/disjoint-tensor-compression.tex",
+      "usage": "input",
+      "git_blob": "0e3cad1b933f532cd83d6a3e93114c4c9361e65c",
+      "sha256": "528cba56872313b8cd63ff11f523a399dfb3c85cae1a764110ae9d26ac9151ac"
+    },
+    {
+      "path": "research/disjoint-joint-ties/README.md",
+      "usage": "input",
+      "git_blob": "fbfadd52d6bbfb8d9f4121a5d7bbcc0f4e01a7cd",
+      "sha256": "10ea35680ee002283a938b7c7afaff8be472f2abbf472f53877ede8e8dcdae74"
+    },
+    {
+      "path": "research/disjoint-joint-ties/circuit.py",
+      "usage": "input",
+      "git_blob": "1ac7613e274ac5c8394c0bcbc94c2da0e23a17d5",
+      "sha256": "2f98e0e21044a7decc7e4dadd2662217626394220e3d62406fff6442ac4a92ba"
+    },
+    {
+      "path": "scripts/binary_phase_frames.py",
+      "usage": "input",
+      "git_blob": "c8e4fa71fe60550324f9e43c1dd5ad6d9bf4e2f4",
+      "sha256": "4148cfa313cf050ed25296e8db36d35871520b8318fd086c7d1facf0c6af67d7"
+    },
+    {
+      "path": "scripts/certify.py",
+      "usage": "input",
+      "git_blob": "a773311b726fd1ef98a056f6f76010e872d7908a",
+      "sha256": "2348d95008276c5d5764f7e028c3918e484582cd589bd4d9b82919161745e53e"
+    },
+    {
+      "path": "scripts/exclusion_circuit.py",
+      "usage": "input",
+      "git_blob": "b0e2f3e03d7de791ca936dfd92cee2134c7dd4f5",
+      "sha256": "f9fbcd6e85e442cbd0926ac0887414e20735b2dc923d2d5822c803ceb46726d3"
+    },
+    {
+      "path": "scripts/experiments/disjoint_tensor.py",
+      "usage": "input",
+      "git_blob": "cc85de3024d191b79bf64ced2b39d782854fe491",
+      "sha256": "23763a4b6086fb3d19f9282fff5c118f53fa52e7a7f17da1bde990bd4cf8b6ac"
+    }
+  ]
+}

research/disjoint-descendant-traversal/TASK.json

@@ -0,0 +1,97 @@
+{
+  "schema_version": 1,
+  "task_id": "complex-rank-shape-decoder",
+  "priority_revision": 8,
+  "base_commit": "de5ec2e7a6074068452f45b1a191b5c72832df4a",
+  "original_card": {
+    "id": "complex-rank-shape-decoder",
+    "question": "Can a legal decoder or coframe change improve the full signed moment, including changed helper targets?",
+    "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",
+      "docs/research/recursive-invoice-preflight.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": "Price one complete changed itinerary with both paid and productive histograms. Check #5693/#5698 for overlap and their exact hypotheses before another coframe search. Use the signed invoice preflight where its boundary contract agrees; an inconclusive concave comparison is not a power crossing. Stop if an optimistic complete budget fails at the chosen target or native delivery remains unspecified.",
+    "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": [
+      "coframe",
+      "signed moment",
+      "5693",
+      "5698"
+    ],
+    "existing_checks": [
+      {
+        "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": "changed",
+  "actual_scope": "Construct a smaller h=22 historical disjoint-triple circuit by changing a proper descendant factor order while retaining the PR981 root recipe.",
+  "scope_change_reason": "The selected supplier is a different P104 construction. This is an explicitly historical circuit side result, outside PR981's fixed-descendant search domain, rather than a current coframe or target split.",
+  "bottleneck_link": "A concrete example of reducing a complete finite helper bill through sharing. It does not improve the selected supplier or change any current admission gate.",
+  "budget_minutes": 60,
+  "stop_rule": "Stop and package the first strictly smaller exact circuit; no broader census or subsequent optimization.",
+  "outcome": "completed",
+  "evidence": "30,676 additions; 32,216 compiled roles; all 2,371,600 integer coefficient positions and both physical frame orientations checked; six rejecting controls.",
+  "author": "Nick Petalas",
+  "ai_assistance": "Independent human and formal proof-kernel review are unclaimed.",
+  "open_questions": [
+    {
+      "question": "Does this descendant sharing mechanism improve an explicit competitive physical caller?",
+      "why_it_matters": "The historical improvement alone cannot raise the selected bound.",
+      "first_step": "Identify one disjoint-subset component and write its complete current boundary bill.",
+      "blocked_by": "No compatibility with the selected P104 supplier is established."
+    },
+    {
+      "question": "How much can changing one proper descendant factor order save under first-decomposition interning?",
+      "why_it_matters": "An exact sharing bound could guide construction choices.",
+      "first_step": "Analyze the supports created by the two 146-cost factorizations.",
+      "blocked_by": "The present evidence is one finite construction, with no universal lower or upper bound."
+    }
+  ],
+  "claim_type": "finite certificate",
+  "claim_url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1166#discussioncomment-19217762",
+  "predecessors": [
+    {
+      "pr": 981,
+      "author": "ToikY",
+      "head": "6c9dc6d180ac0fde42c1c2b0fe549d5a13851cf9",
+      "contribution": "Root traversal and winning root recipe; descendants explicitly fixed."
+    },
+    {
+      "pr": 863,
+      "author": "Curtis Dransfield",
+      "head": "6c0ed3975fda8f0190b34f1b1bbedb33a925d339",
+      "contribution": "Tied-root factor-order improvement."
+    }
+  ]
+}