Research: deferred target basis — V R = I replaces H5 with the H2 target clause; scatter 527 -> 97 on every committed R439 target-basis word (PR1868's PR1188 word 10,489 -> 10,059) (no new kappa)

research/r439-deferred-target-basis-seed06/SOURCES.json

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research/r439-deferred-target-basis-seed06/TASK.json

@@ -0,0 +1,84 @@
+{
+  "schema_version": 1,
+  "task_id": "bit-helper-contract",
+  "priority_revision": 3,
+  "base_commit": "c676548106012571fefa1dce0ec16f1bcfe11dce",
+  "original_card": {
+    "id": "bit-helper-contract",
+    "question": "Can one precisely specified helper-mixing word satisfy a replacement for the inherited H2/K interface?",
+    "starting_points": [
+      "research/r439-bsection-stars-seed01/README.md",
+      "research/r439-copy-path-sharing-barrier/README.md"
+    ],
+    "methods": [
+      "Derive a replacement interface lemma and price its implementation.",
+      "Seek an exact dirty-input or chronological-cut counterexample to the proposed replacement."
+    ],
+    "acceptance_gate": "A full boundary contract and paid profile; unchanged scalar counts alone are insufficient.",
+    "first_step": {
+      "command": [
+        "python3",
+        "-B",
+        "research/r439-bsection-stars-seed01/verify.py"
+      ],
+      "expected": "PASS_R439_BSECTION_STARS",
+      "inspect": "Compare the two false H2/K flags with the unchanged paid profile in its README.",
+      "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay."
+    },
+    "first_experiment": "Write one replacement H2/K implication for a single helper-star operation, then try to falsify it on dirty inputs.",
+    "bottleneck_link": "A legitimate replacement could admit a cheaper bit circuit; scalar savings alone do not alter the selected moment.",
+    "allowed_variations": [
+      "Choose one helper-star or quartet instance; narrow to one boundary implication."
+    ],
+    "scope_change_triggers": [
+      "Changing only source count or scalar addition count without an interface argument."
+    ],
+    "overlap_terms": [
+      "H2_D_frame0_targets_from_helpers",
+      "K_equals_D",
+      "helper-star"
+    ]
+  },
+  "scope_status": "changed",
+  "actual_scope": "Replace H5 (V = I) together with the H2 target clause (R = I) by the deferred-target-basis contract H5-tw: frame-zero, source-free D with operator (x, y, h) -> (x, R y + N h, T h) and raw word W0' = (A, scatter, B) with V R = I, J = I, V N = K'T and C U'(I + T) = I (kept H1, H3, D-shape and z-only full-frame C clauses). Prove it with its converse, instantiate it on every committed PR915-lineage word (as of base c6765481) by deferring the D-tail target-basis undo E^-1 to the start of B and listing the scatter as E S, and check the full dirty boundary, frame paths, paid profile, owner flags, guards, a cut-by-cut bridge and fixed-frame-path maximality among prefix splits of the literal undo order. Add the order-ideal refinement (a commutation-closed split of the undo, found by bounded exhaustive and greedy search, not optimal), fully checked on four words.",
+  "scope_change_reason": "Changed: the card asks for an H2/K replacement for a helper operation; this package also relaxes H5 (V = I), which the card keeps, and its object is the target-basis block, not a helper operation. PR1194 (H2-sem) and PR1868 (twisted helpers) already replace H2/K, but both keep H5 and the H2 target clause (R = I: D restores the target basis at its boundary). This package replaces that pair by V R = I and generalizes K to V N = K'T. It also broadens rather than narrows: the census covers every committed lineage word, not one helper-star instance. It does not attempt hosted adoption, native replay or a global optimum.",
+  "bottleneck_link": "Side result on the bit supplier. A replacement interface admits cheaper bit words (430 complete local ADDs fewer on 18 of 19 lineage words, 432 on PR1040; a further 3 with the order-ideal split found by search) with unchanged frame paths, paid profile and rank mass; the selected moment and kappa are unchanged and the bit side does not bind.",
+  "budget_minutes": 60,
+  "stop_rule": "Stop after the H5-tw lemma and its converse, the per-cut bridge, the fixed-frame-path maximality and prefix-split census, the bounded order-ideal search with four fully checked ideal splits, the live census on every committed lineage word, two committed instances with controls and check-level controls, the PR1868 composition and one heuristic PR589 instance; no basis search, native replay or hosted emission.",
+  "outcome": "completed",
+  "evidence": "EXPECTED.json, PROOF.md, candidate-1062.json.gz and candidate-1188.json.gz; python3 -I -B research/r439-deferred-target-basis-seed06/verify.py prints PASS_R439_DEFERRED_TARGET_BASIS (also under -O and CPython 3.14); --census-scan repeats the word census.",
+  "author": "Sagar Thakrar",
+  "ai_assistance": "Prepared by Sagar Thakrar with substantial Anthropic Claude assistance (Claude Code, including subagents for the exploratory probe, its independent checks, the pre-PR review and package assembly). No independent human review.",
+  "open_questions": [
+    {
+      "question": "Can a target basis chosen jointly for the D reads and the deferred scatter beat PR915's E plus deferral?",
+      "why_it_matters": "E comes from PR915's application of PR794's greedy search, optimized for the reads alone; after deferral the same basis also prices the scatter (nnz(E S)), so the joint objective differs.",
+      "first_step": "Add nnz(E S) to the objective of PR915's application of PR794's greedy search and rerun it under the same 104/192-bit prefix guards.",
+      "blocked_by": "Search budget and a fresh prefix recount; no interface blocker beyond H5-tw adoption."
+    },
+    {
+      "question": "Is there a shorter zero-frame circuit for E^-1 than the literal 306-gate reverse, or a better split of the undo between D and B than the order ideal found here?",
+      "why_it_matters": "Maximality fixes where target-from-target gates may run (zero frame, before the first B climbs), not the circuit for E^-1 or the split. Full deferral is best only among prefix splits of the literal order; the order-ideal search (exhaustive up to size 4, plus greedy) found 3 more ADDs and is not an optimum.",
+      "first_step": "Resynthesize E^-1 at the zero frame with a bounded linear-circuit search, and extend the order-ideal search to larger ideals or to a joint split and resynthesis; recheck the guards.",
+      "blocked_by": "Search budget only."
+    },
+    {
+      "question": "Does the deferral compose with other rewrites of the same words, such as a shear-descent D rewrite or a PR1704-style two-copy pairing on the E S listing?",
+      "why_it_matters": "An exploratory probe suggests composition with a shear descent; PR1704's two-copy saving was computed on S and is not additive with deferral, but pairing may still pay on the 97-ADD E S listing.",
+      "first_step": "Rebuild the shear-descent word, apply the deferral and run this package's checks; separately run PR1704's pair/singleton partition search on E S.",
+      "blocked_by": "A verified composition; PR1704 also needs its two-live-temporary interface."
+    },
+    {
+      "question": "Do the deferred words pass native 5/9/11-stage replay and hosted emission?",
+      "why_it_matters": "This package checks local scalar, frame and precision facts only; the undo now sits in B's exporter phase, which native tools may treat differently.",
+      "first_step": "Run PR1188's native checkers (or PR1902's audit harness) on candidate-1188.json.gz, or PR1806's PR1122 nine-stage hosted-invoice replay on the deferred PR1122 word.",
+      "blocked_by": "A host with Boost headers or PR1509's checked cpp_int stand-in."
+    },
+    {
+      "question": "What is the best scatter basis G for the selected PR589 word under the 2|G| + nnz(G S) cost model?",
+      "why_it_matters": "The minimum-spanning-tree basis here is a heuristic (527 -> 412); an exact optimum or a lower bound would settle how much the selected word's scatter can gain under H5-tw.",
+      "first_step": "Enumerate small Steiner-type extensions of the MST (shared intermediate rows) and compare with a linear-programming lower bound.",
+      "blocked_by": "Search budget; adoption of H5-tw for the selected supplier is a separate maintainer decision."
+    }
+  ]
+}

research/r439-deferred-target-basis-seed06/VERIFY.json

@@ -0,0 +1,60 @@
+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [
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+    "research/e8-bit-p111-tuned/code/xcheck_p.py",
+    "research/e8-bit-p111-tuned/tune/bitE8mut-p111-tuned.json.gz",
+    "research/e8-bit-p111/data/bitE8mut-p111.json.gz",
+    "research/r439-abc-star-composition/candidate.json.gz",
+    "research/r439-abc-zrewrite-seed16/CANDIDATE-WORD.json",
+    "research/r439-b509-boolean-seed05/candidate.json.gz",
+    "research/r439-bsection-stars-seed01/candidate.json.gz",
+    "research/r439-bsection-stars-seed01/composition.json.gz",
+    "research/r439-bsection-stars-seed01/pair_control.json.gz",
+    "research/r439-five-cycle-seed9f01/CANDIDATE.json.gz",
+    "research/r439-five-wire-prefix/candidate.json.gz",
+    "research/r439-four-wire-prefix/candidate.json.gz",
+    "research/r439-gl5-shortest/candidate.json.gz",
+    "research/r439-global-prefix-admission/candidate.json.gz",
+    "research/r439-helper-matching/candidate.json.gz",
+    "research/r439-helper-matching/floor-word.json.gz",
+    "research/r439-helper-stars-seed19/candidate.json.gz",
+    "research/r439-helper-triples/candidate.json.gz",
+    "research/r439-neutral-helper-chain-seed17/CANDIDATE.json.gz",
+    "research/r439-neutral-mixed-shears-seed13/candidate.json.gz",
+    "research/r439-post-helper-shear-seed03/candidate.json.gz",
+    "research/r439-six-wire-boolean/candidate.json.gz",
+    "research/r439-target-compensation/candidate.json.gz",
+    "research/r439-target-retune-seed14/candidate.json.gz",
+    "research/r439-twisted-star-absorption-seed02/absorbed-pr1062.json.gz",
+    "research/r439-twisted-star-absorption-seed02/absorbed-pr1188.json.gz",
+    "research/r439-two-sided-compensation/candidate.json.gz",
+    "research/r439-z3to2-seed13/CANDIDATE-WORD.json"
+  ],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 400,
+      "checks": "SHA-256 and git-blob input pins; census of all 19 committed PR915-lineage words (literal COPY/ERASE boundary on all 661 dirty columns in both directions for base and deferred word, identical ordered frame paths and exporter MOVE records, paid profile from frames and from the pinned exporter, exporter bill, 104/192-bit guards from exporter F/B, unchanged owner checker with exactly H5_V_identity newly false, H5-tw identities V R = I, V N = K'T, J = I with R = E and V = E^-1, per-cut bridge over the deferred word's own D/A/B prefix, maximality and prefix-split census, bounded order-ideal search); four fully checked order-ideal splits; eight outside words; the PR589 heuristic instance; endpoint controls, check-level controls (each rejected by its intended check) and the reorder census on the PR1062 and PR1188 instances; committed payloads and EXPECTED.json equality."
+    },
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-O",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 400,
+      "checks": "The same verification under -O: every check raises ValueError, and the pinned exporter child runs without -O."
+    }
+  ]
+}