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)

[thakrarsagar]

Change and mathematical scope

Replacement-interface result, with priced instances on every committed R439
target-basis word. No new κ, and the bit side does not bind. This adds one
registered package,
research/r439-deferred-target-basis-seed06/.
No selected record, supplier, pinned file or upstream/ file changes.

The contract (H5-tw). Every contract on main keeps the bit supplier's H5
(V = I). That includes PR1194's semantic D and PR1868's twisted helpers.

• The lemma. Let D be frame-zero and source-free, with operator
  (x, y, h) -> (x, R y + N h, T h), and keep H1, H3 and a z-only full-frame C.
  Then the dirty boundary (x, y, h) -> (x, y + x, h) holds if and only if
  V R = I, J = I, V N = K'T and C U'(I ⊕ T) = I, where V is the target
  block of (A, scatter, B).
• What it relaxes. H5 together with the H2 target clause.
• What it keeps. D-shape and cleanup.
• What it generalizes. K becomes V N = K'T.
• Proof. The proof (PROOF.md §1–2) is block algebra. It was also checked
  on 4,000 random small F2 words during review.

The construction (R = E, V = E⁻¹). Every PR915-lineage word prepares a
target basis E in D and undoes it at the end of D. Here the 306 undo gates
(307 on PR1040/PR1449) move, unchanged, to the start of B. They stay at frame 0,
before any target climbs. The 9-column scatter is then listed in the target
basis as E S.

• Bridge. Between the deferred undo and its new position, the targets hold
  E·(original) at frame 0, and no gate reads them. The bridge replays both
  words cut by cut. We argue that it needs no new physical premise, by inherited
  H3 and common-label realization. Unlike PR1194's prefix-only substitution,
  the twisted window runs through A and the scatter.
• Price. The scatter goes 527 → 97. Frame paths, MOVE records and the paid
  profile {1:1323, 2:1342, 3:79, 4:44, 5:102, 6:11, 7:19} (rank mass 5,129)
  are unchanged.
• Precision. F is unchanged and B falls. No guard bit rises.
• Owner checker. The unchanged xcheck_p.py makes exactly H5_V_identity
  newly false.

Census of every committed lineage word (19 distinct words at base c6765481,
complete local ADDs):

word	base	deferred	B (exporter)	bits
PR915	13,208	12,778	9,534,616 → 8,742,940	100/189 → 99/189
PR967	11,783	11,353	10,394,084 → 9,602,408	102/192 → 101/192
PR1040	11,780	11,348 (−432)	10,394,084 → 9,602,408	102/192 → 101/192
PR1062	11,500	11,070	5,911,840 → 5,024,524	95/182 → 95/181
PR1122	10,652	10,222	3,910,388 → 2,996,128	92/176 → 91/174
PR1188	10,492	10,062	3,758,418 → 2,825,146	91/175 → 91/173
PR1709	11,488	11,058	5,921,344 → 5,034,028	96/182 → 95/181
PR1868 absorbed PR1188 (T ≠ I)	10,489	10,059	3,748,680 → 2,816,834	91/175 → 91/173
… 11 more (PR926, PR941, PR941-floor, PR965, PR1047, PR1062-composition, PR1062-pair-control, PR1208, PR1449, PR1543, PR1868-1062)		−430 each

• PR941's floor-calibration word misses the nine-stage guard at 193 bits, and its
  deferred word meets it at 192.
• Eight outside words (PR555/PR589 and others) have no target basis, so deferral
  is vacuous on them.

Maximality and refinement.

• Maximality. It is proved under fixed ordered frame paths.
  • The 111 targets' nonzero frame sets are pairwise disjoint.
  • None of the 585 (undo gate, B write) absorption pairs is frame-legal.
  • Full deferral attains the minimum over prefix splits of the literal undo
    order.
  • If frame paths may change, the package reports loose and strict counts of
    possible partners (up to 58, and up to 7 by the strictest criterion), so the
    claim is scoped.
• Order-ideal refinement. Allowing commuting reorders, keeping the order ideal
  {31, 51, 52} before the scatter gives 94. It goes through the same full checks.
  The results are PR1062 11,067, PR1188 10,059, PR1868-absorbed PR1188 10,056,
  and PR1040 11,345. It was found by exhaustive search over ideals of size ≤ 4
  plus greedy descent, so it is not claimed optimal.
• Selected-word heuristic. On PR589, a minimum-spanning-tree scatter basis G
  gives 24,305 → 24,190 (scatter 527 → 412). It is labelled heuristic. Owner flags
  H2, H5 and K become false there, and B rises slightly.

Not run.

• The native 5/9/11-stage C++ replay (no Boost here; PR1902's harness could take
  it).
• Hosted emission, for example PR1806's PR1122 invoice on the deferred word.
• The undo moves from exporter phase 1 (D) to phase 4 (B). Any phase-specific
  expectation in the native tools is unchecked.

Task and overlap

• Base and track. Base c6765481. Seed 6 → bit supplier, card
  bit-helper-contract (scope key 3475f46c8358c6a9211b), scope changed.
  The card asks for an H2/K replacement for a helper operation. This package
  also relaxes H5, which the card keeps, and its object is the target-basis
  block.
• Nearest construction. PR1704 (Ross Richardson, merged), a two-copy
  scatter, 527 → 407 under a copied-workspace contract. It is a different
  mechanism, and not additive: both rewrite the same block.
• Target-basis packages. PR794 (open), PR915 and the r420/r439 target-basis
  packages all keep E⁻¹ inside D.
• Contrasting deferral results. PR1580/PR1592 defer helper restorations to
  the end; this package defers a target-basis undo.
• Overlap searches. I searched PRs and Discussions for scatter, target basis,
  H5, V_identity, deferred undo, twisted target, 10,062, 11,070 and 10,059,
  including Discussion Handoffs and requests for independent checks #1166 and PRs through Bit ledger frame ranks: from-operations paid-rank mass audit (research/bit-ledger-frame-ranks-seedfeb2) #2099. None defers the target-basis
  undo or lists the scatter in the target basis.

Validation

python3 scripts/research_package.py --package research/r439-deferred-target-basis-seed06 --check-only
python3.12 scripts/research_package.py --package research/r439-deferred-target-basis-seed06

verify.py uses only the standard library and takes about 65 s. Its checks
raise ValueError, and it is registered plain and under -O.

Inputs. All 29 inputs and 2 provenance files are pinned by SHA-256 and git blob. The owner checker
and exporter run from the verified bytes.

Per word, the verifier:

• re-derives the deferral;
• replays the literal 661-column COPY/ERASE dirty boundary forward and reverse;
• checks frame paths, MOVE records, the exporter paid profile and both precision
  guards, the owner-flag delta, the four H5-tw equations exactly, the per-cut
  bridge and the maximality census.

It also rebuilds the committed PR1062 and PR1188 candidates byte for byte, and
adds --census-scan, which found 27 R439 words: 27 listed, 0 unlisted.

33 controls, all rejected:

• the old S listing;
• the undo moved after B[0];
• a dropped undo gate;
• preparation-order undo;
• non-commuting swaps;
• a wrong E S row;
• a corrupted pin;
• the bridge on blind or old-S or swapped words;
• an owner delta on (base, base);
• legal frame raises against paths and against the profile;
• the maximality census with the wrong base;
• the precision guard on the 193-bit floor word.

A 26-mutant run against the verifier caught 20. The 6 survivors are listed in
the README: two call-site removals of pinned outputs, an equivalent </<=
mutant, two redundant pins, and a gzip mtime change. Tested on Python 3.12.15
and 3.14.8.

Pre-PR review. Three lenses (proof, verifier, claims) returned
ship-with-fixes, and all fixes are applied:

• The proof lens confirmed the lemma and its converse and found the order-ideal
  refinement.
• The verifier lens independently reproduced 10,492 → 10,062 byte for byte. It
  found that the bridge rebuilt the deferred side from the base word, which is
  now fixed, and found missing check-level controls, now 33.
• The claims lens found that the scope label should be "changed", that the
  wording implied a public pre-claim, and that the PR794/PR716/Conditional kappa = 0.001291542455423938: two-layer target factoring on R715 (+0.1461% over #470) #476/PR686 credits
  were missing. All are fixed.

Credit

• Target-basis lineage:
  • Gareth Davidson / bitplane (PR915, the E block deferred here; PR926, PR941,
    PR1122, PR1188);
  • commdata2338 (PR794);
  • Scott Woolsey Biggart (PR713);
  • Sagar Thakrar (PR716);
  • Dugongue (Conditional kappa = 0.001291542455423938: two-layer target factoring on R715 (+0.1461% over #470) #476/Conditional kappa = 0.001295508560071773: fourteen target factors on PR473 (+0.1226%) #478).
• Lineage words:
  • Sricharan Vagvala (PR967);
  • Ross Richardson (PR923, PR965, PR936);
  • Aaron Wang / navinor (PR1015, PR1127);
  • Sagar Thakrar (PR1062, PR1868);
  • woklerx (PR1040, PR1047);
  • Hanson Sun / bbMisk (PR1449, PR1221, PR1902);
  • ToikY (PR1543, PR1208);
  • Cinna Davis / 1337isnot1337 (PR1709);
  • DreamingOfClouds (PR589, PR545).
• Interface and checkers:
  • eumemic (PR543 H1–H5 lemma, PR555, xcheck_p.py);
  • Zhihao Chen (PR425);
  • Mikhail R. Gadelha (PR686);
  • woklerx (PR1194);
  • Arham Tahir (PR1311);
  • Dylan Crow (exporter).
• Nearest construction: Ross Richardson (PR1704).

AI disclosure: prepared by Sagar Thakrar with substantial Anthropic Claude
assistance, including explorer, judge, builder and reviewer subagents. No
independent human review. New work is Apache-2.0.

Open next questions

1. Native 5/9/11-stage replay of the deferred words, for example with PR1902's
   harness.
2. Larger order ideals, or a proof that 94 is optimal over commutation-closed
   splits.
3. Re-running PR794's greedy target-basis search with the deferred objective,
   which counts E S instead of S.
4. Hosted invoice of the deferred PR1122 word via PR1806's route.
5. An optimal scatter basis G on the selected PR589 word. The MST gives 412.
6. Composition with the restored helper-shear descent on PR1188's star D. B's
   drop frees nine-stage headroom, which is the descent's binding resource.