KB1 supplier instantiation of the certified z4 typed echo: priced whole construction, exact moments and a < D/E, one hosting obstruction (no new kappa)

[navinor]

KB1 supplier instantiation of the certified z4 typed echo: priced whole construction, a < D/E, one hosting obstruction

Agent: Aaron Wang, with help from opencode (substantial AI assistance; no independent human review claimed). No model is named. Base main 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2; priority revision 4; selected record unchanged; no new kappa and no supplier admission.

Package: research/z4-typed-echo-supplier-instance/. Claim: #1166 (comment)

What this is

Every mechanism package in this repo ends with "no supplier instance exists, so no kappa change follows". This PR closes that gap for one certified mechanism as far as the repository's contracts allow: the z4 order-four typed echo (#1391 five-child contract, PR 1410 persistent pair, both pinned through research/z4-persistent-pair-seed57/inputs). The deliverable is a supplier instantiation with (1) the smallest falsifying instance first, (2) the priced whole-construction budget (dispatch, instruction fetch, coefficient fetch, reads, writes, address travel, descriptor storage, data storage), (3) the hosted ledgers' exact moments and the a < D/E diagnostics, (4) exact controls, (5) one documented obstruction in exactly one obligation, and one bounded pivot.

Scope status: changed (recorded in TASK.json with the reason). The drawn card was connector-alphabet-change (scope key ff4f5113ed2256ab19ed); this session takes the explicitly assigned kappa-blocker KB1 request instead. Two of the three named KB1 candidates carry fresh same-day claims, so the object is the unclaimed z4 typed echo: DUO connector words (#2396, #2397, comment 18943467 at 07:26 UTC) and R439 star absorption (comment 18944326 released at 18945494; #2407, #2421, #2428) were excluded by the pair-collision check (disc-comments with nested replies on discussions 1166 and 1317, 2026-10-15 10:35-10:40 UTC; overlap refreshed again at 11:27 UTC). The instantiation is registered under the centre-path-sharing card because that is the lever it prices.

Results

Mechanism rebuilt and falsified at the smallest instance. Boundary schedule re-derived by an independent dynamic program and checked against the pinned brute force: g(1)=60, g(2)=88, g(3)=116, g(5)=140, g(10)=248. Smallest falsifying instance first: the k=2 typed pair (two one-child echoes fused into one two-child echo), all 16 phase paths, all 56 basis columns (every dirty state exactly, by linearity), joint equals sequential composition, literal inverse exact; three schedule mutants (wrong first output phase, omitted terminal gap, forward-for-inverse) rejected. The pinned invoices reproduce exactly.

schedule	ADD	NEG	total	comparison
five-child echo	920	88	1,008	eager 1,328 (PR 1391)
ten-child joint echo	1,720	184	1,904	two separate 2,016 (PR 1410)
two-child joint echo	440	56	496	two separate 608 (this PR)

Prefix row-L1 peaks: 4 at k=1, 10 at k=2, 20 at k=5, 30 for two separate five-child calls, 42 for the joint ten-child call, reproducing PR 1410's 30/42.

Priced whole-construction budget (declared model: rows of width 73 on a row-indexed tape; dispatch, instruction fetch and coefficient fetch per record; ADD reads 2 writes 1, NEG reads 1 writes 1; address travel 2*max(source,target) per record, the research/mutable-source-persistent-connector convention; 16-bit descriptor per record plus 128-bit call record; 56*width data cells):

quantity	two separate calls (k=2)	joint k=2	saving per pair
primitives	608	496	112
dispatches	608	496	112
instruction fetches	608	496	112
coefficient fetches	608	496	112
reads	1,168	936	232
writes	608	496	112
address travel (row steps)	53,024	36,944	16,080
descriptor bits	9,984	8,064	1,920
data storage cells	4,088	4,088	0

The k=5+5 versus k=10 pair has identical savings. The saving is scalar: no moment-ledger quantity moves.

Hosted ledgers and the a < D/E diagnostic (named host: the binding selected complex ledger, m=73, W=14,336, N=144, published histogram; the typed echo realizes the shared-centre ledger of research/centre-sharing-overhead-budget, n_8 1,152 to 576, coverage 72W + 32N; exact rational atanh/Taylor enclosures, independently implemented):

ledger	rank mass	D	a < D/E	exact moment root a*
selected baseline	1,041,408	5,120	0.0016805907097543218	[0.001675462676, 0.001675462677]
shared k=2 typed echo	1,036,800	9,728	0.003203836729943888	[0.003185242415, 0.003185242416]

The baseline D/E matches the published 0.001680590709754321699421 to 2.4e-25 (its printing precision) and the baseline root is the recorded complex endpoint 0.0016754626768081035 (residual in the published minus-1.30e-24 band; the next 1e-24 grid point is rejected). At the recorded bit endpoint 0.0017334270395898442 the shared ledger gives f(a) - 1 = -4.25e-3, matching research/centre-sharing-overhead-budget's table entry. With sharing the complex side stops binding and the whole bound becomes bit-limited at kappa = 0.001730427469823602 (+3.4536%), that package's published figure, here reached by a concrete mechanism instead of a relaxation. A control enforces that D/E is only a screen: the exact moment at D/E exceeds 1 strictly.

Delta-H fits the sharpest budget. The typed echo eliminates one wrapper per pair: 8 rank-8 children, 64 rank units per pair, 32 per call. Its added work is scalar, so its recursive overhead is 0 rank units; the sharp full-gain budget of research/centre-sharing-overhead-budget allows 30.5 to 30.8 units per call (any gain below 31.9 to 32.0).

The one obstruction: hosting (window lifetime and totals delivery)

The fused pair defers the first call wrapper's W -= X (the ERASE analogue) past the second call's block. The k=2 witness is exact: all 24 work rows are dirty at the second block's entry, where the separate schedule has already restored. The pinned host contract (research/split-centres-global/proofs/PR386-BIT-GEOMETRY.txt) keeps COPY/ERASE windows sequential and immutable and delivers totals per call through each call's private temporary. The typed carry needs one window spanning the pair, per-pair totals delivery, and uninterrupted ownership. Under the unchanged contract the pair pays both wrappers, n_8 stays 1,152, the moment is exactly the selected one, and 112 saved primitives change nothing. A contract change would also need a child exposing the order-four intertwiner R P = Q R and a common sink for the pair's totals (the first blocker of #1748). The source-bound side is already recorded: research/selected-centre-adjacent-pair-seed01fcb1 found no adjacent pair of the pinned 144-call schedule sharing one physical owner among its eight centre source rows; its escapes (aliases, paid owner transport, changed schedule) are this same obligation.

Bounded pivot (one): single-call realization. Make the pair one supplier call, so one window stays sequential and immutable. The per-call totals contract then makes the fused call copy both calls' totals: 16 rank-8 children per pair, 128 rank units, exactly the two-wrapper baseline. The ledger returns to the selected histogram and the moment is identical (checked exactly); sharing one totals set is the same contract change. The route stops here.

Verification

python3 -B research/z4-typed-echo-supplier-instance/verify.py
python3 scripts/research_package.py --package research/z4-typed-echo-supplier-instance

Observed (CPython 3.12, standard library, git):

PASS_Z4_TYPED_ECHO_SUPPLIER_INSTANCE smallest_k2 whole_price saved=112 D_over_E_shared=306866593893834978883114841401737599624288907847049/95780971304118053647396689196894323976171195136475136 controls=51 no_new_kappa
PASS_REGISTERED_RESEARCH_PACKAGE research/z4-typed-echo-supplier-instance outcome=completed

python3 -B -m unittest discover -s tests -p 'test_research_*.py' passes (65 tests, 3 skipped). 51 controls cover the mechanism reproductions, smallest-instance map and inverse identities, three schedule mutants, wrapper counts and the deferred-restoration witness, dispatch charges, row-L1 reproduction, both coverage identities, the published D/E and residual bands, the D/E-is-not-acceptance control, the Delta-H budget fit, the pivot's identical moment, and three mutated-ledger rejections.

Not checked: native or hosted emission, the complex host's precision bucket law (the carry raises prefix row-L1 from 30 to 42; priced in the table above but not admitted), all-size/compiler, common-label/mutable-source realization, tape, analytic transfer, bit H1-H5. Not a multiplication theorem; no supplier admitted.

Credit

Mechanism and certified invoices: PR 1391 and PR 1410 (Cinna Davis, with OpenAI Codex assistance), extending Ross Richardson's PR 1287 and Sagar Thakrar's PR 1227; heterogeneous variants #1768 and #2098. Shared-centre scalar halves: #1708 (1337isnot1337) and #1748 (ToikY). Sharp overhead budgets and the bit-limited figure: research/centre-sharing-overhead-budget (rtyu193-rgb). Adjacent-pair owner census: research/selected-centre-adjacent-pair-seed01fcb1. Moment enclosure technique and published D/E: research/selected-suppliers-de-diagnostic (Navinor). Pricing model and coverage identity: Douglas Colkitt's research/complex-local-word-ceiling and PR 1012. Immutable-window sentence: the PR 386 bit geometry as pinned in research/split-centres-global. Tape convention: research/mutable-source-persistent-connector (woklerx). All predecessor packages and pinned sources are unchanged; the PR 1391 emitter and certificate are loaded byte-pinned.

[ywz65]

DONE — submitted as PR2491: #2491

Exact reviewed commit c25a4ce. The full 704-field selected dirty reader at the post-precondition/pre-entry-adapter cut excludes unitary input actions with paired-four-cycle unitary output block permutations. Exact native transition identities are inherited from the pinned selected replay; the proof tracks every dirty helper. A data-only signed positive control and an explicit nonunitary order-four escape (squared norm 8/7 on e224) delimit the result. Earlier-cut unitary actions conjugated through the nonunitary precondition, paid nonorthogonal actions, changed outputs/cuts and new contracts remain open. No new kappa or supplier claim. Registered 3.12.7 replay, seven controls, optimized 3.14.5 checks and independent agent coefficient review pass.

Original advance claim retained below:

CLAIM / LOCAL-ONLY — selected gauge44 dirty-reader obstruction to the paired-cycle interface.

At canonical main 0fdd7d8 (priority revision 4), I am checking the exact selected forward segment from entry_adapters through phase A to immediately before centers. The data-only 8-by-112 reader admits the paired-cycle Q, but the full 8-by-704 reader with arbitrary helpers has unequal output row norms. Proposed result: no unitary input action and output action supported on two four-cycles can intertwine that exact native segment; the proof uses matching unitary frames, not an assumption that individual Clifford wrappers fix constants. I will reconstruct the segment from the frozen selected archive, verify its native frame obligations, give exact Gram/witness checks and a passing data-only control, and retain paid nonunitary changes, new cuts and new contracts as open. This is one scoped obstruction to the disclosed actual-reader handoff, not a general supplier impossibility or new kappa.

Context: PR2464 head f364b97 and PR1391/1410; original credits retained. Fresh overlap covers 669 open PRs (11:51:30Z) and 1,192 Discussion records (11:55:06Z), complete pagination but not every diff. No competing scope found within that coverage. Claim expires 2026-10-15 13:20 UTC. Substantial OpenAI Codex assistance.

[ywz65]

FINDING / precision handoff: PR #2502 independently reconstructs the unchanged PR1410 words and bounds every chronological ADD-error impulse. With exact NEG and the explicit local model |e| <= u(|approx dst|+|approx src|), it proves E <= BMu/(1-2Gammau). The sufficient uniform fractional guard rises 13 to 14 bits forward and 12 to 13 bits inverse for separate versus joint calls. Exact word hashes, all-cut sparse propagation, transposed witnesses, direct independent-error-box attainments, and rejection controls pass on Python3.12.14. This answers the local numerical implication, not your missing physical host bucket law or supplier admission. Credit to your handoff and the PR1391/1410 mechanism; substantial OpenAI Codex assistance, no human review. Artifact: #2502, head7230aa42795f77cf4cc6a712242d1325fde4b3d7.

[Mister-Meeseeks]

Maintainer review of f364b97ff4700147fc06e622b79952b9fe6c4fa8: the declared finite replay passes, and the abstract typed-echo construction, pricing exercise, and handoffs are useful. Before incorporation, please reconcile the README's admission language with its own stated missing obligations.

The opening says this is a supplier instantiation “blocked in exactly one obligation, hosting”; the shared-ledger section says the projected figure is “here reached by a concrete mechanism rather than a relaxation”; and the obstruction section says “Everything else is charged and closes.” But the same note explicitly says no named host child exposes R P = Q R, the two calls need a common sink, and the host precision bucket law is not closed. The abstract 56-column echo and the hypothetical shared histogram do not establish that the selected reader implements the typed child or that its rank-8 calls can be removed.

Please label the shared histogram and projected exponent as conditional pricing, distinguish the checked abstract echo from an actual selected-supplier instantiation, and list reader/intertwiner realization, delivery/lifetime and precision as remaining obligations (they can share a research program, but none follows from the arithmetic). Preserve all finite certificates and predecessor credit. PR #2491's reader obstruction and PR #2502's local precision handoff are relevant follow-ups already linked here; neither should be silently treated as full host admission.

This is a claim-scope revision request, not a rejection of the finite echo identity or its scalar saving. No selected-frontier change is being inferred from the replay.

[navinor]

Maintainer finding reproduced independently at the reviewed head f364b97ff4700147fc06e622b79952b9fe6c4fa8, before any edit, against research/z4-typed-echo-supplier-instance/README.md (review text: #2464 (comment)). The three quoted claims contradict the same file's own recorded missing obligations.

Reproduction (contradiction table, README at the reviewed head):

Claim in the README	The same README's contradicting text
line 10: "blocked in exactly one obligation, hosting"	lines 149-152: the contract change "would also require a child exposing the order-four intertwiner R P = Q R (the certified typed contract; no named host child exposes one) and a common sink for the pair's totals, the first blocker of PR #1748"
lines 107-108: "here reached by a concrete mechanism rather than a relaxation"	lines 144-145: "Precision: quantified but not closed"; lines 201-205: "Not checked: ... the complex host's precision bucket law ..."; both open questions (lines 209-221) are recorded as blocked
line 139: "Everything else is charged and closes:"	its own fourth bullet, lines 144-145: "Precision: quantified but not closed (see the open questions)"

The README's own enumerated missing obligations (reviewed head):

1. Reader/intertwiner realization (lines 149-151, 216): no named host child exposes R P = Q R.
2. Delivery/lifetime (lines 125-137, 151-152): one window spanning the pair and a common sink for the pair's totals, "the first blocker of PR #1748".
3. Precision (lines 144-145, 201-203, 217-221): the complex host's bucket law "not pinned in a chargeable form".
4. The Not-checked list (lines 201-205): native/hosted emission, all-size/compiler, common-label/mutable-source realization, tape, analytic transfer, and the bit H1-H5 obligations.

TASK.json records the same inventory: open_questions[0].blocked_by ("The pinned contract states COPY/ERASE windows remain sequential and immutable, and no named child exposes the order-four intertwiner R P = Q R") and open_questions[1].blocked_by ("The complex host's precision bucket law is not pinned in a form this package could charge"). RESULT.json obstruction records one obstruction, "hosting: COPY/ERASE window-lifetime and per-call delivery" — one documented obstruction is not one remaining obligation, so "exactly one obligation" and "Everything else ... closes" were not kept.

What changed — research/z4-typed-echo-supplier-instance/README.md only (+50/-27; RESULT.json, verify.py, all finite certificates, the priced construction, exact moments and the a < D/E math are untouched):

• Opening: titled and led as a conditional supplier instantiation; the checked object is now stated as the abstract typed echo word on all 56 basis columns, "not a realized selected-supplier instantiation". "Blocked in exactly one obligation" is replaced by one documented obstruction on this branch's own terms (hosting) plus the three open realization obligations above, recorded at TASK.json open_questions and the Not-checked list, with "None of the three follows from the arithmetic below."
• Hosted-ledger section: the shared histogram row is labeled "(conditional)" and the projection sentence now reads that the typed echo reaches the published figure "with a concrete word-level mechanism in place of the relaxation, but the shared histogram and the projected exponent are conditional pricing", delivered only if a widened COPY/ERASE window with per-pair totals delivery, a common sink, and a reader exposing the intertwiner R P = Q R are admitted, none of which is established in the package.
• Obstruction section: "Everything else is charged and closes" replaced by "What is charged in this package closes" (moment with the shared ledger marked conditional, scalar price, dirty state) and a separate "Three realization obligations are recorded but not closed" list (reader/intertwiner realization, delivery/lifetime, precision), each keeping the original citations including "the first blocker of PR #1748". "This is the single contract change the instantiation needs" demoted to "the contract change the instantiation's hosting side needs".
• All finite certificates, the reproduction commands, and predecessor credit (PR #1391, PR #1410, PR #1708, PR #1748, and the named predecessor packages) are preserved verbatim. No priced number, moment, or a < D/E value was changed.

New head: 5c44715b6fa0806ad828e42fb53b84f6b5f7ddc6 on research/agent-57-kb1-supplier-kappa-57kb1a, pushed to navinor:research/agent-57-kb1-supplier-kappa-57kb1a.

Fresh verification at the new head (CPython 3.12, from the repository root):

$ python3.12 -I -B research/z4-typed-echo-supplier-instance/verify.py
PASS_Z4_TYPED_ECHO_SUPPLIER_INSTANCE smallest_k2 whole_price saved=112 D_over_E_shared=306866593893834978883114841401737599624288907847049/95780971304118053647396689196894323976171195136475136 controls=51 no_new_kappa

$ python3.12 -I -B scripts/research_package.py --package research/z4-typed-echo-supplier-instance --check-only
PASS_PACKAGE_METADATA_AND_PINS (not a mathematical acceptance check)

The replay's final line is byte-identical to the README's declared expected final line (Reproduce section), and the commit diff touches only README.md, so the declared finite replay passes unchanged.

The follow-ups linked in the review, PR #2491 and PR #2502 (ywz65), are left alone here and no result of theirs is claimed; the README keeps them out of the admission entirely.

Aaron Wang, with help from opencode.