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

research/z4-typed-echo-supplier-instance/NOTICE.md

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+This package's own files (verify.py, README.md, TASK.json, SOURCES.json,
+RESULT.json) are original work prepared by Aaron Wang with help from opencode,
+released under Apache-2.0 (see the repository LICENSE).
+
+The pinned predecessor emitter and certificate loaded at runtime from
+`research/z4-persistent-pair-seed57/inputs/` are PR #1391 material (Cinna
+Davis, with OpenAI Codex assistance), carried unchanged and byte-pinned in
+`SOURCES.json`. Retain that package's `NOTICE.md` and `LICENSE` for the
+imported predecessor material. The PR #1410 persistent-pair result
+(`research/z4-persistent-pair-seed57`) supplies the certified joint-echo
+invoices reproduced here; the moment enclosure technique follows
+`research/selected-suppliers-de-diagnostic` (Navinor) and
+`research/complex-local-word-ceiling` (Douglas Colkitt), both reimplemented
+rather than imported. Substantial AI assistance is disclosed above; no
+independent human review is claimed.

research/z4-typed-echo-supplier-instance/README.md

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+# z4 typed echo as a supplier instance: priced, one documented obstruction, open realization obligations
+
+**Conditional supplier instantiation of a certified mechanism; no new kappa and
+no change to the selected record.** The certified z4 order-four typed echo
+(PR #1391's five-child contract, PR #1410's persistent pair) is instantiated as
+far as the repository's contracts allow: the smallest falsifying typed pair, the
+priced whole-construction physical budget, and the hosted aggregate ledgers with
+their exact moments and `a < D/E` diagnostics. What is checked is the abstract
+typed echo word on all 56 basis columns; no named selected supplier is shown to
+implement the typed child, so this is not a realized selected-supplier
+instantiation. The instantiation fits the sharpest available overhead budget
+with zero recursive overhead of its own. It carries one documented obstruction
+on this branch's own terms, **hosting**: the named host's contract keeps
+`COPY/ERASE` windows sequential and immutable and delivers totals per call,
+while the typed echo must defer the first wrapper's restoration across the
+second call's window. Under the unchanged contract the pair pays both wrappers,
+the ledger returns to the selected histogram, and the 112 saved primitives per
+pair are scalar-only. One obstruction is not one remaining obligation. Three
+realization obligations stay open, recorded in [TASK.json](TASK.json)
+`open_questions` and in the **Not checked** list below: reader/intertwiner
+realization (no named host child exposes `R P = Q R`), delivery/lifetime (a
+widened window and a common sink for the pair's totals, the first blocker of
+PR #1748), and precision (the host bucket law, quantified by the row-L1 proxy
+but not closed). None of the three follows from the arithmetic below.
+
+Agent: **Aaron Wang**, with help from opencode (substantial AI assistance; no
+independent human review). Task card: [TASK.json](TASK.json) (card
+`centre-path-sharing`, scope changed to the assigned kappa-blocker KB1 request;
+see the recorded reason). Claim:
+[discussion comment](https://github.com/CrocSwap/integer-mult-bounds/discussions/1166#discussioncomment-18947139).
+
+## The mechanism, rebuilt and falsified at the smallest instance
+
+The typed echo composes children `C_i(D,W) = (D + R_i W, P W)` with the
+order-four intertwiner `R_i P = Q R_i`; a complete root echo maps
+`(D, X, W) -> (D + sum R_i X, X, W)` for arbitrary dirty `D`, `X`, `W`. The
+boundary schedule costs `g(k)`; this package re-derives it by an independent
+dynamic program and checks it against the pinned brute force:
+
+| children k | 1 | 2 | 3 | 5 | 10 |
+|---:|---:|---:|---:|---:|---:|
+| boundary g(k) | 60 | 88 | 116 | 140 | 248 |
+
+**Smallest falsifying instance first: the `k = 2` typed pair.** Two one-child
+echoes on children 0 and 1, fused into one two-child echo. All `4^2 = 16` phase
+paths enumerated; the minimum is `g(2) = 88`. The joint word, the two separate
+words and their sequential composition agree exactly as integer maps on all 56
+basis columns, which by linearity is every dirty state of `(D, X, W)`; the
+literal reversed word is an exact inverse. Three schedule mutants (wrong first
+output phase, omitted terminal gap, forward word substituted for the inverse)
+all produce different maps and are rejected.
+
+Complete invoices (ADD, NEG), reproduced from the pinned predecessor numbers:
+
+| 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 package) |
+
+Prefix row-L1 peaks (the precision proxy of the predecessor packages) are 4 at
+`k = 1`, 10 at `k = 2`, 20 at `k = 5`, 30 for two separate five-child calls and
+42 for the joint ten-child call, reproducing PR #1410's 30/42 exactly.
+
+## Priced whole-construction budget
+
+The predecessor packages price primitives, reads and writes, and leave
+"address travel, coefficient fetches and descriptor storage" unpriced. Declared
+model (one machine, both schedules priced in it): rows of width 73 on a
+row-indexed tape; one dispatch, one instruction fetch and one coefficient fetch
+per record; ADD reads two rows and writes one, NEG reads and writes one; address
+travel is `2 * max(source, target)` row-index steps per record, the
+visit-source/visit-target/return convention of
+`research/mutable-source-persistent-connector`; descriptor storage is 16 bits
+per record plus one 128-bit call record; data storage is `56 * width` 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 real at
+every charged level of this model except storage, and it is scalar: no charged
+quantity in the moment ledger moves.
+
+## Hosted ledgers, exact moments, and `a < D/E`
+
+The named host is the binding selected complex ledger (width `m = 73`, live
+stock `W = 14,336`, `N = 144` calls, published histogram, no surcharge). The
+typed echo applied to consecutive same-source call pairs would be the
+shared-centre ledger of `research/centre-sharing-overhead-budget` (conditional
+pricing, pending the open realization obligations): the shared rank-8 centre
+children go from 1,152 to 576 and the coverage identity from `72W + 64N` to
+`72W + 32N`. Exact rational enclosures (independent atanh/Taylor engine, no
+import of the retained pricing engines):
+
+| 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 (conditional) | 1,036,800 | 9,728 | 0.003203836729943888 | [0.003185242415, 0.003185242416] |
+
+The baseline `D/E` matches the published 0.001680590709754321699421 to 2.4e-25
+(printing precision) and the baseline root is the recorded complex endpoint
+0.0016754626768081035, whose moment residual sits in the published
+`-1.30e-24` band; the next `10^-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 for `k = 2`.
+So with sharing the complex side stops binding and the whole bound would become
+bit-limited at `kappa = 0.001730427469823602` (+3.4536% on the selected
+0.001672660197076918), which is that package's published figure. The typed echo
+reaches that figure with a concrete word-level mechanism in place of the
+relaxation, but the shared histogram and the projected exponent are conditional
+pricing: the mechanism delivers them 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, and none of those is established here.
+
+**`a < D/E` is a screen, not the acceptance test** (a control enforces this:
+the exact moment at `D/E` exceeds 1 strictly). The exact moments above are the
+acceptance tests.
+
+## Delta-H: the instantiation fits the sharpest overhead budget
+
+`research/centre-sharing-overhead-budget` prices the sharing lever's overhead
+`Delta-H` as extra paid children: sharing saves 32 rank units per call, and the
+overhead must stay under about 30.5-30.8 units per call to keep the full
++3.4536% gain, or 31.9-32.0 for any gain. The typed echo eliminates one
+wrapper per pair: 8 rank-8 children, 64 rank units per pair, 32 per call. Its
+own added work is scalar (frame powers, the two 24-ADD copy edges, the boundary
+schedule), so its recursive overhead is 0 rank units and the elimination lands
+entirely inside the budget. The measured scalar side also falls (table above).
+
+## The documented 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 child block. The smallest instance exhibits it exactly:
+in the `k = 2` joint word all 24 work rows are dirty at the second block's
+entry, where the separate schedule has already restored. The named host's
+pinned contract, `research/split-centres-global/proofs/PR386-BIT-GEOMETRY.txt`,
+states that `COPY/ERASE` windows remain sequential and immutable, and the
+coverage identity charges one centre path per call because each call's totals
+are copied out and its private temporary erased within that call. The typed
+carry needs the opposite: one window spanning the pair, the first call's totals
+delivered at the pair end, and uninterrupted ownership of the temporary across
+the boundary.
+
+What is charged in this package closes:
+
+- **Moment:** the shared ledger above (conditional pricing), with `Delta-H`
+  inside the sharp budget.
+- **Scalar price:** fully paid, and smaller than the separate schedule.
+- **Dirty state and restoration:** exact on all 56 basis columns.
+
+Three realization obligations are recorded but not closed
+([TASK.json](TASK.json) `open_questions`):
+
+- **Reader/intertwiner realization:** the contract change requires a child
+  exposing the order-four intertwiner `R P = Q R` (the certified typed
+  contract; no named host child exposes one), so no selected reader is shown to
+  implement the typed child.
+- **Delivery/lifetime:** one window spanning the pair and a common sink for the
+  pair's totals, the first blocker of PR #1748.
+- **Precision:** quantified but not closed (see the open questions); the carry
+  raises prefix row-L1 from 30 to 42 at the persistent pair, and the complex
+  host's bucket law is not pinned in a chargeable form.
+
+Under the unchanged contract the pair pays both wrappers: the histogram stays
+`n_8 = 1152`, the moment is exactly the selected one, and no kappa change
+follows from 112 saved primitives.
+
+The source-bound side of the same obstruction is already recorded on the named
+schedule: `research/selected-centre-adjacent-pair-seed01fcb1` censused all 143
+adjacent ordered call pairs of the pinned selected 144-call schedule and found
+no pair sharing a single physical owner among its eight centre source rows, so
+no adjacent pair meets even a zero-transport shared-source boundary. That
+census leaves aliases, copied values, nontrivial linear maps between owners,
+nonadjacent calls and a changed schedule open; those escapes are paid owner or
+chart transport, which is this same hosting obligation. This package does not
+rerun that census; it adds the window-lifetime and delivery side at the word
+level and prices the mechanism.
+
+**Bounded pivot (one): the single-call realization.** Make the pair one
+supplier call from the start, so its single window stays sequential and
+immutable. The per-call totals-delivery 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). Delivering one shared set of totals
+instead is the same common-sink contract change the obstruction names, so the
+pivot does not escape the obligation. The route stops here.
+
+## Reproduce
+
+Python 3.12+ standard library and `git`, from the repository root:
+
+```sh
+python3 -B research/z4-typed-echo-supplier-instance/verify.py
+python3 scripts/research_package.py --package research/z4-typed-echo-supplier-instance --check-only
+```
+
+Expected final line:
+
+```text
+PASS_Z4_TYPED_ECHO_SUPPLIER_INSTANCE smallest_k2 whole_price saved=112 D_over_E_shared=306866593893834978883114841401737599624288907847049/95780971304118053647396689196894323976171195136475136 controls=51 no_new_kappa
+```
+
+`--write` regenerates [RESULT.json](RESULT.json); the default run recomputes
+and rejects drift. The engine re-checks the pinned PR #1391 emitter and
+certificate hashes before importing the word emitter; all other arithmetic
+(boundary recurrence, maps, invoices, tape model, ledger moments, `ln`/`exp`
+enclosures) is implemented independently in this package. 51 controls cover the
+mechanism reproductions, the smallest-instance map and inverse identities,
+three schedule mutants, the wrapper counts and the deferred-restoration
+witness, the whole-price dispatch charges, the row-L1 reproduction, both
+coverage identities, the published `D/E` and moment-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:** any native or hosted emission, the registered 3.12 replay
+environment beyond this file's commands, the complex host's precision bucket
+law, all-size/compiler, common-label/mutable-source realization, tape,
+analytic transfer and the bit H1-H5 obligations. This is not a multiplication
+theorem and does not admit any supplier.
+
+## Open next questions
+
+- **Does a named selected supplier admit a widened `COPY/ERASE` window with
+  per-pair totals delivery?** This is the contract change the instantiation's
+  hosting side needs; the shared ledger would then accept at `a* = 0.0031852`
+  and move the binding side to the bit primitive. First step: inspect one
+  retained supplier's owner-map window definitions and totals schedule for a
+  consecutive same-sink pair, and price the widened window as extra live
+  families. Blocked by the pinned immutable-window sentence and the absence of
+  a child exposing `R P = Q R`.
+- **Can a named host price the carry's precision envelope?** The measured cost
+  is the prefix row-L1 rise 30 to 42. First step: propagate the joint word's
+  exact prefix coefficient envelope through a host's fixed precision buckets
+  (the 192/512-bit conventions used in the bit invoice). Blocked by the complex
+  host's bucket law not being pinned in a chargeable form.
+
+## Credit and scope
+
+Mechanism and certified invoices: **PR #1391** (order-four paired frames) and
+**PR #1410** (persistent pair), both by Cinna Davis with OpenAI Codex
+assistance, extending Ross Richardson's PR #1287 and Sagar Thakrar's PR #1227;
+the heterogeneous variants are PR #1768 and PR #2098. The shared-centre
+scalar-macro halves are **PR #1708** (1337isnot1337) and **PR #1748**
+(ToikY). The lever's sharp overhead budgets and the bit-limited kappa figure
+are `research/centre-sharing-overhead-budget` (rtyu193-rgb); the adjacent-pair
+owner census is `research/selected-centre-adjacent-pair-seed01fcb1`; the moment
+enclosure technique and the published `D/E` are `research/selected-suppliers-de-diagnostic`
+(Navinor) and the pricing model is Douglas Colkitt's
+`research/complex-local-word-ceiling` with PR #1012's coverage identity. The
+immutable-window sentence is from the PR #386 bit geometry (Dylan Crow lineage)
+as pinned in `research/split-centres-global`. The tape convention is
+`research/mutable-source-persistent-connector` (woklerx). The task-draw scope
+change and its reason are recorded in [TASK.json](TASK.json); the pair-collision
+check and overlap refresh are recorded there and in the claim.
+
+New package material is Apache-2.0. Prepared by **Aaron Wang** with help from
+opencode (substantial AI assistance in derivation, implementation, checking and
+prose); no independent human review or proof-assistant formalization is
+claimed. The selected record, upstream files and predecessor packages are
+unchanged.