Research: F17 block-scale scan bill at the exact entry width (no new kappa)

research/qq16-f17-scan-bill/CERTIFICATE.json

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+{
+  "schema_version": 1,
+  "status": "PASS_QQ16_F17_SCAN_BILL",
+  "producer": "F_0_then_B_1_2",
+  "consumer": "PR2707_zero_retention_decoder_in_F17",
+  "priced_term": "block_scale_scan",
+  "physical_bill": "F17 direct Boolean block-scale scan gate evaluations",
+  "parameters": {
+    "h": 73,
+    "lambda": 1,
+    "f": 64,
+    "e": 0,
+    "beta": 64
+  },
+  "Q0": 80,
+  "b": 79,
+  "k": 137,
+  "Qmax": 497,
+  "E": 15,
+  "W": 532,
+  "w": 529,
+  "p": 137,
+  "popcount_span": 392,
+  "popcount_sum": 1628,
+  "lines": 336,
+  "scan_per_line_nd": 4232,
+  "scan_per_line_const": 2415,
+  "scan_nd_coefficient": 1421952,
+  "scan_owner_coefficient": 811440,
+  "control_W": 456,
+  "control_w": 453,
+  "control_p": 122,
+  "control_scan_per_line_nd": 3624,
+  "control_scan_per_line_const": 1984,
+  "control_scan_nd_coefficient": 1217664,
+  "control_scan_owner_coefficient": 666624,
+  "selected_kappa": "0.001672660197076918",
+  "kappa_changed": false
+}

research/qq16-f17-scan-bill/MASTER-HANDOFF.md

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+# Handoff
+
+Pinned CrocSwap main: `6f100d4bb5083f8c35d96fd95a539811c62f245c`.
+Selected kappa, unchanged: `0.001672660197076918`.
+
+Did not switch cards. The scan term of #3374 was not evaluated at `W=532`
+on that main. The pair-kernel and field-bit coefficients stay the submitted
+#3374 values.
+
+Claim: at `lambda=1`, `f=64`, `e=0`, `beta=64`, `W=532`, the F17 decoder's
+common block-scale scans cost at most `1421952 N D + 811440 N` gate
+evaluations. That is the scan subtotal of the direct Boolean arithmetic bill.
+
+Stop. Scalar ADDs, wrappers, maps, addressing, movement and cleanup remain
+unpaid. This is not a new kappa.

research/qq16-f17-scan-bill/NOTICE.md

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+# Notice
+
+New derivation, checker, tests and prose in this directory are Apache-2.0,
+following the repository license.
+
+Predecessor files are not modified. Their authors and licenses remain as
+recorded in those packages. In particular, the exact F0/B_1_2 entry contract
+and the common block-scale scan keep their original attribution.
+
+Prepared by Wentao Li with substantial AI assistance.
+No independent human review is claimed.

research/qq16-f17-scan-bill/PROOF.md

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+# One block-scale scan term at the exact F0/B_1_2 entry width
+
+The selected conditional kappa remains **0.001672660197076918**. This note
+does not change it.
+
+## Why this term
+
+Pinned main `6f100d4bb5083f8c35d96fd95a539811c62f245c` records Arham Tahir's
+common block-scale scan in `research/qq16-block-scale-scan`. Its stated
+invoice is evaluated at the published finite-format example `W=456`,
+`w=453`, `p=122`. A search of that tree finds no evaluation at decoder
+width `W=532`. The pair-kernel coefficient `26744256` and the named-field
+bit coefficient `493696` are the submitted #3374 terms and are left
+untouched. The incorporated scalar-ADD count `5408*N*D` does not depend on
+`W`, so repeating it would reprint that receipt. The scan polynomial does
+depend on the entry width, and it is the term priced here.
+
+## Inherited width
+
+The literal producer is exact **F0 followed by B_1_2**, and the consumer is
+ywz65's PR2707 decoder, which reads X in F17 and Y in `F17 C_q^{-1}`. Nick
+Petalas's entry contract, at `lambda=1`, `f=64`, `e=0`, `beta=64`, gives
+
+```text
+Q0 = 80, b = 79, k = 137, Qmax = 497, E = 15, W = 532.
+```
+
+The scan proof binds `p=k` and `w=W-3`. At this width that is `w=529` and
+`p=137`, with `0 <= p < w`. The largest emitted exponent is `w-1-p=391`,
+which lies in the scan proof's stated range `[0, w]`.
+
+## The scan polynomial
+
+The pinned formula, for `q` signed `w`-bit components and reserve `p`, is
+
+```text
+G_scan(w,q,p) = w*(4q+2) - 2p + S(w-p) + 3,
+S(n) = sum_{0 <= i < n} popcount(i).
+```
+
+One owner-local line scans `q=2D` real components once. The `D` coefficient
+is `8w` and the remaining term is `2w - 2p + S(w-p) + 3`. The same proof's
+gate roles (absolute-value ripples, magnitude ORs, leading-bit hits,
+constant-bit ORs, low ORs, and three flag gates) sum to this polynomial.
+At `w=529` and `p=137`, `S(392)=1628`, so one scan costs
+
+```text
+4232 D + 2415
+```
+
+gates. The unchanged 336-line decoder, one scan per line per owner, costs
+
+```text
+1421952 N D + 811440 N
+```
+
+gate evaluations. The published control `w=453`, `p=122` still costs
+`3624 D + 1984` per line and `1217664 N D + 666624 N` for 336 lines.
+
+These counts are irreversible AND/XOR/OR/NOT evaluations in the scan
+model. Wires, constants and fan-out stay free there. The count is an exact
+invoice of that construction, with redundant gates retained.
+
+## Which physical bill changes
+
+The term that changes is the **common block-scale scan subtotal** of the
+F17 zero-retention decoder's direct Boolean arithmetic bill. At the
+published `W=456` example that subtotal is `1217664 N D + 666624 N`. At the
+exact entry width `W=532` it is `1421952 N D + 811440 N`. Scalar ADDs,
+wrappers, maps, addressing, movement and cleanup stay unpaid. The pair
+kernel and the 464-field bit count stay the submitted #3374 coefficients.
+
+## Stop
+
+Stop after this one scan term and this one parameter tuple. A scan subtotal
+is not a complete consumer, a recursive rank tariff, or a new kappa.

research/qq16-f17-scan-bill/README.md

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+# One F17 block-scale scan at the exact F0/B_1_2 entry width
+
+**Same card, one unpaid term.** #3374 already binds the F17 runtime pair
+kernel and the 464-field bit count at `lambda=1`, `f=64`, `e=0`, `beta=64`,
+`W=532`. This package prices the common block-scale **scan** at those
+parameters. Selected kappa remains `0.001672660197076918`.
+
+The incorporated scan polynomial, with `w=W-3=529` and `p=k=137`, gives one
+owner-local line
+
+```text
+4232 D + 2415
+```
+
+gates. Across the 336-line decoder, one scan per line per owner, the scan
+subtotal is
+
+```text
+1421952 N D + 811440 N
+```
+
+gate evaluations. The published `W=456` control remains
+`1217664 N D + 666624 N`. The physical bill that changes is that scan
+subtotal of the F17 direct Boolean arithmetic invoice.
+
+```sh
+python3.12 -I -B research/qq16-f17-scan-bill/verify.py
+```
+
+Expected:
+
+```text
+PASS_QQ16_F17_SCAN_BILL W=532 scan=1421952*N*D+811440*N control=1217664*N*D+666624*N no_new_kappa
+```
+
+## What is bound
+
+`W=532` is the published example in Nick Petalas's exact F0/B_1_2 entry
+contract. Arham Tahir's block-scale scan states
+
+```text
+G_scan(w,q,p) = w*(4q+2) - 2p + S(w-p) + 3
+```
+
+and binds `p=k`, `w=W-3`, `q=2D`, and one scan per line per owner on the
+336-line decoder. The proof is in [PROOF.md](PROOF.md). The receipt is
+[CERTIFICATE.json](CERTIFICATE.json).
+
+## What stays unpaid
+
+Scalar ADDs, wrappers, maps, addressing, movement and cleanup remain
+outside this scan count. The pair-kernel and named-field coefficients stay
+the submitted #3374 values.
+
+## Reproduce
+
+Python 3.12, standard library only, from the repository root:
+
+```sh
+python3.12 -I -B research/qq16-f17-scan-bill/verify.py
+python3.12 -I -O -B research/qq16-f17-scan-bill/verify.py
+python3.12 -I -B research/qq16-f17-scan-bill/independent.py
+python3.12 -I -B research/qq16-f17-scan-bill/test_package.py
+python3.12 -B scripts/research_package.py --package research/qq16-f17-scan-bill
+```
+
+Default verification is read-only. `--write` creates a missing certificate
+and refuses to overwrite one.
+
+## Open next questions
+
+1. **Scalar ADDs under a width-dependent model.** The incorporated finite
+   format already charges `5408*N*D` real ADD/subtracts, and that count does
+   not use `W`. It matters because a Boolean ADD circuit at `w=529` would be
+   a different unit from that real-operation count. The first step is to pin
+   one incorporated ADD circuit whose gate count is a stated function of the
+   component width. The blocker is that no such width-dependent ADD circuit
+   is the formula already attached to these 2,704 sites.
+
+2. **Wrappers and maps at W=532.** The scan proof leaves exact signed
+   coordinate wrappers and the 464 full-cover maps as separate charges. The
+   first step is to instantiate one pinned wrapper or map tariff at `w=529`.
+   The blocker is that the scan invoice treats those permutations as unpaid
+   routing.
+
+3. **Addressing, movement and cleanup.** The scan model gives wires and
+   fan-out for free and does not erase the exponent. The first step is to
+   bind one admitted caller layout and charge address travel plus exponent
+   cleanup in that layout. The blocker is that neither pinned word supplies
+   that physical lifetime.
+
+## Credit
+
+Arham Tahir supplied the block-scale scan polynomial and its `W=456`
+evaluation. Nick Petalas supplied the exact F0/B_1_2 entry contract and the
+finite-format width `w=W-3`. ywz65 supplied the PR2707 F17 decoder. The
+#3374 pair-kernel and field-bit coefficients are used only as the terms this
+package does not recompute. Predecessor files are unchanged.
+
+Prepared by Wentao Li with substantial AI assistance.
+No independent human review is claimed. New work is Apache-2.0.

research/qq16-f17-scan-bill/SOURCES.json

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+{
+  "schema_version": 1,
+  "base_commit": "6f100d4bb5083f8c35d96fd95a539811c62f245c",
+  "files": [
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "67f085acd86acd7d4e03922d9cf4b26bca66fed5",
+      "sha256": "47b42433f5a85809a3aadd29c2c339da2c6ed728e4f7762df6b88bccb7874cf0"
+    },
+    {
+      "path": "research/qq16-block-scale-scan/README.md",
+      "usage": "input",
+      "git_blob": "8e57abbf0fa1649d1359a74c987e6017218b9c41",
+      "sha256": "86b082070985c89efc43448bd0a8d3426f74720ff0d901a48b81b205432f17ec"
+    },
+    {
+      "path": "research/qq16-producer-entry-contract/README.md",
+      "usage": "input",
+      "git_blob": "d3f66aac46ac8edbc6660715e586276909b0eac4",
+      "sha256": "83029c16c55be649e223bd583a14529d26a9c2e44afcf2766a3f70504b641ffe"
+    }
+  ]
+}

research/qq16-f17-scan-bill/TASK.json

@@ -0,0 +1,89 @@
+{
+  "schema_version": 1,
+  "task_id": "joint-query-controller",
+  "base_commit": "6f100d4bb5083f8c35d96fd95a539811c62f245c",
+  "author": "Wentao Li",
+  "ai_assistance": "Substantial AI assistance for derivation, implementation, checking and writing.",
+  "scope_status": "refined",
+  "scope_change_reason": "The catalogue asks for one literal producer and an affordable physical consumer. The pair-kernel and named-field coefficients at the exact F0/B_1_2 entry width are already submitted, and the incorporated scalar-ADD count does not depend on that width. This package instantiates only the incorporated block-scale scan polynomial at W=532.",
+  "actual_scope": "At lambda=1, f=64, e=0, beta=64 and the inherited decoder width W=532, evaluate the incorporated common block-scale scan once per line per owner for the 336-line F17 decoder, and name that scan subtotal as the physical bill term that changes.",
+  "bottleneck_link": "The entry width and the scan gate polynomial are already proved, while the scan subtotal of the F17 Boolean bill was instantiated only at the W=456 example.",
+  "stop_rule": "Stop after the scan term at lambda=1, f=64, e=0, beta=64, h=73. Leave scalar ADDs, wrappers, maps, addressing, movement and cleanup unpaid, and do not recompute the pair-kernel or field-bit coefficients.",
+  "evidence": "Exact integer evaluation of the pinned G_scan polynomial at w=W-3 and p=k, checked against the published W=456 scan total, with source-text checks that one scan is charged per line per owner.",
+  "outcome": "partial",
+  "original_card": {
+    "id": "joint-query-controller",
+    "question": "Can a literal QQ16 producer meet the proposed completed-output error budgets with dirty helpers and an affordable physical consumer?",
+    "starting_points": [
+      "docs/research/research-family-status.md",
+      "research/joint-query/README.md",
+      "research/joint-query/evidence/QQ16-SELECTED-WITNESS.md",
+      "research/joint-query/evidence/JOINT-QUERY-TRANSFER.md",
+      "docs/research/community-efficient1000-review.md",
+      "research/qq16-producer-defect-transfer/README.md"
+    ],
+    "methods": [
+      "Derive one literal producer's completed-output defects and intermediate dirty-helper bounds, with its physical bill.",
+      "Design or audit one consumer, retention or hosting boundary and its complete cost for the pinned producer/decoder."
+    ],
+    "acceptance_gate": "Name the changed premise of the fixed F0/B1 observation obstruction. Show exactly which query is recovered, legal native reads and restoration, and a full favorable budget including cover maps, helpers and endpoints. Local inverse identities alone do not close the global controller. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.",
+    "first_step": {
+      "command": [
+        "python3",
+        "-B",
+        "scripts/research_baseline.py"
+      ],
+      "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+      "inspect": "Read the revision-6 family record and #2965 producer-defect transfer after the local QQ16 decoder contract. Its author-checked output-error estimate does not implement producer interiors, bound dirty helpers, or pay for the consumer; independently check the implication used.",
+      "scope": "Source-bound orientation only. Read the named package and review before relying on its local evidence; this command is not its replay or supplier admission."
+    },
+    "first_experiment": "Pin one literal F0/B1 producer and its native-child contracts; derive the actual intermediate magnitude ledger and completed-output defects, including dirty helpers and correlations. Compare with #2965 budgets and price storage, movement, cleanup and F17 consumption. Stop with a precise missing bound if no producer contract supplies it; do not optimize another decoder precision constant in isolation.",
+    "bottleneck_link": "The native local words exist; retained query information and its physical access are the missing link to a composed recursive interface.",
+    "allowed_variations": [
+      "One paid query, one changed first pair, or one precisely specified affine helper state.",
+      "A counterexample or lower bound for that exact proposed repair.",
+      "One unresolved obligation of a newer local decoder, with exact source heads and a distinct claim/domain."
+    ],
+    "scope_change_triggers": [
+      "Retaining the fixed first pair and ordinary schedule while allowing only homogeneous selected-only control, already excluded by the witness.",
+      "Treating cover-map counts as zero-cost physical address operations.",
+      "Recreating the pending complete local decoder or early-record/output-bank coalescing already under investigation without a distinct audit or changed premise.",
+      "Treating a completed-output defect inequality as a producer-interior, dirty-range or physical-cost certificate."
+    ],
+    "overlap_terms": [
+      "QQ16",
+      "joint-query",
+      "changing-chart controller",
+      "selected observation",
+      "1969",
+      "2540",
+      "early record",
+      "output-bank retention",
+      "complete native decoder",
+      "2965",
+      "producer defect",
+      "dirty-helper range",
+      "F17 consumer"
+    ]
+  },
+  "open_questions": [
+    {
+      "question": "What Boolean gate count do the 2,704 scalar ADD sites have at component width w=529?",
+      "why_it_matters": "The incorporated real-operation count 5408*N*D does not use W, so it does not price those sites in the same gate model as the scan.",
+      "first_step": "Pin one incorporated ADD circuit whose gate count is a stated function of the component width and instantiate it at w=529.",
+      "blocked_by": "The finite-format ADD charge is a real-operation count, and no width-dependent ADD circuit is attached to these sites on the pinned main."
+    },
+    {
+      "question": "What do the exact signed wrappers and 464 full-cover maps cost at W=532?",
+      "why_it_matters": "The scan proof preserves the line maximum under exact wrappers and still leaves their routing unpaid.",
+      "first_step": "Instantiate one pinned wrapper or map tariff at w=529 and 464 maps.",
+      "blocked_by": "The scan invoice treats permutations as separate routing rather than gates inside G_scan."
+    },
+    {
+      "question": "What addressing, movement and exponent cleanup does one admitted caller pay for this scan?",
+      "why_it_matters": "The scan model leaves wires and fan-out free and does not erase the shared exponent.",
+      "first_step": "Bind one admitted caller layout and charge address travel plus exponent cleanup in that layout.",
+      "blocked_by": "Neither the entry contract nor the scan proof supplies that physical lifetime."
+    }
+  ]
+}

research/qq16-f17-scan-bill/VERIFY.json

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+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [
+    "research/qq16-producer-entry-contract/README.md",
+    "research/qq16-block-scale-scan/README.md"
+  ],
+  "commands": [
+    {
+      "argv": ["{python}", "-Werror", "-I", "-B", "{package}/verify.py"],
+      "timeout_seconds": 60,
+      "checks": "Recompute the exact-entry F17 block-scale scan subtotal and the published W=456 control."
+    },
+    {
+      "argv": ["{python}", "-Werror", "-I", "-O", "-B", "{package}/verify.py"],
+      "timeout_seconds": 60,
+      "checks": "Repeat the primary check with assertions disabled."
+    },
+    {
+      "argv": ["{python}", "-Werror", "-I", "-B", "{package}/independent.py"],
+      "timeout_seconds": 60,
+      "checks": "Recompute the same scan integers from the pinned polynomial in a separate program."
+    },
+    {
+      "argv": ["{python}", "-Werror", "-I", "-B", "{package}/test_package.py"],
+      "timeout_seconds": 120,
+      "checks": "Reject certificate corruption, duplicate JSON keys and drifted source bytes, including under -O."
+    }
+  ]
+}