Research: F17 pair-kernel bill at the exact F0/B1 entry width (no new kappa)

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

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+{
+  "schema_version": 1,
+  "status": "PASS_QQ16_F17_PAIR_BILL",
+  "producer": "F_0_then_B_1_2",
+  "consumer": "PR2707_zero_retention_decoder_in_F17",
+  "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,
+  "L": 531,
+  "exponent_bits": 10,
+  "gates_per_pair": 159192,
+  "pair_kernel_coefficient": 26744256,
+  "field_bit_coefficient": 493696,
+  "control_gates_per_pair": 124028,
+  "control_pair_kernel_coefficient": 20836704,
+  "dirty_width_supplied": false,
+  "selected_kappa": "0.001672660197076918",
+  "kappa_changed": false
+}

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

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+# Handoff
+
+Pinned CrocSwap main: `6f100d4bb5083f8c35d96fd95a539811c62f245c`.
+Selected kappa, unchanged: `0.001672660197076918`.
+
+The selected stock coefficient was not rederived. `8194`, `6748` and the
+lcm reserve are already registered, and the `m=73` shape lemma is already
+an obstruction. This package switched to `joint-query-controller`.
+
+Claim: at the exact F0 then B_1_2 entry parameters `lambda=1`, `f=64`,
+`e=0`, `beta=64`, the F17 zero-retention decoder's runtime pair kernel is
+at most `26744256 lambda N D` gates and its 464 named fields use at most
+`493696 N D` data bits. The dirty-helper magnitude ledger does not supply
+the width those counts use.
+
+Stop. Do not treat this as a complete consumer, a new precision constant,
+or a new kappa.

research/qq16-f17-pair-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,
+the finite dyadic format, the rounded pair circuit and the rounded producer
+envelope keep their original attribution.
+
+Prepared by Wentao Li with substantial AI assistance.
+No independent human review is claimed.

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

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+# Exact-producer width of one F17 decoder arithmetic bill
+
+The selected conditional kappa remains **0.001672660197076918**. This note
+does not change it.
+
+## Why this is not a stock-coefficient package
+
+On the pinned main, the selected ordinary BIT parent reserve is already
+derived: Adam Gall's package gives the conditional coefficient 8194, Nick
+Petalas's ceiling-free refinement gives 6748, and the later lcm-reserve
+package binds `269241600 |GL_64(F_q)| q^(4096(w-1))` to the same depth
+recurrence. The complex `m=73` shape coefficients `A`, `B` and `rho` are
+already recorded as unbound. Repeating those derivations is not a new fact.
+The open joint-query obligation is the one taken below.
+
+## Pinned producer and consumer
+
+The literal producer is the exact full-cover word **F0 followed by B_1_2**
+in the retained joint-query certificate, as used by Nick Petalas's
+producer-entry contract and by the #2965 defect transfer. The consumer of
+its completed charts is ywz65's PR2707 zero-retention decoder. At the
+completed B1 cut that word reads X in chart F17 and Y in chart
+`F17 C_q^{-1}`, and it returns the original 224 logical arrays **in F17**.
+F17 means the product of the signed Fourier lines on address axes 0 through
+16. This package does not replay the producer or the decoder word.
+
+## Inherited exact entry
+
+Under the entry contract's hypotheses (exact producer arithmetic, the
+inherited helper contract, `h=73` address axes, and positive tensor depth),
+post-B1 fields satisfy
+
+```text
+B = 17628*H < 2^(e+15),
+Q0 = f + ceil(lambda/2) + 6 + 9*lambda,
+```
+
+whenever `H <= 2^e`. The displayed `17628` is the predecessor's triangle
+bound. This note checks the slack `17628 < 2^15`, which is what makes
+`B < 2^(e+15)` follow from `H <= 2^e`. For an original-input error `H 2^{-beta}`,
+that contract sets the decoder's relative target to `b = beta+15` and quotes
+PR2807's width
+
+```text
+k = beta+37 + ceil_log2(lambda) + floor(73 lambda / 2),
+Qmax = Q0 + 3k + 6,
+W = Qmax + e + 35.
+```
+
+At `lambda=1`, `f=64`, `e=0`, `beta=64` this is
+
+```text
+Q0 = 80, b = 79, k = 137, Qmax = 497, E = 15, W = 532.
+```
+
+`E = e+15` is the entry exponent in PR2807's notation `B <= 2^E`. The same
+proof's completed-field majorant is `32369 B`. Because `32369 < 2^15` and
+`B < 2^E`, that majorant is strictly below `2^(E+15)`, so the inherited
+overflow argument still applies at this `E`.
+
+## Pair inputs at this width
+
+PR2807 bounds every common-grid component by `2^(Qmax+E+16) = 2^(W-4)` and
+every pair numerator by `2^(Qmax+E+18) = 2^(W-2)`, strictly. Signed `w`-bit
+integers hold absolute values strictly below `2^(w-1)`. The choice
+
+```text
+w = W-3, L = w+2 = W-1
+```
+
+therefore stores the components and the numerators. At `W=532` this is
+`w=529`, `L=531`. The published `W=456` control is the same rule:
+`w=453`, `L=455`.
+
+PR2811's runtime-exponent circuit, for `k = bit_length(L-2)`, has
+
+```text
+24 L k + 52 L + 4 * 2^k + 4 k + 4
+```
+
+gates. The control is `k=9` and **124,028** gates. There are 336 lines and
+at most `lambda D / 2` pairs per line per owner, so the kernel coefficient
+is `gates * 168`. The control coefficient is `124028 * 168 = 20836704`,
+matching the published `20836704 lambda N D` subtotal.
+
+At `L=531`, `k = bit_length(529) = 10` and the gate count is **159,192**.
+The kernel subtotal is at most
+
+```text
+159192 * 168 * lambda * N * D = 26744256 lambda N D
+```
+
+gate evaluations. PR2807's named-field representation uses at most
+`2 * 464 * N * D * W` data bits. At this width that coefficient is
+
+```text
+2 * 464 * 532 = 493696,
+```
+
+so at most `493696 N D` data bits for the 224 borrowed arrays, 224 outputs
+and sixteen private arrays.
+
+These two coefficients are sufficient conditional upper bounds in the
+incorporated gate and register models. They are not tape time, not a
+recursive rank tariff, and not a complete machine invoice.
+
+## Dirty-helper ledger does not supply the width
+
+The rounded-producer envelope is the registered intermediate
+magnitude/dirty-state ledger for this same literal producer. It bounds the
+noisy all-cut B1 norm by `2^(delta+80) H` and states that component
+representation, the entry grid, and subsequent F17 consumption are unknown.
+PR2807 states that a norm bound alone does not determine the adaptive line
+exponent: inputs `2^{-j}` can have bounded norm and arbitrarily negative
+exponent. Substituting `E = delta+80` into `W` is therefore not licensed.
+The missing bound is a proved entry grid `2^{-Q0} Z` for the actual dirty
+helpers. `dirty_width_supplied` is false.
+
+## What remains outside the bill
+
+Scans, the 2,704 scalar ADDs, wrappers, cover maps, address arithmetic,
+movement, cleanup and a later endpoint adapter are unpaid here. A caller
+that does not accept F17 outputs still needs its own frame conversion.
+The entry contract already says that adapter is a separate invoice.

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

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+# One F17 pair-kernel bill at the exact F0/B_1_2 entry width
+
+**Switched card.** The selected stock coefficient is already registered:
+Adam Gall's parent reserve gives conditional `sigma=8194`, Nick Petalas's
+ceiling-free refinement gives `6748`, and the lcm-reserve package binds the
+same depth recurrence to `269241600 |GL_64(F_q)| q^(4096(w-1))`. The complex
+`m=73` coefficients `A`, `B` and `rho` are already recorded as unbound.
+This package takes card `joint-query-controller` instead.
+
+**Partial arithmetic bill; no new kappa.** For the literal exact producer
+F0 followed by B_1_2, the inherited entry contract at
+
+```text
+lambda=1, f=64, e=0, beta=64, h=73
+```
+
+gives decoder width `W=532`. Under the incorporated runtime-exponent pair
+model, the F17 zero-retention decoder's pair kernel costs at most
+
+```text
+26744256 lambda N D
+```
+
+gate evaluations, and its 464 named fields use at most
+
+```text
+493696 N D
+```
+
+data bits. The registered dirty-helper magnitude ledger does **not** supply
+this width. The selected kappa remains `0.001672660197076918`.
+
+```sh
+python3.12 -I -B research/qq16-f17-pair-bill/verify.py
+```
+
+Expected:
+
+```text
+PASS_QQ16_F17_PAIR_BILL W=532 gates_per_pair=159192 pair_kernel=26744256*lambda*N*D field_bits=493696*N*D dirty_width=unsupplied control_gates=124028
+```
+
+## What is bound
+
+The producer and the post-B1 norm `B=17628*H < 2^(e+15)` are Nick Petalas's
+exact entry contract. The width chain `Q0=80`, `b=79`, `k=137`, `Qmax=497`,
+`W=532` is that contract's published example, recomputed here. PR2807's
+component and numerator bounds give signed pair inputs `w=W-3=529` and
+`L=531`. PR2811's runtime gate formula then gives `159192` gates per pair.
+The published control `L=455` still gives `124028` gates and kernel
+coefficient `20836704`. The field-bit formula `2*464*N*D*W` is PR2807's.
+
+The consumer is the PR2707 decoder: it reads the producer's F17 and
+`F17 C_q^{-1}` charts and returns the original arrays in F17. The proof is
+in [PROOF.md](PROOF.md). The receipt is [CERTIFICATE.json](CERTIFICATE.json).
+
+## What the dirty ledger does not give
+
+The rounded-producer envelope already records this producer's intermediate
+magnitude and dirty-helper state, including the all-cut bound
+`2^(delta+80) H`. It leaves the component grid and F17 consumption unknown.
+PR2807 states that a norm bound alone does not determine the adaptive line
+exponent. That is the obstruction: the dirty ledger cannot be substituted
+for `E` and `Q0`. No second magnitude table is computed here.
+
+## Reproduce
+
+Python 3.12, standard library only, from the repository root:
+
+```sh
+python3.12 -I -B research/qq16-f17-pair-bill/verify.py
+python3.12 -I -O -B research/qq16-f17-pair-bill/verify.py
+python3.12 -I -B research/qq16-f17-pair-bill/independent.py
+python3.12 -I -B research/qq16-f17-pair-bill/test_package.py
+python3.12 -B scripts/research_package.py --package research/qq16-f17-pair-bill
+```
+
+Default verification is read-only. `--write` creates a missing certificate
+and refuses to overwrite one.
+
+## Open next questions
+
+1. **Entry grid for the dirty ledger.** The question is which proved grid
+   `2^{-Q0} Z` and exponent `E` the rounded F0/B_1_2 helpers actually meet.
+   It matters because without them the pair-kernel count above does not
+   apply to the noisy contract. The first step is to pin one finite producer
+   implementation and prove its completed components lie on that grid. The
+   blocker is that the rounded envelope leaves the grid unknown.
+
+2. **The remaining physical terms at W=532.** Scans, scalar ADDs, wrappers,
+   maps, addressing, movement and cleanup are still unpaid. The first step
+   is to apply the incorporated finite-format operation counts at this width.
+   The blocker is that the pair-circuit proof leaves those terms outside its
+   gate count, and the navigation scan formula is a separate pending model.
+
+3. **Whether the caller accepts F17.** A caller that needs the original
+   `C_q`/`I` frames pays an additional frame conversion. The first step is
+   to bind one admitted caller to either the F17 output contract or that
+   adapter tariff. The blocker is that neither pinned word chooses the caller.
+
+## Credit
+
+Nick Petalas supplied the #2965 defect transfer, the exact F0/B_1_2 entry
+contract, PR2807's finite format and PR2811's pair circuit, and the
+rounded-producer magnitude ledger. ywz65 supplied the PR2707 F17 decoder.
+Arham Tahir supplied the logical inverse that decoder lowers. Ali Romman and
+the retained joint-query authors supplied the literal F0/B_1_2 words.
+Adam Gall and Nick Petalas supplied the selected BIT stock coefficients that
+this package does not repeat. Hiroki KUMAZAKI's cutoff chain remains the
+stock-margin record. 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-pair-bill/SOURCES.json

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