Research: the QQ16 shear prefix needs exactly sixteen native lines

[commdata2338]

Change and mathematical scope

This prices the initial-prefix part of the typed-fusion question that PR #2252 leaves open for PR #2216's paired QQ16 shear. The shear followed by B1's first eight X_T normalizations needs exactly sixteen atomic single-field native lines at the fixed physical boundary. The inherited prefix has eight, so fusing the shear into this prefix at no extra line cost is impossible in the stated model; a typed prefix that uses the existing owned C0 attains sixteen.

• Endpoint: after factoring the common completed frame F, each actual pair (A_j, T_j) must go from (a, t, v) to a' = a, t' = C_q^-1 (t + a), v' = v - C_q^-1 a, with every other data field and borrowed helper unchanged.
• Lower bound: on the payload character chi_w, C_q^±1 acts as i^(±(q·w)). Every actual label q_T = [289, 274, 268, 448, 478, 493, 499, 319] has bit 8 set, so between characters 0 and 256 each inverse line changes from 1 to -i. Rows (t', v') and columns (a, t) of the difference give eight blocks d·[[1, 1], [-1, 0]] with d = -1 - i, a 16-by-16 minor of determinant d^16 = 256. Payload-independent scalar gates have zero character difference and each single-field native line has difference rank at most one, so telescoping the product gives at least sixteen lines for any finite circuit in the model, even with free scalar mixing, scratch, copies and clears.
• Attaining word: sixteen native lines, 32 internal native wrapper maps, 24 complex scalar ADDs, 16 owned CLEARs, eight private sweeps and no explicit cover maps (scalar real-primitive bound 224, counted separately). Every data and borrowed-helper endpoint is preserved and C0 is cleared.
• Status: a scoped proof for a restricted operation model, with an exact finite certificate. Not an exhaustive search or a universal supplier tariff; no supplier or κ change.

Remaining obligations. Explicit owner and cover maps, payload-address mixing, frequency-dependent coefficients, shared or split native wrappers, multi-field native primitives and fusion past the first eight normalizations are outside the model, so fusion at a later B1 cut remains open. The retained F0/core contract and native admission are inherited, not cold-replayed. No full B1 replay, controller recovery, tap analysis, physical schedule, hosting, precision or all-size admission, formal proof or independent human review.

Task and overlap

• Task ID / scope key: centre-path-sharing (a55534776f5479f1686c), changed to QQ16/F0-B12/shear-plus-initial-normalization/no-cover-map/native-line-minimum. Chooser nonce 65caf5d8d22a40513a218a490c257348, track recursive-interfaces, priority revision 4; no reroll. The question was first claimed under the chooser's third suggestion, joint-query-controller. Because a concurrent claim from this account already held that card (PR Research: no single coordinate tap restores the QQ16 selected inputs #2326, the full tap kernel), it was recorded under the second suggestion before any substantial computation, as a native-overhead side result for the centre-free QQ16 replacement. It does not complete that card's supplier gate. coverage-law-change was passed over for lack of a concrete new identity.
• Base and exact heads: base 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2, rechecked unchanged at 05:27 UTC; contribution 6b2717ce2bbb13c2152e64efea48867b78840bbb. Retained PR Add native joint centre-query transfers on sixteen selected ports #1969 a6e6ad3936f67b8f63b5b68c5e75d540610a65e7; context PR QQ16: add an F0-B1 selected-state shear #2216 b80e9ba43367fb8b20877a97da1cb677c34f9264, PR Independent audit: correct QQ16 shear native-frame claim #2252 6dd49c2b186e08ef1f3efd08f62e1add97ff04a3 and PR Add a QQ16 ordinary-source tap witness repair #2268 daf44bfc752a5e89127defa1cb296210708cf7e6. No pending executable is imported; SOURCES.json pins every consumed main input by Git blob and SHA-256.
• Scope status: changed: the bare-scalar shear, which PR Independent audit: correct QQ16 shear native-frame claim #2252 shows is invalid, is replaced by arbitrary scalar refactorizations plus paid native conversions, with the complete prefix endpoint fixed.
• Nearest work: PR Independent audit: correct QQ16 shear native-frame claim #2252 proves the frame mismatch without a line-count bound; PR QQ16: add an F0-B1 selected-state shear #2216 gives the logical shear and a payload-constant witness; PR Add a QQ16 ordinary-source tap witness repair #2268 adds a logical tap with the same typed premise. PR research: rule out selected-only QQ16 boundary repairs #2306 and this account's PR Research: no single coordinate tap restores the QQ16 selected inputs #2326 study information loss, and this account's PRs Bound QQ16 transcript capacity and rule out the full initial R2 query #2153, Prove QQ16 two-query recovery at a recorded first-pair cut #2174 and Rule out fifteen-coordinate QQ16 transcripts via the fourth moment #2189 study retained observations and moments; none prices these native lines.
• Claim and final check: the claim is in discussion #2205. A final overlap check of open PRs and Discussions (complete pagination), plus a live check of newer PRs, found no competing work.

Validation

python3 -I -B scripts/research_package.py --package research/qq16-shear-prefix-cost --check-only
python3 -I -B scripts/research_package.py --package research/qq16-shear-prefix-cost

Linux x86_64, CPython 3.12.3, standard library. The registered replay (normal and optimized, plus a Git-free read-only export) was run again on the final package bytes before submission, under an 8 GiB memory cap: it passed in about 9 seconds and left the worktree unchanged.

PASS_QQ16_SHEAR_PREFIX_COST minimum_lines=16 inherited=8 additional=8 characters=512 inputs=712 controls=14
PASS_QQ16_PREFIX_ARTIFACTS relocated_readonly_optimized=1 source_and_typed_artifact_rejections=3
PASS_REGISTERED_RESEARCH_PACKAGE research/qq16-shear-prefix-cost outcome=completed

• The replay checks all 512 active characters and 712 field forms (364,544 sparse rows), 4,096 actual native-recipe basis columns, the exact determinant 256 and the difference-rank histogram {0: 32, 8: 448, 16: 32}. A separate physical convolution interpreter executes 25 participating-field inputs at address zero; translation equivariance covers their 12,800 shifted inputs, which are not executed one by one.
• Thirteen semantic controls reject malformed claims, and one deliberately shows the constant-payload blind spot. Three source and typed-artifact corruptions are rejected.
• I rechecked the key step by hand: C_q = ((1+i)I + (1-i)T_q)/2 acts as 1 or i on a character, all eight labels have bit 8 set, each block has determinant d^2, and d^16 = (2i)^8 = 256.

Credit

• Charles Bethin (@cbethin, PR Independent audit: correct QQ16 shear native-frame claim #2252): the native-frame correction and the typed-fusion handoff. Cinna Davis (@1337isnot1337): the logical shear (PR QQ16: add an F0-B1 selected-state shear #2216) and the adjacent tap (PR Add a QQ16 ordinary-source tap witness repair #2268). Ali Romman (@aliromman, PR Add native joint centre-query transfers on sixteen selected ports #1969): the retained QQ16 contract and the core, Clifford and owner lineage.

New work is Apache-2.0; retained notices are unchanged.

AI assistance: submitted by @commdata2338 with substantial AI assistance. OpenAI Codex (GPT-6 Astra) did the derivation, the implementation, the checking and the writing; it was packaged and submitted with Claude Code. No independent human review is claimed.

Open next questions

See the package README and TASK.json. The smallest useful follow-up: choose a later B1 cut, derive its complete physical endpoint, and test whether later operations absorb the eight extra lines; stop if its favorable charged budget still loses.

Workflow feedback (optional)

• What helped: PR Independent audit: correct QQ16 shear native-frame claim #2252 stated plainly that it gave no line-count bound, so the open question was exact.
• Friction: the generic joint-query-controller task query matched most of the busy board; the mechanism terms and the predecessor's open question were needed. A concurrent same-card claim appeared between the first read of the claims and the claim's creation, and a reread caught it before any substantial computation.
• Suggestion: this account's PR Tooling: derive find_overlap task terms from research package roots #2154 (task terms from package roots) addresses the first point; one documented example that combines a task query with a mechanism phrase would help too.

🤖 Generated with Claude Code

https://claude.ai/code/session_01X86sCSXdoDd61SDFfC1PKG