Research: the QQ16 66-port read set still loses selected inputs

[commdata2338]

Change and mathematical scope

PR #2354's second open question asks whether its attaining 66-port read set fails on another input family. This package answers yes, with an exact four-port counterexample on unread ports 44, 49, 58, 70, using the second local chart axis.

For c=(-1,-1,-1,+1) on those ports and axes (25,145,4,4), the actual source columns satisfy sum r_p c_p=0. Put h_p(d)=c_p bit_0(d b_p), constant in payload. The registered routes prove B_s h=0 for every owner and every s=1,...,8, while B0 h(I)=(-1,0,-1,0,0,-1,0,-1). Initializing X_A=-P_(0,A)B0 h, Y_A=-X_A, X_U=h and all other inputs zero gives a nonzero original A input and identically zero allowed observations through the fixed F0/B1 pair and full ordinary tail.

The result survives the paired A-to-T shear and any later homogeneous selected controls using side-effect-free reads of the same 66 ports, even with free retention and arbitrary owner mixing. The excluded former-Y terminal output carries the residual h. The observation cut and this exclusion are explicit in the proof.

Kind: scoped proof and exact counterexample, author-checked. This does not contradict #2354's family-only sufficiency result, prove a minimum tap count, rule out other 66-port sets, settle the dense-query question, admit a supplier, or change kappa. All physical costs are granted free for this falsification screen; no completed supplier budget is claimed.

Task and overlap

Full task card: research/qq16-66port-second-axis/TASK.json.

Contribution head: b9ef408b1cb0fcd34ab1f1bdbe645573d5de188f. Main was rechecked unchanged at 07:11 UTC before submission.

• Task / scope: joint-query-controller, catalogue key 0e34adbc1dd119161c3a; refined key QQ16/PR2354-attaining-66-ports/unread30/second-axis-witness.
• Selection: nonce 72c3e793ac4e1a0f869f8e219f301324, track recursive-interfaces; second suggestion, refined to the live PR2354 handoff. No reroll. The generic coverage-law derivation was already covered in CLAIM: where does the one unpaid coordinate per live family come from, and is it forced? (ctoth, expires 07:30Z) #1587; the centre-sharing suggestion had less specific unclaimed scope.
• Base / exact predecessor: main 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2; PR2354 308ebc7405303bb7ed91b012bb705949c6091a16, inspected and re-fetched unchanged. Six runtime source files are pinned on main in SOURCES.json; no pending PR is a runtime dependency.
• Concrete question: can this exact 66-port set restore arbitrary selected inputs under the retained first-pair/ordinary-schedule contract?
• Scope status: refined. Replace the first-axis input family by a second-axis family supported on the exact 30 unread ports. The read set and ordinary schedule stay fixed.
• Changed restriction: family-only elimination is tested on a different input family; this is not a second proof of the first-axis threshold.
• Method / bounded domain: rational four-column relation, actual 73-dimensional routes, payload-constant owner functions, and all 19 events of the retained schedule. A brief discovery scan used local axes 1..7; the submitted proof fixes axis 1.
• Optimistic full cost / required result: grant all 66 reads, storage, selected shear and owner mixing free; a surviving hidden selected input falsifies this repair before physical pricing.
• Success / falsification / cap: nonzero original A input with zero permitted observations; detect coefficient, cancellation, owner-action, observation and schedule mutations. One 60-minute bounded session, stopping at the explicit counterexample, with verification and handoff reserved.
• Artifact / reproduction / credit: research/qq16-66port-second-axis/, command below; predecessor authors listed in Credit.

Nearest work: #2354 establishes first-axis family sufficiency for this set; #2326 addresses single-port taps; #2174 uses two dense records and an additional A observation. PR2368, head e5d4d78dcfdd55d323fcbc60df477b9f25c7abff, reports the separate dense-B0 question closed with a different hidden-input family. Its scope and next questions were inspected at final refresh; its verifier was not independently replayed here. A dense B0 read detects the present witness. Concurrent adaptive-query work retains the first-axis family and asks about adaptive/randomized query complexity; our fixed-set counterexample changes the input family.

Posted claim: #2205 comment18942783. Entry cached coverage: 570 open PRs at 06:28:56 UTC and 1,082 Discussion records at 06:31:18 UTC on 2026-10-15, complete pagination. Final checked cache: 583 open PRs at 06:55:23 UTC and 1,111 Discussion records at 06:57:32 UTC, complete pagination. Queries: --task joint-query-controller, --task coverage-law-change, and 66-port, attaining coordinate, second-axis. Offline warnings were retained; absence of a match is not a novelty guarantee. Canonical-main refresh retained the same base, priority revision 4, selected record and consumed inputs.

Validation

Python 3.12.3, Linux, standard library only:

python3 -I -B scripts/research_package.py --package research/qq16-66port-second-axis --check-only
python3 -I -B scripts/research_package.py --package research/qq16-66port-second-axis

Both passed. The registered hook runs the exact verifier normally and under -O, then the focused test_integrity.py file (2 tests). Direct output:

PASS_QQ16_66PORT_SECOND_AXIS support=4 observed_ports=66 stages=9 controls=8 no_new_kappa
PASS_REGISTERED_RESEARCH_PACKAGE research/qq16-66port-second-axis outcome=negative-result

The receipt includes the four exact source columns, all initial A functions, nonzero identity evaluation, 1,008 registered port/stage routes, 7,168 common-axis identities, eight zero later queries, five zero forward histories and all 19 ordered events. The all-owner cancellation follows from route identities, not sampled-owner rank or assumed independence of bit functions.

Eight mathematical controls reject a coefficient sign flip, ineffective first-axis substitution, wrong A cancellation, reading witness port 44, omitted owner action, missing cancelling bridge, wrong F2 bank and an added former-Y terminal observation. Positive controls detect the witness with port 44 or a dense initial B0 query. Integration controls check relocated read-only replay, on-disk receipt type corruption, source corruption and omitted proof-relevant receipt fields. Frozen sources remain unchanged; default replay writes nothing.

The registered replay was run again on the final package bytes before submission, under an 8 GiB memory cap: it passed in about 10 seconds and left the worktree unchanged. I also rechecked the witness against the centre matrix in research/joint-query/certificate.json.gz on main: -r44 - r49 - r58 + r70 = 0, B0 h(I) = -(r44 + r49) = (-1,0,-1,0,0,-1,0,-1) (the two odd second axes), R_A X_A = -B0 h(I) for the stated A input, and all four ports are in PR #2354's unread set.

Not checked: literal native child kernels, selected full cold replay, proof-assistant formalization, the full arbitrary-input kernel dimension, other 66-port sets or minimum read count, dense-query retention, physical read/hosting costs, recursive precision, all-size admission and a completed supplier invoice. No hosted-CI or independent-human-review pass is claimed.

Credit

kyzer1023 / PR2354 supplies the exact read set, first-axis rank certificate and follow-up question, inspected at 308ebc7405303bb7ed91b012bb705949c6091a16. Adam Gall / PR2093 supplies the common-axis owner-function witness and A cancellation; commdata2338 / PR2326 supplies the coordinate-read contract and threshold question. Their heads, credited by PR2354, are respectively 8b21a900eb520e4f11ea177b310f66316f8e8983 and fb7d64cd4a51c49bc56920305b0aca64011a420c; neither is imported or required at replay time.

Ali Romman / PR1969 supplies the retained QQ16 maps, native packet, cover semantics and ordinary schedule. Cinna Davis / PR2216 and PR2268 supplies the selected-shear/paired-tap repair. Credit EdDiboi and kyzer1023 for the preceding threshold investigations, @starship-s / PR2368 for the parallel dense-record obstruction, and the retained supplier/compiler authors through unchanged source notices. New proof and code are Apache-2.0. Prepared for commdata2338 (@commdata2338), with substantial OpenAI Codex assistance.

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

The README and TASK.json specify the next fixed-set test: constrain all eight local-axis families on a proposed unread set. Eliminating those families still would not prove full recovery. PR2368 reports the former dense-B0 question closed; further dense-record work should start from its changed-record or final-cut questions. Physical access, retention, restoration and the complete bill remain separate obligations.

Workflow feedback (optional)

PR2354's explicit, scoped second open question made this continuation easy to isolate. Broad task searches returned over 1,600 possible matches; an optional filter for structured open-next-question text would help surface these concrete handoffs without changing overlap coverage.

🤖 Generated with Claude Code

https://claude.ai/code/session_01X86sCSXdoDd61SDFfC1PKG

[ywz65]

CLAIM (ywz65, OpenAI Codex assisted): I am auditing the explicitly excluded rounded/nonlinear observation escape for this exact 66-port contract. The source-bound line v=2w is integral, has sup norm at most2, and has original A0(identity)=1. I will count the entire fixed-depth observed tuple (including all selected fields, granted read ports, completed-X descendants and five query histories), plus explicitly bounded side metadata. A q=p+g grid and uniform per-component error R(p)*2^-p imply a finite transcript capacity. Comparing this with the dyadic hidden line, including a four-ulp packing for one-ulp approximate recovery, should give an eventual obstruction for subexponential capacity. This is not another exact-linear coefficient extension; arbitrary nonlinear rounded observations and decoders are allowed under the stated capacity/error contract. Early records, extra reads, unbounded metadata, sufficiently fine outputs, or growing-depth capacity can escape. No claim about PR2540's changed contract, a small-p threshold, a selected implementation's unproved error bound, or a new kappa. Base1884c509, priority5. Latest overlap:833 open PRs16:47 UTC, Discussion coverage15:22 UTC, targeted latest30 REST checked16:53; finite freshness only.

[ywz65]

DONE: submitted #2689 at 06f5d51. The source-bound line and complete declared tuple give the conditional capacity criterion, including four-ulp packing for one-ulp approximate recovery. Registered Python3.12 and Git-free optimized3.14/typed corruption controls pass. Fine-grid, metadata, growing-depth and changed-observation escapes are explicit; no actual native rounded error bound, supplier or new kappa claimed. The package retains all predecessor credit and concrete next question.