Exhibit a QQ16 kernel invisible to nonzero-chart source queries

[adamgall]

Research claim

For the actual QQ16 first F0/B1 pair and retained ordinary schedule, adding the exact pre-F0 ordinary-to-selected record B2 X_U still does not determine the original selected A input. This package gives an explicit three-port counterexample with

B1 h = B2 h = 0,   B0 h != 0.

The same input is invisible to every nonzero-chart query B_s, 1 <= s <= 8. All selected endpoints, all completed-X descendants and all five forward-query histories also agree with the zero input. Hence even an arbitrary final decoder cannot recover the required A input from that expanded observation set.

This is a scoped exact obstruction, not a search failure, new supplier, or exponent improvement. It leaves changed first pairs, old-chart reads, other observations and their physical pricing open.

Predecessors and changed premise

• Ali Romman's merged PR1969 supplies the actual QQ16 maps, owner routes, native contracts and prior selected-observation witness. Its independent review already proves eight lost directions with B1 h=0 and B2 h!=0; that result is not repeated as new.
• Cinna Davis's PR2079, inspected at immutable head 49df8190b158e3028e702b2c6b798117006f7249, adds B2 X_U and proves it separates those eight directions. It explicitly leaves full-controller injectivity open. This contribution answers that open question for the fixed first pair by supplying a different kernel, losing initial A rather than the prior initial T. It does not contradict PR2079's bounded separation claim.
• The gauge44/t16 source notices retain icekylinx, chafreaky and the earlier supplier lineage. No frozen predecessor or selected record is changed.

Exact construction and proof-critical step

The operation-derived query columns satisfy r_2=r_8+r_85. The actual first local chart axes at those ports have binary masks 37,38,506. For owner d, let f_v(d)=bit_0(d v) as an integer bit and set

h_2(d)=-f_37(d),   h_8(d)=f_38(d),   h_85(d)=f_506(d),
h_p(d)=0 otherwise.

The actual owner involution sends each port's first local axis to the same stage axis:

rho_s(p) b_(p,0) = e_(9+8(s-1)),   1 <= s <= 8.

Therefore B_s h=(-r_2+r_8+r_85) f_(e_stage)=0 at every owner, while B0 h(I)=-r_2 != 0. The functions are constant only in payload coordinates, not in owner coordinates. Native payload translations and endpoint line operators fix them.

Set pair zero to

X_U=h, Y_U=0,
X_A=-P_(0,A)B0h, Y_A=-X_A,
X_T=Y_T=0,

and all other banks to zero. The original A input at the identity owner is
(1/2,0,1/2,1/2,0,-1/2,0,0). The exact ordered F0 has zero query and leaves X_U=Y_U=h with zero selected state. Then q2=B2h=0 and b1=B1h=0, so B1 leaves only Y_0,U=h. The added pre-read is also zero.

The source-template tail puts -h into Y_1,U, removes it around the zero-source F2, and leaves every later active pair zero. All five forward histories vanish. Arbitrary later homogeneous selected-only controls preserve the zero selected state. The terminal exchange moves h to named final X0 with the old-Y native type, not a completed-X descendant; all permitted observations remain zero.

The README provides the full all-owner proof. This is not inferred from a finite sample of owners.

Cost boundary and stop decision

Grant B2 extraction, all eight output coordinates, source/address/frame access, storage, restoration, endpoint conversion, chronological hosting and precision zero additional cost. Even this maximally favorable complete observation budget fails recovery. More payment for the same observation cannot remove the kernel.

For orientation only, the retained F/B native masses are 5530/5546 (11076 for the first pair); a hypothetical separately charged rank-8 record would give 11084 before other charges. No native implementation of that record or completed recursive moment is claimed. Feedback that changes the first pair is outside this audit.

Artifact, provenance and reproducibility

Package: research/qq16-b2-observation-kernel/.

• Scientific base: 564148b82ae9df72163f22106f15e73efca8aff2.
• Latest guidance checkpoint: 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2; priority revision 4, scientific inputs and selected record unchanged.
• Single chooser seed: 20e7cbb51ab8b49eac12de2f825e100a, track independent-verification; complete output retained in SELECTION.json.
• Selected-record SHA256: 10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32.
• Exact live-input Git blobs/SHA256 pins: SOURCES.json; exact archive members and canonical observation receipt: RESULT.json.
• The complete overlap snapshot at 2026-10-14T19:02:09Z covered 353 open PRs including drafts, 738 discussion/comment/reply records, and 1536 local records. PR2079's body, immutable proof and current head were checked directly. This is not a guarantee of absence or novelty.

The standard-library verifier authenticates source bytes before parsing, imports no predecessor Python, independently reconstructs R from original scalar operations and owner routes from the phase axes, executes the ordered maps on exact sparse functions, and replays the original hosted-template schedule. Regeneration compares the complete canonical result, not compression headers.

uv run --python 3.12 --no-project python -I -O -B research/qq16-b2-observation-kernel/verify.py
uv run --python 3.12 --no-project python -B scripts/research_package.py --package research/qq16-b2-observation-kernel

Observed final output:

PASS_QQ16_B2_OBSERVATION_KERNEL
3 ordinary ports; B1h=B2h=0; original A nonzero; 8 zero observations; 8 rejecting controls
PASS_REGISTERED_RESEARCH_PACKAGE research/qq16-b2-observation-kernel outcome=negative-result

The eight controls reject a changed dependency coefficient, changed chart axis, omitted A cancellation, missing negative bridge, old-Y/completed-X type confusion, replacement by a detecting B0 observation, payload-only routing and source-byte mutation. The required selected-baseline binding-only working example also passed. No full selected cold replay, proof-assistant run, human review or hosted-CI pass is claimed.

Open next questions

1. Does adding B0 together with B2 and retained observations recover the whole fixed-pair kernel? First derive the full ordered kernel; the B0 positive escape control here proves only that it detects this witness. Actual native access and complete pricing remain open.
2. Can a changed first pair preserve both old-chart components cheaply? Establish its arbitrary-input identity and full output/hosting/restoration invoice before synthesis.

Prepared for Adam Gall with substantial OpenAI Codex assistance in research, proof, implementation and verification. Apache-2.0; predecessor credit and source notices remain intact.