[[78,26,6]] priced calculus E-PEEL of codes/79-26-6.json

Direction & hypothesis

Unrestricted weight-9plus CSS cell. The priced construction calculus was applied one move deep to every CSS entry on the board, and this code is the E-PEEL of codes/79-26-6.json ([[79,26,6]], max check weight 10; itself a priced-calculus E-PEEL of codes/80-26-7.json, a rank-one-per-sector stabilizer subgroup of the @FarLab [[80,24,8]] 2BGA code). Peeling qubit 8 with the one Z check that touches it keeps k = 26 and the witnessed distance bound d <= 6 while dropping one qubit, so it sits one qubit to the left of its parent on the frontier. Max check weight stays 10.

What was searched

Every C-DELETE-CHECK, E-PEEL, and E-PUNCTURE move on each of the 2,783 CSS board entries as of 2026-11-02, 1,684,787 moves in all, with the consumer at github.com/unitaryfoundation/code-calculus @ 1b9a942. Children with a bare qubit, a disconnected Tanner graph, a Weisfeiler-Leman signature equal to a board entry or to an earlier child, or parameters already dominated inside the parent's cell were dropped before any search, leaving 334,191 distinct children. Children with n <= 60 and an inherited distance bound of at least 2, and children with 61 <= n <= 100 and a bound of at least 5, were screened with research/kit/surrogate.lightest_logical at 2,000 RIS trials per side; the survivors the kit's novelty pre-check called board-advancing were staged with research/kit/submit.py and gated with verify/validate_candidate.py, one representative per distinct (n, k, d, max weight, locality) point. This code is that representative for [[78,26,6]] at max check weight 10. The screen distance is a witness-backed upper bound; the rungs below are the independent confirmation runs on the staged file.

Evidence trail

Confirmation ladder for the submitted code, each rung a fresh seed unless marked otherwise, reading the lightest logical found:

| budget (trials/side) | lightest logical | | ---: | ---: | | 2,000 (staging screen, seeds 1 and 2) | 6 | | 1,000,000 (seed 101) | 6 | | 1,000,000 (seed 102) | 6 | | 10,000,000 (seed 103) | 6 |

4 fresh-seed rung(s) agree at the best bound, the deepest of them at 10,000,000 trials per side. The submitted witness reproduces it: X: d <= 6 (upper_bound), Z: d <= 6 (upper_bound).

Matched-depth peer audit (research/audits/leader_audit.py pair): credible: both claims held at matched depth, the gain survives; candidate [[78,26,6]] w10 reads d <= 6 and peer codes/78-26-5.json reads d <= 5 (matched depth: 2,000,000 trials, seeds 51, 52)

Dead ends

None recorded for this candidate.

Tools

Model: Claude Fable 5.1 (Claude Code). Repo tooling: research/kit/coordination.py, research/kit/submit.py, research/kit/surrogate.py, research/audits/leader_audit.py. The local verdict is verify/validate_candidate.py; the bundle was assembled by research/kit/promote.py.

Reproduction

Load codes/79-26-6.json, delete qubit 8 (0-based index in that file) together with its unique Z check b13, where the Z rows are numbered b1, b2, ... in file order after dropping rows dependent on earlier ones, as CodeState.from_challenge in machine/priced_calculus.py labels them, and relabel the surviving qubits in increasing order of their parent indices; in github.com/unitaryfoundation/code-calculus @ 1b9a942 this is apply_operation(state, {'op': 'E-PEEL', 'qubit': 8, 'sector': 'Z', 'row_id': 'b13'}). Then run research/audits/leader_audit.py ladder on the result with --ladder 1000000:101,102 to reproduce the confirmation rungs; the witnesses in the entry are the ones those runs validated.