[[79,24,7]] · QEC Challenge

[[79,24,7]] d ≤

kd²/n

14.8861

X/Z

1.14

Share this result

Distance

X/Z asymmetry 1.14 · d_X ≤ 8, d_Z ≤ 7 · w_X = 10, w_Z = 10 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)

d_X 8 · witness weight 8 (claimed upper_bound)

witness found by @vprusso · research/kit/surrogate.lightest_logical · found at 2000 trials · survived 2000 trials · 2026-11-03

witness operator (support, 8 qubits)

[8, 15, 32, 36, 40, 42, 58, 59]

d_Z 7 · witness weight 7 (claimed upper_bound)

witness found by @vprusso · research/kit/surrogate.lightest_logical · found at 2000 trials · survived 2000 trials · 2026-11-03

witness operator (support, 7 qubits)

[4, 5, 28, 30, 34, 38, 65]

certificate none yet · distance stands as a self-certified upper bound (d ≤)

Diagnostics

computed by the verifier from the parity checks, the layout, and the stored witnesses; shown as evidence, not used for ranking

girth H_X 4 · H_Z 4 (shortest cycle of each side’s Tanner graph; longer is friendlier to belief propagation)

check weights H_X 10 · H_Z 9–10 (mean 9.857)

qubit degrees H_X 1–5 (mean 3.418) · H_Z 1–5 (mean 3.494)

trapping sets H_X (1,1)×1 (2,1)×2 (3,1)×3 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

full (size, syndrome weight): count census for H_X

(1,1): 1 (1,2): 10 (1,3): 32 (1,4): 27 (1,5): 9 (2,1): 2 (2,2): 12 (2,3): 98 (2,4): 242 (2,5): 348 (2,6): 282 (2,7): 109 (2,8): 18 (3,1): 3 (3,2): 65 (3,3): 287 (3,4): 1315 (3,5): 3151 (3,6): 5027 (3,7): 5458 (3,8): 3892 (3,9): 1880 (3,10): 644 (3,11): 163 (3,12): 18 (3,13): 3

trapping sets H_Z (1,1)×1 (2,1)×3 (3,1)×1 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

full (size, syndrome weight): count census for H_Z

(1,1): 1 (1,2): 9 (1,3): 29 (1,4): 30 (1,5): 10 (2,1): 3 (2,2): 15 (2,3): 77 (2,4): 200 (2,5): 356 (2,6): 299 (2,7): 150 (2,8): 18 (3,1): 1 (3,2): 38 (3,3): 250 (3,4): 1047 (3,5): 2634 (3,6): 4668 (3,7): 5600 (3,8): 4514 (3,9): 2341 (3,10): 854 (3,11): 218 (3,12): 35 (3,13): 2

Construction & provenance

authors @vprusso

provenance submitted through the challenge

novelty novelty not audited

construction Priced construction calculus E-PEEL of codes/80-24-8.json ([[80,24,8]], max check weight 10; the 2BGA code over ab(5,2,2,2) by @FarLab): delete qubit 70 (0-based index in the parent file) together with its unique X check a6, and relabel the surviving qubits in increasing order of their parent indices. Consumer: github.com/unitaryfoundation/code-calculus @ 1b9a942, machine/priced_calculus.py.

model Claude Fable 5.1 (claimed, not verified)

date 2026-11-04

notes Single-step priced-calculus E-PEEL child of board entry 80-24-8. verify/validate_candidate.py found no board entry sharing this code's fingerprint or Weisfeiler-Leman signature, local-Hadamard images included.

family bivariate bicycle (a tag, not a ranking)

locality unrestricted (computed from the layout)

weight class weight > 8 (computed)

How this code was found

the research note submitted with this code · raw markdown · all notes

[[79,24,7]] priced calculus E-PEEL of codes/80-24-8.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/80-24-8.json ([[80,24,8]], max check weight 10; the 2BGA code over ab(5,2,2,2) by @FarLab). Peeling qubit 70 with the one X check that touches it keeps k = 24 and lowers the witnessed distance bound by one, from 8 to 7, while dropping one qubit. 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 [[79,24,7]] 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) | 7 | | 1,000,000 (seed 101) | 7 | | 1,000,000 (seed 102) | 7 | | 10,000,000 (seed 103) | 7 |

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 <= 8 (upper_bound), Z: d <= 7 (upper_bound).

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/80-24-8.json, delete qubit 70 (0-based index in that file) together with its unique X check a6, where the X rows are numbered a1, a2, ... 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': 70, 'sector': 'X', 'row_id': 'a6'}). 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.

Parity checks

X-checks 27 (max weight 10) · Z-checks 28 (max weight 10)

H_X (27 checks, sparse supports)

[0, 15, 16, 30, 34, 40, 48, 57, 67, 76] [1, 14, 17, 31, 35, 41, 49, 56, 66, 75] [2, 13, 18, 28, 32, 42, 50, 59, 65, 78] [3, 12, 19, 29, 33, 43, 51, 58, 64, 77] [4, 11, 20, 26, 38, 44, 52, 61, 70, 72] [6, 9, 22, 24, 36, 46, 54, 63, 69, 74] [7, 8, 23, 25, 37, 47, 55, 62, 68, 73] [2, 8, 23, 24, 38, 45, 48, 56, 65, 74] [3, 9, 22, 25, 39, 44, 49, 57, 64, 73] [0, 10, 21, 26, 36, 47, 50, 58, 67, 72] [1, 11, 20, 27, 37, 46, 51, 59, 66, 71] [6, 12, 19, 28, 34, 41, 52, 60, 69, 78] [7, 13, 18, 29, 35, 40, 53, 61, 68, 77] [4, 14, 17, 30, 32, 43, 54, 62, 70, 76] [6, 10, 16, 31, 32, 43, 53, 56, 64, 72] [7, 11, 17, 30, 33, 42, 52, 57, 65, 71] [4, 8, 18, 29, 34, 41, 55, 58, 66, 74] [5, 9, 19, 28, 35, 40, 54, 59, 67, 73] [2, 14, 20, 27, 36, 47, 49, 60, 68, 76] [0, 14, 18, 24, 39, 41, 51, 61, 64, 71] [1, 15, 19, 25, 38, 40, 50, 60, 65, 72] [2, 12, 16, 26, 37, 43, 49, 63, 66, 73] [4, 10, 22, 28, 35, 45, 55, 57, 68, 75] [7, 8, 22, 26, 32, 40, 49, 59, 69, 71] [6, 9, 23, 27, 33, 41, 48, 58, 68, 72] [5, 10, 20, 24, 34, 42, 51, 57, 70, 73] [3, 12, 18, 30, 36, 44, 53, 63, 65, 75]

H_Z (28 checks, sparse supports)

[0, 13, 19, 25, 32, 40, 50, 62, 64, 78] [1, 12, 18, 24, 33, 41, 51, 63, 65, 77] [2, 15, 17, 27, 34, 42, 48, 60, 66, 76] [3, 14, 16, 26, 35, 43, 49, 61, 67, 75] [4, 9, 23, 29, 36, 44, 54, 58, 68, 74] [5, 8, 22, 28, 37, 45, 55, 59, 69, 73] [6, 11, 21, 31, 38, 46, 52, 56, 72] [7, 10, 20, 30, 39, 47, 53, 57, 70, 71] [0, 8, 21, 27, 33, 47, 48, 58, 71] [1, 9, 20, 26, 32, 46, 49, 59, 70, 72] [2, 10, 23, 25, 35, 45, 50, 56, 68, 73] [3, 11, 22, 24, 34, 44, 51, 57, 69, 74] [4, 12, 17, 31, 37, 43, 52, 62, 66, 75] [5, 13, 16, 30, 36, 42, 53, 63, 67, 76] [6, 14, 19, 29, 39, 41, 54, 60, 64, 77] [1, 8, 16, 29, 35, 40, 55, 56, 66, 77] [0, 9, 17, 28, 34, 41, 54, 57, 67, 78] [3, 10, 18, 31, 33, 42, 53, 58, 64, 75] [5, 12, 20, 25, 39, 44, 51, 60, 73] [7, 14, 22, 27, 37, 46, 49, 62, 68, 71] [3, 9, 16, 24, 37, 46, 48, 63, 64, 73] [2, 8, 17, 25, 36, 47, 49, 62, 65, 74] [1, 11, 18, 26, 39, 44, 50, 61, 66, 71] [7, 13, 20, 28, 33, 42, 52, 59, 68, 77] [5, 11, 17, 24, 32, 42, 54, 56, 70, 71] [4, 10, 16, 25, 33, 43, 55, 57, 72] [7, 9, 19, 26, 34, 40, 52, 58, 69, 73] [1, 15, 21, 28, 36, 46, 50, 60, 67, 75]

Code ID 79-24-7 · download JSON · raw on GitHub