← back to the board
[[62,18,7]] d ≤
n
62
k
18
d
7
kd²/n
14.2258
w
8
X/Z
1

Share this result

Distance

X/Z asymmetry 1 · d_X ≤ 7, d_Z ≤ 7 · w_X = 8, w_Z = 8 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)
d_X 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)
[2, 10, 18, 26, 36, 45, 52]
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)
[1, 22, 25, 31, 32, 41, 59]
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 6 · H_Z 6 (shortest cycle of each side’s Tanner graph; longer is friendlier to belief propagation)
check weights H_X 7–8 (mean 7.909) · H_Z 7–8 (mean 7.864)
qubit degrees H_X 1–4 (mean 2.806) · H_Z 1–4 (mean 2.79)
trapping sets H_X (1,1)×3 (2,1)×4 (3,1)×11 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,1): 3 (1,2): 17 (1,3): 31 (1,4): 11 (2,1): 4 (2,2): 32 (2,3): 128 (2,4): 241 (2,5): 165 (2,6): 32 (3,1): 11 (3,2): 105 (3,3): 533 (3,4): 1603 (3,5): 2549 (3,6): 2165 (3,7): 1054 (3,8): 407 (3,9): 99 (3,10): 11
trapping sets H_Z (1,1)×3 (2,1)×3 (3,1)×12 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,1): 3 (1,2): 18 (1,3): 30 (1,4): 11 (2,1): 3 (2,2): 35 (2,3): 135 (2,4): 227 (2,5): 165 (2,6): 30 (3,1): 12 (3,2): 107 (3,3): 560 (3,4): 1630 (3,5): 2441 (3,6): 2097 (3,7): 1036 (3,8): 368 (3,9): 106 (3,10): 7

Construction & provenance

authors @vprusso
provenance submitted through the challenge
novelty novelty not audited
construction Priced construction calculus E-PEEL of codes/63-18-7.json ([[63,18,7]], max check weight 8; itself a priced-calculus E-PEEL of codes/64-18-8.json, a Lin and Pryadko 2BGA code over SmallGroup(32,21)): delete qubit 60 (0-based index in the parent file) together with its unique Z check b12, 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 Claude Fable 5.1 (claimed, not verified)
builds on arXiv:2306.16400
date 2026-11-04
notes Single-step priced-calculus E-PEEL child of board entry 63-18-7. verify/validate_candidate.py found no board entry sharing this code's fingerprint or Weisfeiler-Leman signature, local-Hadamard images included.
family other (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

[[62,18,7]] priced calculus E-PEEL of codes/63-18-7.json

Direction & hypothesis

Unrestricted weight-8 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/63-18-7.json ([[63,18,7]], max check weight 8; itself a priced-calculus E-PEEL of codes/64-18-8.json, a Lin and Pryadko 2BGA code over SmallGroup(32,21)). Peeling qubit 60 with the one Z check that touches it keeps k = 18 and the witnessed distance bound d <= 7 while dropping one qubit, so it sits one qubit to the left of its parent on the frontier. Max check weight stays 8.

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 [[62,18,7]] at max check weight 8. 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 <= 7 (upper_bound), Z: d <= 7 (upper_bound).

Matched-depth peer audit (research/audits/leader_audit.py pair): credible: both claims held at matched depth, the gain survives; candidate [[62,18,7]] w8 reads d <= 7 and peer codes/62-18-6.json reads d <= 6 (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/63-18-7.json, delete qubit 60 (0-based index in that file) together with its unique Z check b12, 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': 60, 'sector': 'Z', 'row_id': 'b12'}). 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 22 (max weight 8) · Z-checks 22 (max weight 8)
H_X (22 checks, sparse supports)
[0, 8, 12, 30, 31, 40, 53, 59] [0, 1, 18, 23, 32, 43, 46, 57] [0, 2, 17, 19, 33, 39, 49, 56] [3, 19, 23, 27, 34, 42, 51, 61] [1, 4, 24, 26, 35, 41, 49, 52] [2, 5, 21, 25, 32, 36, 48, 60] [1, 2, 3, 6, 31, 37, 55] [3, 7, 12, 26, 38, 48, 54, 56] [4, 8, 27, 29, 36, 39, 47, 55] [5, 6, 9, 10, 33, 35, 40, 61] [3, 8, 10, 25, 41, 46, 50, 58] [4, 6, 7, 11, 32, 42, 45, 59] [5, 12, 27, 28, 37, 43, 44, 52] [7, 13, 18, 29, 33, 44, 58] [10, 14, 17, 28, 38, 45, 55, 57] [9, 11, 15, 16, 37, 39, 46, 54] [0, 7, 10, 16, 34, 47, 52, 60] [8, 11, 13, 17, 35, 43, 48, 51] [9, 12, 14, 18, 36, 42, 49, 50] [13, 19, 24, 30, 37, 45, 50, 60] [2, 14, 16, 20, 41, 44, 51, 59] [15, 17, 21, 22, 31, 42, 52, 58]
H_Z (22 checks, sparse supports)
[0, 6, 21, 29, 31, 32, 33, 47] [1, 5, 11, 30, 32, 35, 37, 53] [2, 9, 13, 27, 33, 36, 37, 51] [3, 16, 24, 28, 34, 37, 38, 41] [4, 9, 17, 23, 35, 39, 42, 57] [5, 8, 18, 22, 36, 40, 43, 58] [6, 12, 15, 19, 37, 40, 42, 56] [7, 14, 22, 27, 38, 42, 44, 47] [2, 8, 15, 26, 31, 39, 41, 48] [0, 9, 24, 25, 40, 46, 49, 60] [4, 10, 20, 30, 40, 41, 45, 47] [1, 12, 17, 31, 38, 43, 49] [12, 13, 20, 25, 44, 48, 50, 53] [11, 14, 19, 26, 45, 49, 51, 54] [1, 10, 15, 27, 46, 52, 55, 61] [8, 16, 23, 46, 47, 51, 53] [5, 7, 17, 24, 33, 45, 48, 52] [2, 4, 18, 28, 32, 44, 49, 55] [10, 18, 19, 33, 34, 50, 57] [3, 17, 20, 29, 51, 55, 56, 58] [4, 12, 16, 21, 36, 52, 54, 59] [0, 22, 26, 28, 52, 53, 56, 57]
Code ID 62-18-7 · download JSON · raw on GitHub