[[46,8,7]] · QEC Challenge

[[46,8,7]] d ≤

kd²/n

8.52174

X/Z

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 3000 trials · survived 3000 trials · 2026-11-03

witness operator (support, 7 qubits)

[5, 10, 13, 14, 15, 37, 39]

d_Z 7 · witness weight 7 (claimed upper_bound)

witness found by @vprusso · research/kit/surrogate.lightest_logical · found at 3000 trials · survived 3000 trials · 2026-11-03

witness operator (support, 7 qubits)

[13, 18, 21, 23, 31, 36, 40]

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 7–8 (mean 7.789) · H_Z 7–8 (mean 7.789)

qubit degrees H_X 1–5 (mean 3.217) · H_Z 1–5 (mean 3.217)

trapping sets H_X (1,1)×1 (2,2)×14 (3,1)×5 (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): 11 (1,3): 17 (1,4): 11 (1,5): 6 (2,2): 14 (2,3): 56 (2,4): 105 (2,5): 145 (2,6): 99 (2,7): 48 (2,8): 10 (3,1): 5 (3,2): 37 (3,3): 188 (3,4): 597 (3,5): 1203 (3,6): 1596 (3,7): 1333 (3,8): 879 (3,9): 443 (3,10): 174 (3,11): 45 (3,12): 10

trapping sets H_Z (1,1)×1 (2,2)×11 (3,1)×5 (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): 11 (1,3): 17 (1,4): 11 (1,5): 6 (2,2): 11 (2,3): 58 (2,4): 119 (2,5): 124 (2,6): 109 (2,7): 43 (2,8): 13 (3,1): 5 (3,2): 28 (3,3): 196 (3,4): 647 (3,5): 1184 (3,6): 1529 (3,7): 1372 (3,8): 862 (3,9): 443 (3,10): 168 (3,11): 47 (3,12): 13 (3,13): 1

Construction & provenance

authors @vprusso

provenance submitted through the challenge

novelty novelty not audited

construction Priced construction calculus E-PEEL of codes/47-8-7.json ([[47,8,7]], max check weight 8; itself a priced-calculus E-PEEL of codes/48-8-8.json, a two-block group-algebra code over SmallGroup(24,4) from arXiv:2610.13880): delete qubit 23 (0-based index in the parent file) together with its unique Z check b7, 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)

builds on arXiv:2610.13880

date 2026-11-04

notes Single-step priced-calculus E-PEEL child of board entry 47-8-7. 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

[[46,8,7]] priced calculus E-PEEL of codes/47-8-7.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/47-8-7.json ([[47,8,7]], max check weight 8; itself a priced-calculus E-PEEL of codes/48-8-8.json, a two-block group-algebra code over SmallGroup(24,4) from arXiv:2610.13880). Peeling qubit 23 with the one Z check that touches it keeps k = 8 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 3,000 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 [[46,8,7]] 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 | | ---: | ---: | | 3,000 (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).

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/47-8-7.json, delete qubit 23 (0-based index in that file) together with its unique Z check b7, 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': 23, 'sector': 'Z', 'row_id': 'b7'}). 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 19 (max weight 8) · Z-checks 19 (max weight 8)

H_X (19 checks, sparse supports)

[0, 1, 5, 10, 11, 24, 38, 41] [0, 2, 12, 19, 20, 25, 27, 39] [1, 2, 3, 7, 21, 26, 32, 40] [1, 4, 14, 16, 21, 23, 27, 44] [2, 5, 6, 16, 17, 28, 30, 42] [3, 4, 6, 12, 18, 29, 36, 43] [0, 4, 7, 13, 18, 24, 30, 45] [3, 5, 8, 13, 31, 33, 44] [4, 5, 9, 19, 25, 32, 34] [6, 7, 9, 10, 15, 26, 33, 39] [6, 7, 11, 21, 22, 27, 31, 34] [1, 8, 9, 12, 22, 35, 37, 45] [2, 9, 13, 14, 22, 28, 36, 38] [3, 10, 11, 14, 19, 29, 37, 42] [3, 4, 11, 15, 20, 30, 35, 38] [11, 12, 13, 17, 23, 32, 39] [1, 14, 15, 17, 18, 25, 33, 40] [8, 9, 17, 20, 21, 24, 36, 42] [0, 10, 18, 21, 28, 37, 43]

H_Z (19 checks, sparse supports)

[0, 4, 17, 23, 24, 25, 30, 43] [1, 7, 20, 24, 26, 27, 35, 40] [2, 9, 18, 25, 26, 28, 36, 45] [3, 10, 22, 26, 29, 31, 37, 38] [2, 4, 11, 27, 29, 30, 32, 38] [5, 13, 21, 24, 28, 31, 32, 44] [5, 7, 15, 26, 30, 33, 34, 41] [8, 11, 16, 23, 31, 35, 41, 42] [3, 9, 17, 32, 33, 35, 36, 42] [8, 10, 18, 24, 33, 37, 43] [0, 9, 11, 24, 34, 37, 38, 39] [12, 15, 19, 25, 29, 35, 39] [6, 13, 20, 30, 31, 36, 39] [12, 14, 21, 23, 27, 36, 37, 40] [1, 13, 15, 23, 33, 38, 40, 45] [2, 10, 17, 28, 39, 40, 41, 42] [3, 16, 18, 29, 30, 40, 43, 44] [5, 14, 20, 25, 38, 42, 44] [6, 19, 21, 26, 27, 34, 42, 43]

Code ID 46-8-7 · download JSON · raw on GitHub