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[[49,17,3]] d =
n
49
k
17
d
3
kd²/n
3.122
w
6
X/Z
1
g
0.0488
r
4.0
layers
1
swaps
54

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Distance

X/Z asymmetry 1 · d_X = 3, d_Z = 3 · w_X = 6, w_Z = 6 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)
d_X 3 · witness weight 3 (claimed upper_bound)
witness operator (support, 3 qubits)
[33, 40, 48]
d_Z 3 · witness weight 3 (claimed upper_bound)
witness operator (support, 3 qubits)
[5, 33, 48]
certificate exact, d = 3 · scipy/HiGHS cutoff IP
X: no logical < 3 exists; Z: no logical < 3 exists

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 5–6 (mean 5.688) · H_Z 5–6 (mean 5.562)
qubit degrees H_X 1–3 (mean 1.857) · H_Z 1–3 (mean 1.816)
trapping sets H_X (1,1)×14 (2,1)×56 (3,0)×36 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,1): 14 (1,2): 28 (1,3): 7 (2,1): 56 (2,2): 104 (2,3): 40 (2,4): 2 (3,0): 36 (3,1): 188 (3,2): 366 (3,3): 292 (3,4): 132 (3,5): 32
trapping sets H_Z (1,1)×15 (2,1)×65 (3,0)×43 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,1): 15 (1,2): 28 (1,3): 6 (2,1): 65 (2,2): 92 (2,3): 33 (2,4): 1 (3,0): 43 (3,1): 198 (3,2): 305 (3,3): 246 (3,4): 98 (3,5): 21 (3,6): 1
witness diameter X 2.2361 · Z 6.0828 (Euclidean support diameter of the stored distance witnesses in the layout; an upper bound on the exhibited logicals’ spread, not a minimum over all logicals)

Verified 2D layout

as measured by the verifier: every check drawn over the submitted coordinates; the interaction radius is the longest dashed pair
r = 4
X checkZ checkqubit site (49)dashed: the pair setting the interaction radiushover a check to isolate its qubits; click to pin — repeated clicks cycle through overlapping checks; click empty space to release
routing cost 54 nearest-neighbor SWAPs per round in total, at most 4 for one check (heuristic: MST lower bound on the layout, with one lattice step = the minimum qubit spacing 1; not a rank)

Construction & provenance

authors @mathysrennela
provenance submitted through the challenge
novelty novelty not audited
construction SAT search (local_sat, n_side=7, G=16, max_weight=6, t=2 detection, radius 2.0, shared_t3) over 2D-local CSS codes on a 7x7 grid; found a weight-6 code with k=17, d>=3.
model DeepSeek V4 Flash 0731 (claimed, not verified)
date 2026-09-18
notes Checked against the current board: the trusted gate's dedup found no exact duplicate and no WL-equivalent existing entry; this is a new SAT-found code, not equivalent to a prior submission.
family other (a tag, not a ranking)
locality 2D-local single (computed from the layout)
weight class weight ≤ 6 (computed)

How this code was found

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

[[49,17,3]] — SAT t=2 weight-6 2D-local code on a 7×7 grid

Direction & hypothesis

Hackathon (#1155) SAT-search. The 2026-09-18 t=2 session placed [[16,6,3]], [[25,9,3]], [[36,12,3]] on the weight-6 × local-2d-single frontier. The 7×7 (n=49) grid was budget-walled in-session; this code is the night campaign's T3 result: a t=2 weight-6 code at n=49 with k=17, d=3, filling the frontier gap between n=36 and n=40 in the weight-6 × local-2d-single cell.

What was searched

local_sat.py `enumerate_local_sat_codes(n_side=7, G=16, w=6, t=2, radius=2.0, shared_t3=True, solver="cadical")`, run overnight with per-solve conf/time budgets. G=15 was UNSAT; G=16 produced [[49,17,3]] codes. Screened at 800-trial RIS d≥3, dominance-checked against the current single-layer w≤6 board, and gate-packaged.

Evidence trail

Witness-backed upper_bound d=3 (weight-3 logicals on both sides). validate_candidate: passed=true, verify.ok=true, refute.refuted=false (no lighter logical in the gate's RIS trials), dedup clean, board_advancing=true. Independent deep confirmation at 100,000 RIS trials found no logical lighter than weight 3 on either side (lightest X-logical weight 3, lightest Z-logical weight 3). Interaction radius 4.00 (hackathon-eligible).

Dead ends

7×7 t=2 at G=15 is UNSAT (too few checks to satisfy t=2 detection). The t=4 (d≥5) stages at 5×5/6×6 produced no codes within budget.

Tools

local_sat.py (shared_t3, cadical, per-solve budgets), kit {css,surrogate,submit}, verify/validate_candidate.py (untouched). Model: DeepSeek V4 Flash 0731.

Reproduction

from local_sat import enumerate_local_sat_codes
gen = enumerate_local_sat_codes(7, 16, 6, 2, 2.0, seed=0, max_codes=80,
    solver="cadical", conf_budget=2_000_000, time_budget=600.0,
    stream=True, shared_t3=True)
# pick a k=17, d>=3 code, package with make_submission(coordinates=..., layers=1)

Parity checks

X-checks 16 (max weight 6) · Z-checks 16 (max weight 6)
H_X (16 checks, sparse supports)
[19, 26, 27, 40, 41, 47] [8, 15, 16, 21, 28, 30] [1, 3, 8, 9, 23] [20, 26, 33, 34, 40, 48] [0, 2, 10, 14, 15] [25, 31, 37, 39, 46, 47] [17, 23, 24, 29, 31, 38] [6, 12, 13, 20, 26, 34] [0, 7, 8, 9, 15] [4, 10, 11, 16, 18, 19] [14, 21, 22, 29, 35, 36] [22, 30, 36, 42, 43] [36, 37, 43, 44, 45] [2, 3, 9, 12, 18, 24] [5, 11, 13, 20, 25, 33] [32, 38, 40, 41, 45, 46]
H_Z (16 checks, sparse supports)
[35, 36, 37, 39, 43, 44] [1, 7, 8, 17, 21, 29] [0, 1, 7, 8, 15] [17, 18, 19, 24, 27] [4, 5, 19, 20, 26] [22, 31, 32, 36, 37, 38] [3, 9, 10, 15, 16] [3, 11, 18, 23, 25, 31] [39, 40, 44, 45, 47, 48] [20, 26, 32, 33, 41, 48] [25, 26, 33, 34, 40, 46] [37, 42, 43, 44, 45, 46] [0, 7, 14, 21, 28] [2, 4, 6, 10, 12] [2, 8, 9, 14, 22, 30] [6, 11, 13, 19, 27]
Code ID 49-17-3 · download JSON · raw on GitHub