n
103
Target: the CSS unrestricted / any-weight frontier. Start from Jong Yeon Lee's [[104,30,8]] pair-partition CPM baseline in codes/104-30-8.json (Okada and Kasai, arXiv:2607.14091). Shortening one check row space and puncturing the other can trade one physical qubit and some distance for a new blocklength while keeping the logical-qubit count.
This is a derived code using a standard shortening operation, not a new code family. The resulting maximum check weight is 14, versus the parent's 8, so it does not compete on the weight-8 board. The gain is a nondominated tradeoff, not a strict improvement over the parent or a headline record. Literature novelty is unverified.
One deterministic candidate was constructed: remove parent qubit 0, shorten the X-check row space, and puncture the Z checks. No sweep over qubits, pivot choices, or other parent codes was performed. The source was the board at upstream commit c665b033956000ca1c058de851b8cd25b1ab289b.
The resulting matrices have 38 X checks and 39 Z checks on 103 qubits. Their ranks are 36 and 37, so k = 103 - 36 - 37 = 30. CSS commutation, connectivity, and both distance witnesses are checked by the repository's trusted verifier. No geometric layout is claimed.
Initial packaging used research/kit/submit.py with 100 NumPy RIS trials per side, seed 290926 for X and 290927 for Z. It returned weight-8 X and weight-7 Z logicals; both witnesses are stored in the submitted JSON.
Independent screens used research/kit/surrogate.py's distance_rand_witness, the unmodified verify/gf2_fast.cpp backend, pair depth 16, and two threads:
| Trials per side | Seed | Lightest logical | | ---: | ---: | ---: | | 10,000 | 290927 | 7, Z | | 100,000 | 290928 | 7, Z | | 2,000,000 | 290930 | 7, Z |
The deepest screen took about 69 seconds locally. These searches cover both sides but return only the lighter side's witness. No lower witness was found, and no candidate collapsed along this ladder.
The initial verify/validate_candidate.py run (seed 290929) returned passed: true, board_advancing: true, no dominators, and no exact or WL-equivalent board entry. The final document passed again with seed 291001. The full verify/gate_changed.py submission gate then passed with seed 291002: one Python RIS seed with a 37,360-trial target and a 120-second cap, plus 5,604,000 accelerated trials, found no logical lighter than 7. The gate reported the new code on its deep path. This is not a distance-only comparison with an existing entry.
The claim is strictly witness-backed: d_X <= 8, d_Z <= 7, and d <= 7. Repeated failed refutations are evidence, not an exact lower-bound proof.
There were no rejected construction candidates in this one-candidate pilot. The important limitation is check growth: eliminating the shortened column combines pairs of weight-8 X checks into weight-14 checks. This trades check locality for one fewer physical qubit. No circuit or decoder performance improvement has been tested.
GPT-6 (Codex), running locally on Windows with Python 3.12 and NumPy. Packaging used research/kit/submit.py; distance screening used research/kit/surrogate.py; validation used the pinned verify/ stack. The optional C++ accelerator was built from unchanged upstream source and its three dedicated tests passed. The model generated the shortening recipe and this note; the parent construction is credited above.
Read codes/104-30-8.json at the pinned upstream commit above. Convert its X and Z support lists to binary matrices, preserving their row order.
1. Let p be the first X-check row containing parent qubit 0 (p = 0). 2. XOR row p into every other X row containing qubit 0. 3. Remove X row p, then delete column 0 from both matrices. 4. Keep all remaining row and column orders. New qubit j is parent qubit j + 1. These matrices reproduce codes/103-30-7.json exactly.
All surviving X rows are zero on the deleted column, so removing that column cannot change their commutation with any punctured Z row. Row operations preserve the original X row space before its pivot is removed.
Package with make_submission using the initial budget and seed above, then run the three witness-returning screens with the listed settings. The submitted witnesses are from initial packaging; the later searches did not lower either submitted bound. Re-run the trusted checks with:
python verify/validate_candidate.py codes/103-30-7.json python verify/gate_changed.py --seed 291002 codes/103-30-7.json
For the candidate validator's duplicate/frontier result, stage the JSON outside codes/ and compare against the pinned base board before adding the candidate itself. Once added, a same-checkout duplicate check naturally finds its own board entry.