Bacon–Shor — Level-2 map

The phrase "local subsystem repetition code" compresses several different statements. These pages separate the algebra that is recomputed from the protocol claims that remain tied to literature.

1. Gauge group, center, and subsystem qubit count: the declared orientation, pair-generator ranks, strip stabilizers, noncommutation, center containment, protected-qubit count, and gauge-qubit count.
2. Dressed distance and the two repetition decoders: row/column parity quotients, exact sector lower bounds and witnesses, bare-versus-dressed representatives, and worked perfect-syndrome tables.
3. Gauge measurement and fault-tolerance boundaries: reconstructing center outcomes from pair measurements, why time order is decoder data, and why static, encoded-ancilla, concatenated, and Floquet performance claims cannot be merged.
4. Operations, gauge fixing, and variants: pairwise CNOT, square-block Hadamard with transposition, exact Shor row-space recovery with the logical-label dictionary, and the resources consumed by cited non-Clifford and surgery mechanisms.
5. Representation and realization ledger: compass, tensor, frustration-graph, autonomous, and Floquet dictionaries; static trapped-ion versus dynamical superconducting evidence; and explicit non-equivalences.

Reproduction contract

Run from the repository root:

source .venv/bin/activate
python atlas/bacon_shor/pedagogy/reproduce.py
make verify-entry E=atlas/bacon_shor

reproduce.py builds all three shipped rectangles and independently derives their gauge and center support matrices. It asserts generator counts and ranks, center containment, noncommuting local pairs, protected and gauge dimensions, bare logical commutation, exact pure-X and pure-Z dressed distances, repetition-syndrome factorization, pair-outcome reconstruction, square-block Hadamard/transposition symmetry, the exact Shor gauge-fixed row space and logical-label swap, scene/tour integrity, and T3 packet state.

The shared qeclib.distance API now minimizes physical Pauli weight in C(S)/G: exact search finishes complete weight layers and the verifier recomputes the three shipped finite d claims. The committed evidence rows also retain one seeded 5 × 7 witness of achieved weight 12 as bounded, with method rand-subsystem-dressed-logical-coset-v1, seed 17, and not-certified optimality. The independent witness gate checks stabilizer commutation, gauge nontriviality, and physical weight. This row is not a lower bound, an exact distance, or evidence for the family formula.

The card also omits a construction: tree. No registered operation adapter currently expresses the rectangular pair-gauge construction with exact row and qubit order. The deterministic constructor and this transcript establish the shipped presentation without pretending that an unsupported generic replay exists. The broader problem of certifying equality across gauge-fixed, subsystem, and subspace presentations is tracked by wanted:code-equivalence; the exact square-to-Shor row-space witness on this entry is evidence for one pair, not a general canonicalizer.

Provenance split

• Recomputed facts: qubit order; local gauge and center supports; all finite-instance ranks; center/gauge containment; n=rc, k=1, and (r-1)(c-1) gauge qubits; bare logical row/column algebra; exact pure-sector dressed distances for the shipped rectangles; repetition quotient and single-error syndrome tables; center-outcome products; square Hadamard/transposition mapping; exact 3 × 3 gauge-fixed Shor stabilizer row space and the cross-entry logical-label dictionary; constructor-derived scene and tour data.
• Bounded facts: the committed 5 × 7, seed-17, 32-trial search achieves a weight-12 dressed-logical representative and independently validates it. Its only guarantee is an upper bound; optimality is explicitly not-certified.
• Literature claims: historical subsystem construction; fault-tolerant extraction and decoder behavior beyond perfect gauge outcomes; biased-noise optimization; thresholds or logical rates of named circuits; transversal controlled-phase families; surgery, teleportation, deformation, and autonomous-dynamics resources; compass, tensor, and frustration-graph dictionaries; and every hardware demonstration.

No threshold, pseudo-threshold, one-point logical error rate, or device error rate is quoted in this packet. Dated negative findings are retained at the reader-facing location where they are used.