One card per basic rewrite rule: the fraction of applicable instances that preserve distance, the Δd distribution, and the structural neighborhoods where distance always breaks. All figures are computed per city and only enter a card after the T2 gate (dual-implementation agreement + anchors + Prop 3.3 oracle) passes.
Merging same-color spiders. The gentlest rule — and the first question is whether "gentle" survives contact with boundary (measurement) spiders.
applicable instances on anchors (T3 layer 2, 2026-10-04): 14 / 26 / 42 / 31 on [[4,2,2]] / [[5,1,3]] / Steane / Shor — candidates equal applicable on this circuit class.
Δd: not measured — circuit extraction (extract_simple) proved non-faithful on the tensor-verifiable anchors (support mismatch), and full-tensor verification of the largest anchor exceeds memory. "Not measured" is reported, never read as zero. Planned path: graph-side fault semantics (RPK25 gadget orbit).
Complementing a spider's neighborhood with π/2 phase dressing. Known to be powerful — power is exactly what distance fears.
applicable instances: 0 / 0 / 0 / 0 — lc is structurally absent on bare check circuits: PyZX's lc precondition requires a Z-type spider with phase exactly π/2 or 3π/2, and bare syndrome extraction uses only 0/π phases. Reported as observed on this circuit class, not as a general claim.
Swapping two connected spiders of opposite color. The workhorse of circuit optimization; its distance profile across the three cities is one of this atlas' headline charts.
candidate pairs: 4 / 13 / 17 / 24, applicable after preconditions: 0 / 0 / 0 / 0 — PyZX pivot requires a HADAMARD edge, both spiders Z-type with phase ∈ {0, π}, and ≤ 1 boundary neighbor each; bare check graphs violate these. Candidates ≠ applicable is itself the census datum.
| Field | Definition | Discipline |
|---|---|---|
| Preserve ratio | #(Δd = 0) / #applicable | denominator = total applicable instances, sampled source declared |
| Δd histogram | counts over {0, −1, ≤ −2} | per city, per code distance |
| Break neighborhoods | structural contexts where Δd < 0 in 100% of sampled instances | conjecture-level language only: "we observe" |
| Observation | Value | Note |
|---|---|---|
| Circuit-level fault distance dcirc on bare check circuits | 1 / 2 / 2 / 1 | vs published d = 2 / 3 / 3 / 3 — expected physics, not a bug: single-location ancilla phase faults spread into undetected partial stabilizers under bare syndrome extraction (C0 invariance gate PASS on all four anchors). |
| Extraction faithfulness | non-faithful | extract_simple output tensor mismatches the post-rewrite diagram on the tensor-verifiable anchors (support mismatch, not a tolerance effect); full-tensor verification exceeds memory on Shor. A gate bug that let "inconclusive" silently count as verified was found and fixed the same day — the flip is why some numbers moved. |
| H-edge same-color pairs (sp-h family) | refused | naive fusion through a HADAMARD connector would create a non-trivial H self-loop; such pairs are reported as not-applicable, pending a π-phase-correction variant. |