attested · 2/1600 re-run certificate script asserted: CERTIFIED chi(cat_7) >= 5; re-ran 2 of 1600 stored batches from scratch chosen from seed 20261017 and only checked the SHA-256 of the other 1598 against research/cat7_rank4/batch_manifest.json; the full enumeration (110.9 CPU-h on one Perlmutter CPU node (AMD EPYC 7763, 128 workers) for the corrected census of the full 4-covers of compressed cat_5, job 59930310, 1261 s wall, 2026-10-18 UTC; two earlier census runs (jobs 59924919 and 59926124, 736 s and 1,120 s) listed a fifth of the covers because their hash functionals wrapped int64 and are superseded; stages beta, B, C and A on an Apple silicon laptop (one core)) was not re-run
6 runs; 111.7 CPU-hours; 4 h wall-clock; on one Perlmutter CPU node (AMD EPYC 7763, 128 workers, 1,261 s) for the corrected census of the full 4-covers of compressed cat_5, after two superseded census runs (736 s and 1,120 s) whose hash functionals wrapped int64; Apple silicon laptop for the completion stages, the exact confirmation and the controls; claude-fable-5-1, designed, wrote and ran the exclusion and its planted controls.
Strict improvement of bounds/cat-m7-lower-4.json (de Messieres, PR 170). With bounds/cat-m7-upper-6.json the cell is 5 ≤ χ(cat_7) ≤ 6. Compression χ(cat_m) = χ(cm) as in bounds/cat-m5-lower-3.json; the two-qubit slices of c7 are c5, i c5 and the diagonal Clifford image i (-i)^{par(y)} c5(y) (asserted in the run). Planted positive controls for every stage (independent, dependent, repeated and invisible-term bases) recover their planted completion in the same code path (attacks/round31-J-lower-bounds/plants.py in the research record).
Vincent Russo · stabrank-research, round 31 (attacks/round31-J-lower-bounds) · two-qubit base slice of the even-weight compressed cat_7: every rank-4 decomposition has three or four terms visible at the base point; the bases (a census of full 4-covers of compressed cat_5, the rank-3 decompositions with an invisible, dependent or repeated term) are completed point by point under the qubit slice structure lemma and nothing completes
{
"schema_version": "0.1",
"orbit": "cat",
"m": 7,
"direction": "lower",
"rank": 5,
"certificate": {
"script": "verify_challenge/cert_cat_m7_rank4_attested.py",
"budget_s": 3600,
"attested": {
"batches": "research/cat7_rank4/batch_manifest.json",
"recomputed": 2,
"compute_hours": 110.9,
"hardware": "one Perlmutter CPU node (AMD EPYC 7763, 128 workers) for the corrected census of the full 4-covers of compressed cat_5, job 59930310, 1261 s wall, 2026-10-18 UTC; two earlier census runs (jobs 59924919 and 59926124, 736 s and 1,120 s) listed a fifth of the covers because their hash functionals wrapped int64 and are superseded; stages beta, B, C and A on an Apple silicon laptop (one core)",
"note": "The census lists every 4-set of four-qubit stabilizer states whose span contains c_5 = cat_5(y, parity(y)) with four nonzero coefficients and independent states, one per orbit of the group generated by permutations of the four qubits, R(x)R on a pair and the parity swap of cat_7 (100 pivot orbits, 2,292,776 pivot pairs, 16,705 covers), stored per work unit (pivot orbit, partner stride class, 1,600 batches) under research/cat7_rank4/results/. The certificate verifies every stored batch hash, re-enumerates two units from scratch (seed 20261017) and compares, then runs the whole exclusion: stages beta (one invisible term), B (dependent bases: none exist), C (a repeated base state) and A (the stored covers), with every candidate completion rebuilt and decided exactly; a decomposition with fewer than four terms would fail the run. The census functionals reduce every product modulo P before summing (research/cat7_rank4/census_control.py plants targets: the corrected functional lists all ten, the wrapped one none). Completeness of the census rests on the stored outputs and on research/cat7_rank4/census4_run.py, which regenerates any unit."
},
"expect": "CERTIFIED chi(cat_7) >= 5"
},
"provenance": {
"author": "Vincent Russo",
"reference": "stabrank-research, round 31 (attacks/round31-J-lower-bounds)",
"date": "2026-10-17",
"github": [
"vprusso"
],
"method": "two-qubit base slice of the even-weight compressed cat_7: every rank-4 decomposition has three or four terms visible at the base point; the bases (a census of full 4-covers of compressed cat_5, the rank-3 decompositions with an invisible, dependent or repeated term) are completed point by point under the qubit slice structure lemma and nothing completes",
"compute": {
"cpu_hours": 111.7,
"wall_clock_hours": 4.0,
"runs": 6,
"hardware": "one Perlmutter CPU node (AMD EPYC 7763, 128 workers, 1,261 s) for the corrected census of the full 4-covers of compressed cat_5, after two superseded census runs (736 s and 1,120 s) whose hash functionals wrapped int64; Apple silicon laptop for the completion stages, the exact confirmation and the controls",
"llm": [
{
"model": "claude-fable-5-1",
"role": "designed, wrote and ran the exclusion and its planted controls"
}
]
}
},
"notes": "Strict improvement of bounds/cat-m7-lower-4.json (de Messieres, PR 170). With bounds/cat-m7-upper-6.json the cell is 5 <= chi(cat_7) <= 6. Compression chi(cat_m) = chi(c_m) as in bounds/cat-m5-lower-3.json; the two-qubit slices of c_7 are c_5, i c_5 and the diagonal Clifford image i (-i)^{par(y)} c_5(y) (asserted in the run). Planted positive controls for every stage (independent, dependent, repeated and invisible-term bases) recover their planted completion in the same code path (attacks/round31-J-lower-bounds/plants.py in the research record)."
}