attested · 2/859 re-run certificate script asserted: CERTIFIED chi(qubit_sqrtT^7) >= 7; re-ran 2 of 859 stored batches from scratch chosen from seed 20261023 and only checked the SHA-256 of the other 857 against research/sqrtt_m5_rank6/batch_manifest.json; the full enumeration (46.3 CPU-h on Perlmutter CPU node (two AMD EPYC 7763, 128 worker processes), NERSC job 60159879, 2026-10-23 16:04 to 16:41 UTC; the representatives stage single-threaded (846 s), the pivot census 46.1 CPU-h over 128 workers (about 23 min wall)) was not re-run
0 runs; 0 CPU-hours; 0 h wall-clock; on none beyond the m = 6 certificate, which prints this line from the same computation.
(⟨0| ⊗ I)|sqrtT⟩⊗7 = 2^{-1/2} |sqrtT⟩⊗6 and a computational-basis slice of a stabilizer state is a stabilizer state or zero, so χ(|sqrtT⟩⊗7) ≥ χ(|sqrtT⟩⊗6) ≥ 7 (qubit_sqrtT-m6-lower-7.json). The certificate is the attested m = 6 script, which prints the projection claims for m = 7 to 10 from the same computation; the attested block is the same stored census, see that file's notes. First lower bound for this cell; with the annealer witness qubit_sqrtT-m7-upper-12.json the cell is 7 ≤ χ ≤ 12, and χ ≤ 11 here would beat the published exponent 1/2 (log_2(11)/7 = 0.4941).
Vincent Russo · this repository (stabrank-research, round 33) · projection monotonicity applied to the attested slice-and-lift bound χ(|sqrtT⟩⊗6) ≥ 7
{
"schema_version": "0.1",
"orbit": "qubit_sqrtT",
"m": 7,
"direction": "lower",
"rank": 7,
"certificate": {
"script": "verify_challenge/cert_sqrtt_m6_rank6_attested.py",
"expect": "CERTIFIED chi(qubit_sqrtT^7) >= 7",
"budget_s": 3600,
"attested": {
"batches": "research/sqrtt_m5_rank6/batch_manifest.json",
"recomputed": 2,
"compute_hours": 46.3,
"hardware": "Perlmutter CPU node (two AMD EPYC 7763, 128 worker processes), NERSC job 60159879, 2026-10-23 16:04 to 16:41 UTC; the representatives stage single-threaded (846 s), the pivot census 46.1 CPU-h over 128 workers (about 23 min wall)",
"note": "The complete list of six-term stabilizer decompositions of |sqrtT>^5 lives in the stored batch outputs under research/sqrtt_m5_rank6/results/: for each of the 8,585 orbit representatives of the five-qubit stabilizer states under S_5 x <S^(x)5>, the residue classes modulo V4 + span(pivot) under two primes and every class that could carry a decomposition (one candidate set in all, the 18 symmetric states). The certificate re-enumerates the dictionary and checks its hash, verifies that the stored pivots meet every orbit exactly once, re-runs two blocks from scratch (seed printed) and compares them byte for byte, re-decides the candidate set exactly over Q(zeta_16) (3,375 decompositions, their exact coefficients), closes the list under the group, and runs the lift to six copies in full; completeness rests on the stored outputs and on research/sqrtt_m5_rank6/census.py, which regenerates any block (census.py run 5 OUT --pivots ...)."
}
},
"provenance": {
"author": "Vincent Russo",
"reference": "this repository (stabrank-research, round 33)",
"method": "projection monotonicity applied to the attested slice-and-lift bound chi(|sqrtT>^6) >= 7",
"date": "2026-10-23",
"github": [
"vprusso"
],
"compute": {
"cpu_hours": 0.0,
"wall_clock_hours": 0.0,
"runs": 0,
"hardware": "none beyond the m = 6 certificate, which prints this line from the same computation"
}
},
"notes": "(<0| (x) I)|sqrtT>^7 = 2^{-1/2} |sqrtT>^6 and a computational-basis slice of a stabilizer state is a stabilizer state or zero, so chi(|sqrtT>^7) >= chi(|sqrtT>^6) >= 7 (qubit_sqrtT-m6-lower-7.json). The certificate is the attested m = 6 script, which prints the projection claims for m = 7 to 10 from the same computation; the attested block is the same stored census, see that file's notes. First lower bound for this cell; with the annealer witness qubit_sqrtT-m7-upper-12.json the cell is 7 <= chi <= 12, and chi <= 11 here would beat the published exponent 1/2 (log_2(11)/7 = 0.4941)."
}