attested · 2/459 re-run certificate script asserted: CERTIFIED chi(T3^6) >= 8; re-ran 2 of 459 stored batches from scratch chosen from seed 20260919 and only checked the SHA-256 of the other 457 against research/t3_rank7/batch_manifest.json; the full enumeration (80.1 CPU-h on Apple silicon laptop (18 cores), four batches at a time at nice 19 under a shared load; 2026-09-19 13:33 to 2026-09-20 11:33 UTC) was not re-run
0 runs; 0 CPU-hours; 0 h wall-clock; on none beyond the m=3 certificate, which this cell re-runs.
χ(ψ ⊗ φ) ≥ χ(ψ) when φ has a nonzero computational amplitude, applied 3 times to χ(T3^3) ≥ 8. The certificate is the m=3 attested one, which prints this line after certifying the exclusion, so the cell inherits the attested tier. Puts the cell at 8 ≤ χ ≤ 27; the cell had no lower bound before. Completeness rests on the stored batch outputs under research/t3_rank7 and the committed runner that regenerates any of them, exactly as for T3-m3-lower-8.json; the enumeration is not re-run under the budget, and the certificate re-runs the declared batches from scratch and hashes the rest.
this repository · stabrank research/t3_rank7 · projection monotonicity applied to the attested exact rank-7 exclusion at m=3
{
"schema_version": "0.1",
"orbit": "T3",
"m": 6,
"direction": "lower",
"rank": 8,
"certificate": {
"script": "verify_challenge/cert_t3m3_rank8_attested.py",
"expect": "CERTIFIED chi(T3^6) >= 8",
"budget_s": 3600,
"attested": {
"batches": "research/t3_rank7/batch_manifest.json",
"recomputed": 2,
"compute_hours": 80.1,
"hardware": "Apple silicon laptop (18 cores), four batches at a time at nice 19 under a shared load; 2026-09-19 13:33 to 2026-09-20 11:33 UTC",
"note": "The enumeration of every rank-7 candidate class set (1.31e13 inner steps, 1.21e9 class sets, all decided exactly) lives in the 459 stored batch outputs; the certificate verifies their hashes, geometry and totals and re-runs two of them from scratch, so completeness rests on the stored outputs and on the committed runner that regenerates any batch."
}
},
"provenance": {
"author": "this repository",
"reference": "stabrank research/t3_rank7",
"method": "projection monotonicity applied to the attested exact rank-7 exclusion at m=3",
"date": "2026-10-17",
"github": [
"vprusso"
],
"compute": {
"cpu_hours": 0.0,
"wall_clock_hours": 0.0,
"runs": 0,
"hardware": "none beyond the m=3 certificate, which this cell re-runs"
}
},
"notes": "chi(psi (x) phi) >= chi(psi) when phi has a nonzero computational amplitude, applied 3 times to chi(T3^3) >= 8. The certificate is the m=3 attested one, which prints this line after certifying the exclusion, so the cell inherits the attested tier. Puts the cell at 8 <= chi <= 27; the cell had no lower bound before. Completeness rests on the stored batch outputs under research/t3_rank7 and the committed runner that regenerates any of them, exactly as for T3-m3-lower-8.json; the enumeration is not re-run under the budget, and the certificate re-runs the declared batches from scratch and hashes the rest."
}