χR(∣T3⟩⊗4) ≥ 8

T₃ orbit, qutrit.

Participate

Run it yourself, or point a coding agent at it.

git clone https://github.com/unitaryfoundation/stabrank
cd stabrank
# describe your decomposition in bounds/mybound.json
make fit BOUND=bounds/mybound.json ARGS=--write
make verify BOUND=bounds/mybound.json

fit solves for the exact coefficients, or tells you no exact combination of your terms reproduces the target. verify rebuilds the identity in exact arithmetic. If it passes, open a pull request adding the file and the leaderboard picks it up on the next build.

A bound the pipeline cannot check is recorded as cited and never takes a record.

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Verification

attested · 2/459 re-run   certificate script asserted: CERTIFIED chi(T3^4) >= 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

Compute

0 runs; 0 CPU-hours; 0 h wall-clock; on none beyond the m=3 certificate, which this cell re-runs.

Notes

χ(ψ ⊗ φ) ≥ χ(ψ) when φ has a nonzero computational amplitude, applied 1 time to χ(T3^3) = 8. The certificate is the m=3 attested one, which prints this line after certifying the rank-7 exclusion; the cell inherits the attested tier. Puts the cell at 8 ≤ χ ≤ 9, replacing the lower bound of 6 carried from the earlier m=3 exclusion.

Attribution

this repository · stabrank research/t3_rank7 · projection monotonicity applied to the attested exact rank-7 exclusion at m=3

Submission

JSON
{
  "schema_version": "0.1",
  "orbit": "T3",
  "m": 4,
  "direction": "lower",
  "rank": 8,
  "certificate": {
    "script": "verify_challenge/cert_t3m3_rank8_attested.py",
    "expect": "CERTIFIED chi(T3^4) >= 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": "2026-09-20",
    "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 1 time to chi(T3^3) = 8. The certificate is the m=3 attested one, which prints this line after certifying the rank-7 exclusion; the cell inherits the attested tier. Puts the cell at 8 <= chi <= 9, replacing the lower bound of 6 carried from the earlier m=3 exclusion."
}