χR(∣T5⟩⊗4) ≥ 5

Tâ‚… orbit, ququint.

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.

← back to the board

Verification

reproduced   certificate script asserted: CERTIFIED chi(T5^4) >= 5

Compute

0 runs; 0 CPU-hours; 0 h wall-clock; on none beyond the m=2 certificate, which this cell re-runs.

Notes

χ(ψ ⊗ φ) ≥ χ(ψ) when φ has a nonzero computational amplitude, applied 2 time(s) to χ(T5^2) ≥ 5 (Lean: stabRankP_powVecP_mono in lean_proofs/LeanProofs/Stabilizer/SliceP.lean); every amplitude of |T5⟩ is nonzero. The certificate is the m=2 rank-4 exclusion, which prints this line after certifying χ(T5^2) ≥ 5. Puts the cell at 5 ≤ χ(T5^4) ≤ 25 (bounds/T5-m4-upper-25.json), the first lower bound on the board for this cell. Whether χ(T5^3) < 15 is open: no Z-type sector route exists at m = 3 (docs/notes/t5q_m2_rank5_exclusion.md, section 8).

Attribution

this repository · stabrank verify_challenge · projection monotonicity applied to the exact rank-4 exclusion at m=2

Submission

JSON
{
  "schema_version": "0.1",
  "orbit": "T5",
  "m": 4,
  "direction": "lower",
  "rank": 5,
  "certificate": {
    "script": "verify_challenge/cert_t5_m2_rank4.py",
    "expect": "CERTIFIED chi(T5^4) >= 5"
  },
  "provenance": {
    "author": "this repository",
    "reference": "stabrank verify_challenge",
    "method": "projection monotonicity applied to the exact rank-4 exclusion at m=2",
    "date": "2026-09-24",
    "github": [
      "vprusso"
    ],
    "compute": {
      "cpu_hours": 0.0,
      "wall_clock_hours": 0.0,
      "runs": 0,
      "hardware": "none beyond the m=2 certificate, which this cell re-runs"
    }
  },
  "notes": "chi(psi (x) phi) >= chi(psi) when phi has a nonzero computational amplitude, applied 2 time(s) to chi(T5^2) >= 5 (Lean: stabRankP_powVecP_mono in lean_proofs/LeanProofs/Stabilizer/SliceP.lean); every amplitude of |T5> is nonzero. The certificate is the m=2 rank-4 exclusion, which prints this line after certifying chi(T5^2) >= 5. Puts the cell at 5 <= chi(T5^4) <= 25 (bounds/T5-m4-upper-25.json), the first lower bound on the board for this cell. Whether chi(T5^3) < 15 is open: no Z-type sector route exists at m = 3 (docs/notes/t5q_m2_rank5_exclusion.md, section 8)."
}