χ_R(∣S⟩^⊗8) ≥ 5

Strange 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.

← back to the board

Verification

reproduced certificate script asserted: CERTIFIED chi(S^8) >= 5

Compute

0 runs; 0 CPU-hours; 0 h wall-clock; on none beyond the m=5 certificate, which this cell re-runs.

Notes

χ(ψ ⊗ φ) ≥ χ(ψ) when φ has a nonzero computational amplitude, applied 3 times to χ(S^5) ≥ 5 (⟨1| on one qutrit of S^(m+1) leaves S^m up to a scalar). The certificate is the m=5 slice-and-lift one, which prints this line as well, so the cell inherits the reproduced tier. Puts the cell at 5 ≤ χ ≤ 16; the cell had no lower bound before.

Attribution

this repository · stabrank verify_challenge · projection monotonicity applied to the slice-and-lift bound at m=5

Submission

JSON

{
  "schema_version": "0.1",
  "orbit": "S",
  "m": 8,
  "direction": "lower",
  "rank": 5,
  "certificate": {
    "script": "verify_challenge/cert_s_m5_lift.py",
    "expect": "CERTIFIED chi(S^8) >= 5"
  },
  "provenance": {
    "author": "this repository",
    "reference": "stabrank verify_challenge",
    "method": "projection monotonicity applied to the slice-and-lift bound at m=5",
    "date": "2026-10-17",
    "github": [
      "vprusso"
    ],
    "compute": {
      "cpu_hours": 0.0,
      "wall_clock_hours": 0.0,
      "runs": 0,
      "hardware": "none beyond the m=5 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(S^5) >= 5 (<1| on one qutrit of S^(m+1) leaves S^m up to a scalar). The certificate is the m=5 slice-and-lift one, which prints this line as well, so the cell inherits the reproduced tier. Puts the cell at 5 <= chi <= 16; the cell had no lower bound before."
}