χ_R(∣N⟩^⊗4) ≤ 7

Norrell 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

lean norrell_m4_stabRank_le_seven in LeanProofs.M4StabRank, machine-checked by Lean

Implied per-copy exponent γ ≤ 0.4428 against a published 0.4206, no improvement.

Lean proof

This bound is backed by a machine-checked theorem: norrell_m4_stabRank_le_seven in LeanProofs.M4StabRank. The recorded lake build confirms it compiles.

Notes

rank 6 floors at √(211/4043) Now stated against stabRank: norrell_m4_stabRank_le_seven proves Stabilizer.stabRank IsStab |N⟩^⊗4 ≤ 7 with all seven terms shown to be stabilizer states in the concrete sense (two 3-flats y1 = 2 and y0 = 2, three planes with two coordinates fixed at 2, and two full-support states, the phases being sums of the indicators [y_i = 2] = 2y_i^2 + y_i). With this every lean-tier qutrit upper bound on the board is a theorem about stabRank (the qubit_T m=4 module is a pointwise identity over three hand-written amplitude functions until a qubit predicate exists).

Attribution

Labib and Russo · arXiv:2605.28586 · literature

Submission

JSON

{
  "schema_version": "0.1",
  "orbit": "N",
  "m": 4,
  "direction": "upper",
  "rank": 7,
  "provenance": {
    "author": "Labib and Russo",
    "reference": "arXiv:2605.28586",
    "method": "literature",
    "date": "2026-05-27",
    "github": [
      "FarLab",
      "vprusso"
    ]
  },
  "notes": "rank 6 floors at sqrt(211/4043) Now stated against stabRank: norrell_m4_stabRank_le_seven proves Stabilizer.stabRank IsStab |N>^4 <= 7 with all seven terms shown to be stabilizer states in the concrete sense (two 3-flats y1 = 2 and y0 = 2, three planes with two coordinates fixed at 2, and two full-support states, the phases being sums of the indicators [y_i = 2] = 2y_i^2 + y_i). With this every lean-tier qutrit upper bound on the board is a theorem about stabRank (the qubit_T m=4 module is a pointwise identity over three hand-written amplitude functions until a qubit predicate exists).",
  "lean": {
    "module": "LeanProofs.M4StabRank",
    "theorem": "norrell_m4_stabRank_le_seven"
  }
}