Extending v_p^max Code Classification: Testing the Mahler Spectral Conjecture on Additional Stabilizer Code Families

In the paper's words

ACRP-06: Tests UF paper C7.3 on 8 additional codes. Golay CSS confirmed v_p^max=28; all other stabilizer codes cluster at random baseline (1-6). C7.3 bound to Golay-type self-dual codes.

The abstract, verbatim, and its opening sentence is the claim. Every line below is quoted from the text.

Numbers it reports

No sentence of this paper reports a figure with a unit or a quantity word, so none is shown.

How it is done

1. Confirmation: The Golay CSS code and extended Golay CSS code achieve $v_{p}^{\max}=28$ — EXACTLY the UF paper's claim for "optimal" codes.

   from 4. Analysis

What would falsify it

1. [CHECK: 2027-08] [STRONG] If any standard published stabilizer code (not Golay-derived) is shown to achieve v_p^max >= 20 from its exact weight distribution, this bounding result is FALSIFIED.

   from 8. Calibration Register

Where the claim stops

1. The "28 vs 4" gap does not generalize.

   from 7. Conclusion

2. This note extends the test to eight additional stabilizer code families using EXACT weight distributions (where known) and approximate distributions (where only [[n,k,d]] parameters are available), and finds that the conjecture does not generalize.

   from Abstract

3. However, for general stabilizer codes — including the [[5,1,3]] perfect code, the [[7,1,3]] Steane code, the [[9,1,3]] Shor code, and surface codes of sizes [[16,1,4]] through [[36,1,6]] — $v_{p}^{\max}$ clusters between 1 and 6, indistinguishable from the random-ensemble baseline (mean=4).

   from Abstract

Where to read

1. Abstract201 words · 1 min
2. 1. The Conjecture Under Test229 words · 1 min
3. 2. Mahler Spectrum Computation47 words · 1 min
4. 3. Results90 words · 1 min
5. 4. Analysis210 words · 1 min
6. 5. Conjecture Survival52 words · 1 min
7. 6. Mandatory Symmetry (KIF-18)88 words · 1 min
8. 7. Conclusion87 words · 1 min
9. 8. Calibration Register42 words · 1 min
10. 9. Declarations43 words · 1 min
11. Version History8 words · 1 min