spectral-o31

Withdrawal Notice for O31: Unsupported Colour-Triplet Co-admissibility and Gauge-Group Claims

Cosmochrony — Spectral Admissibility Sub-programme.

Status

This record carries a withdrawal notice, not a paper. Eight results of the previous version are withdrawn, three counterexamples are given in full, and the remaining material is under re-audit.

No positive conclusion about groups, gauge factors, or the Standard Model gauge group is asserted by this record, and none should be inferred from it.

Earlier versions remain available and citable in the record's version history, for traceability.

Withdrawn

1. Uniqueness of SU(3) among connected compact subgroups acting irreducibly on C^3.
2. Irreducibility of the group of Born–Infeld-compatible fibre-preserving transformations.
3. Co-admissibility of the individual profiles sigma_{c_1}, sigma_{c_2}, sigma_{c_3}.
4. The arithmetic criterion "colour triplets exist iff q = 1 (mod 3)".
5. The metaplectic identity as used, which changes the central character while the automorphism invoked fixes the centre.
6. The Delta(27) spectral proposition relating characters and adjacency eigenvalues.
7. The rank-8 test in End(C^3), which is mistyped: dim_C End(C^3) = 9.
8. Every derivation of a gauge factor and of the Standard Model gauge group as a composite, together with the determinant-one condition, the commutation of the putative factors and the direct-product structure.

Counterexamples

• Uniqueness fails. SO(3) ⊂ SU(3) is a proper connected compact subgroup (dim 3 < 8) whose action on C^3 is the complexification of its defining representation, irreducible over C by Schur.
• Irreducibility fails. The diagonal torus T^2 = {diag(e^{i a}, e^{i b}, e^{-i(a+b)})} ⊂ SU(3) satisfies every constraint imposed while preserving the three coordinate lines. Requiring each sector to be mapped to itself in fact forces reducibility.
• The arithmetic criterion fails. For every prime q >= 7, {1, 2, q-3} is an admissible colour triplet under the published definition: its pairwise sums are 3, q-2 and q-1, none divisible by q. q = 5 fails only because q-3 = 2 duplicates. For instance q = 11 admits {1, 2, 8}, and 11 = 2 (mod 3).

Under re-audit

The scalar, arithmetic and discrete-group material of the previous version is under re-audit and is not asserted. The generator-twist isospectrality statement at fixed central character may be recoverable; if an autonomous proof is established it will appear as a separate work.

DOI

Concept DOI (always resolves to the latest version): https://doi.org/10.5281/zenodo.20030491

Compilation

The notice carries no bibliography, so compile.sh (which runs bibtex under set -e) is not used:

mkdir -p out
pdflatex -file-line-error -interaction=nonstopmode -output-directory=out tex/Spectral-O31.tex
pdflatex -file-line-error -interaction=nonstopmode -output-directory=out tex/Spectral-O31.tex

Output: out/Spectral-O31.pdf