The exact affine-fiber threshold in a simplex tensor

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_proof: Translation of the additive Fourier transform proves independence below q factors, and a difference of two codimension-two fibers constructs a ternary relation at and above q factors.

evidence/: Exact small tensors certify rational independence below the threshold and check the displayed ternary trades at and above it over both a prime field and a non-prime finite field.

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The Fourier proof, recorded by Plasma AI, gives an exact boundary for scalar linear fiber colorings. Below the boundary, one frequency translate avoids every zero coordinate. At the boundary, a difference of two affine codimension-two fibers supplies a flat relation, and fixing the extra coordinates gives the same support above it. The characteristic-zero relation convention is essential.

Standing

Proved at tier 0 by the displayed finite-field Fourier argument. Local exact evidence checks the boundary at $q=3$ and $q=4$, including a non-prime field and direct integer tensor images. The evidence is diagnostic; the proof covers all prime powers and all numbers of factors. No independent verification or formal proof is claimed. No other native L-claim is consumed.

Roadmap

The statement has no remaining mathematical gap. Its obstruction applies to scalar linear fibers and their coarsenings or coordinatewise symbol permutations. Arbitrary palettes remain open in the repeated-simplex route; failure of these algebraic colorings alone does not imply unbounded covering number.