This preprint packages the remaining geometric inputs (GS3–) needed for the prime-power trace decomposition in the TEBAC Hilbert–Pólya program. The arguments are organized in a referee-contract format. The key device is a discrete arithmetic weight decomposition coming from an independent arithmetic circle symmetry S¹₀ₑ₈ₓ₇ (parameter) and the corresponding weight-zero projection P₆₋. Branches that are relevant for the trace but are not associated with prime powers carry a nonzero arithmetic weight and are annihilated after P₆₋-compression. A complementary escape mechanism is also recorded for exceptional weight-zero non-prime branches. Status of this Zenodo release. This version includes a fully explicit prototype END generator catalogue (one escape generator and a prime-switch family of weight generators) that demonstrates how the sieve becomes purely mechanical (word bookkeeping). A TEBAC-specific 100% unconditional closure requires replacing the prototype catalogue by the actual END generator list from the main TEBAC geometry and verifying (i) generator formulas in (u, y, ), (ii) integer weights, (iii) the TEBAC word-reduction/prime-switch mechanism, and (iv) trace-zero remainder conditions.
Tosho Lazarov Karadzhov (Mon,) studied this question.