Current claim boundary
Operation Komorebi · Lehmer · Series 07 · 9 October 2026
The conjecture in this edition is the nonvanishing of Ramanujan's tau function. The six recovered packages concern that problem. They do not concern Lehmer's Mahler-measure conjecture or his totient problem.
The mathematical results and computations have separate evidence records. Written proofs rely on the external theorem contracts checked in literature/. Bounded replays are identified in computation/. The proof audit reconstructs the exact implications rather than treating an old status label as evidence.
The primitive residual is
Its square theorem and zero-set equivalence do not remove the prime obligation, because R(p)=tau(p). Packet sign certificates prove nonvanishing at their stated target indices. Finite transfer ranks do not prove a universal span theorem. Conserved content masses obstruct common-sign corrections at the specific composite example n=121, while prime shells have only one content class.
The arithmetic survivor theorem uses the actual joint finite Galois image. It has the quantifier order “for each fixed modulus, a positive-density prime set exists.” It does not produce a prime where tau is zero as an integer. Local trace-zero filtered Frobenius objects satisfy their stated local conditions, but their identification with the global Delta representation is absent.
The synthetic multiplicative sequence tests an implication from a weaker set of arithmetic hypotheses. Its zero is a zero of the constructed sequence. It is not claimed as an actual zero of tau, and its nonmodularity is not an unconditional conclusion.
The remaining conjectural target is still tau(p) != 0 for every actual rational prime p. The edition claims no proof of that target, no proof-assistant certification and no historical priority for the project-specific reformulations.