CURRENT_STATUS.md
Lehmer: source and evidence
CURRENT_STATUS.md
1 # Current claim boundary
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3 Operation Komorebi · Lehmer · Series 07 · 9 October 2026
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5 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.
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7 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.
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9 The primitive residual is
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11 \[
12 R(n)=\sum_{d^2\mid n}\mu(d)\chi_5(d)d^{10}\tau(n/d^2).
13 \]
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15 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.
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17 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.
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19 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.
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21 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.