# Version 2 — 18 October 2026

Previous version: Zenodo 10.5281/zenodo.22171137, concept DOI 10.5281/zenodo.22171136.
Previous title: Products of the per-prime Tate curves of absolute geometry carry no correspondence calculus for the Weil explicit formula.
Revised title: Classical correspondences between per-prime Tate curves: a matching obstruction.

This is a substantive mathematical scope correction.

- The universal no-assignment conclusion of former Theorem 6 is withdrawn. Multiplicative prime indexing does not itself force nonzero maps between different prime fibers; p-dependent test coefficients were not prohibited by the old hypotheses.
- The replacement Theorem 6 defines the cross-fiber graph and proves that its components have at most two vertices. It excludes an explicitly connected system on three or more distinct prime fibers, including an all-pairs nonzero-correspondence requirement.
- Unsupported claims that a prime-independent phase factor excludes archimedean terms, or that no pole-term construction can exist, are removed. Constancy of the unmarked diagonal intersection lattice is stated with its actual limitations.
- Theorems 1–5 retain the lattice criterion, Hom generator/degree, matching bound, Neron-Severi decomposition and diagonal non-CM/intersection results. The zero multiplication map is treated separately in the graph-degree proof.
- The title, abstract and introduction state the narrowed scope. The original attribution to Winkelmann is retained. No resolution of the open rational-product/four-exponentials question is claimed.
- Optional numerical transcendence scans and the broad prior-art survey are omitted from the revised article because no theorem depends on them; the original record and public tag preserve that history.
- Portable exact integer diagnostics, source, build instructions, outputs and licenses accompany this version. The AI disclosure now records the Codex revision and checks; the stale claim that the full working record is public is removed.

The original version remains part of the publication history. This revision does not claim that every broader explicit-formula realization has been excluded.