Exact Locality Bounds for Gilbreath (1,2) Frontier Evacuations: Three Finite Theorems, a 64-Million-Prime Audit, and the Schimmel Locality Conjectures
Year: 2026
Type: preprint
Abstract: This preprint studies exact local determinacy of frontier evacuation in a normalized Gilbreath-type absolute-difference construction generated from consecutive primes. A frozen computational audit was carried through prime index 64,000,000, partitioned into 256 independent consecutive blocks of 250,000 primes. The authenticated corpus contains 9,533 (1,2) frontier events. Three finite computational results are established for this corpus. First, an exact 8-cell present-row window does not determine either the subsequent evacuation distance or its scale class. Second, no exact present-row width W ≤ 23 determines evacuation throughout the authenticated corpus; explicit equal-window/unequal-evacuation collision certificates are supplied. Third, all 9,533 width-24 windows in the released corpus are distinct, making width 24 the smallest collision-free exact present-row width observed in the 64-million-prime audit. The paper introduces two explicitly conjectural extensions: the Schimmel Finite-Locality Conjecture, proposing that some finite exact present-row width universally determines evacuation, and the stronger Schimmel Frontier-24 Conjecture, proposing that width 24 suffices. The width-24 result is finite and retrospective: because all authenticated width-24 states are distinct, the released corpus contains no same-state replication at width 24. The manuscript therefore does not claim a universal proof of Frontier-24, a proof of Gilbreath's conjecture, or a proof that width 24 remains optimal beyond the audited corpus. A prospective frozen width-24 test begins beyond the 64-million-prime boundary. The work is accompanied by a reproducibility package containing the authenticated master ledger, frozen audit specification, raw-prime Python reproducer, independent verifier, independent C++17 reproducer, executed verification and sanity-check records, environment requirements, and SHA-256 integrity records. Historical and contemporary context includes work of François Proth, Andrew M. Odlyzko, Zachary Chase, Zachary Hunter, and Terence Tao.
Author: Schimmel, Kevin Mark
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212449180
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