Meridians on the Markov Surface: Geometry, Residues, and Collision Windows
Year: 2026
Type: preprint
Abstract: This edition organizes Markov configurations by reversed Meridian addresses, geometric descent, Fibonacci-modulus and modulo-27 behavior, equal-degree separation, finite unequal-degree collision windows, corridor recurrences and a numerator–denominator collision window. It retains the snake-graph arguments and the archived degree-10,000 certificate. The unrestricted unicity problem remains open within this framework. The revised computational chronology includes the earlier Claude-assisted historical search and the separately archived fifty-billion numerical-order verification. The working draft reports 9,581,528,580 triples against a cutoff of 10^100000 in 24 minutes on two cores with 7 GB memory. A public LinkedIn announcement is timestamped 23 October 2026, 14:54:57.771 UTC (09:54:57.771 CDT), with caption wording of 9.3 billion in 24 minutes. This is the announcement timestamp, not a recovered execution start or finish. The earlier draft's qualification about uncertified historical logs and cutoff error bounds is retained. This search is not the later ten-billion anchor. The fifty-billion verifier completed on 28 October 2026. Its recorded start was 08:32:57.096455198 UTC and its audit-inclusive finish was 10:38:33.644612263 UTC (03:32:57–05:38:34 CDT, rounded). Two closed invocations total 7,492.102807105 seconds (2 h 04 min 52.103 s). The calendar span is 7,536.548157065 seconds, including the invocation pause. Including the separate original ten-billion anchor gives 8,330.980040248007 seconds (2 h 18 min 50.980 s). These historical execution dates are distinct from this edition's release date. The exact numerical envelope covers 71,517,775,875 configurations. After anchored omissions and certified lower-bound exclusions, 54,940,210,994 new configurations were compared. All 346 repeated primary-residue pairs separated; the final auditor reconstructed all 692 candidate triples and rechecked the 38 anchor candidates. The protocol establishes uniqueness for the first 50,000,000,000 distinct Markov values in numerical order. It used eight workers, an eight-CPU-equivalent quota and an 8-GiB memory limit. Included are the 31-page main paper, six-page computational proof and timing supplement, editable source, all figure assets, selected historical evidence and receipts, and a new read-only reconciliation of 26,151 archive member checksums and 8,522 closed stage receipts. The full frozen historical verifier archive is available separately at https://doi.org/10.5281/zenodo.23874075. This release is an editorial revision, not a new enumeration; no completed 500-billion result is claimed. Licensing: Original software is licensed under MIT; original documentation and data under CC BY 4.0. Third-party materials and external dependencies retain their own terms. Copyright (c) 2026 Elleard Felix Webster Heffern, to the extent copyright applies. Funding: No funding. Substantial generative-AI assistance is disclosed in the manuscript; the author directed the research and is responsible for the work.
Author: Heffern, Elleard Felix Webster
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225458248
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