A Characterization Theorem for Bounded Pair Algebras: The Unique O(1) Enclosure-Preserving Algebra over the EB Carrier (r4)
Eric D. Martin · Zenodo (CERN European Organization for Nuclear Research) · 2026
Manuscript revision r4. RSOS-260797 planar carrier-set theorem; this revision succeeds r2 (the ScholarOne submission to RSOS, RSOS-260797) and incorporates external structural review findings plus tonight's verification work. Changelog r2 → r3 → r4: r2 → r3 (intermediate revision; not separately deposited on Zenodo): Bibliography additions: Dawood (2019), Skowron & Dutta (2018), Bustince (2010, 2015) — prior-work coverage strengthened in §9 (formal comparisons to bilattices, rough sets, fuzzy logic, interval arithmetic). Abstract scope-tightening: cosmological-application content scoped explicitly to companion preprints rather than carried in the abstract; abstract now describes the planar theorem only. §8.4 reproducibility discussion expanded; engagement with Boldo et al. (2023) floating-point certification framework added. r3 → r4 (post-Manusights-corrected-review revision; this deposit): Seven essential revisions and five recommended revisions from the Manusights structural review incorporated. Thirteen additional references added: Atanassov, Boldo et al. (2023), Bustince, Dawood, de Figueiredo & Stolfi, Dubois & Prade, Fitting, Ginsberg, JCGM 100:2008, Moore/Kearfott/Cloud, Pawlak, Perez-Fernandez et al., Skowron/Jankowski/Dutta, Skowron & Dutta — the prior-work mesh now covers the standard pair-algebra and interval-arithmetic literature. Manuscript-load reframe sentence inserted as the structural framing: "Within the A1–A6 constant-memory summary-state class, the EB pair algebra is uniquely forced; richer methods that retain auxiliary state are outside this class rather than incorrect." Backup-venue list catalogued (Reliable Computing, J. Symbolic Computation, J. Logic and Algebraic Methods in Programming, Numerical Algorithms, Soft Computing). Page count: ~35 pp. Tonight's (2026-04-26 / 2026-04-27) line-by-line verification work on the broader Memoirs monograph (10.5281/zenodo.19822813) verified the base rigidity proof (Stage 1/2/3 of the three-stage characterisation), the four-cell classification across the Cayley-Dickson tower (Cell 1 ℂ, Cell 2 ℍ, Cell 3 provably empty by Hurwitz, Cell 4 𝕆), Definition 4.3 (native O(1) two-way criterion), and the universality theorem. Several specification tightenings identified by that verification work apply to the RSOS planar theorem as well; they are scheduled for a future r5 revision and are not yet incorporated in r4 deposited here. Status: r4 is the rapid-hardening revision prepared after the Manusights structural review surfaced four legitimate findings on the originally-deposited r2 (ScholarOne r2, RSOS-260797). Venue update (2026-05-22): Royal Society Open Science returned manuscript RSOS-260797 after initial editorial assessment as “beyond the scope of the journal’s Editorial Board.” The Editors stated this “is not a judgement on the quality of the science” and recommended submission to a field-specific preprint server and a field-appropriate journal. This Zenodo record serves as that field-specific preprint. YouTube: @EricDMartin @CarrierSet @HubbleTension Updated 2026-05-28