Shows that OD-1 through OD-4 are special cases of a single rate inequality rather than four separately derived frameworks. The unifying invariant is the D-normalized signal construction rate: signal construction rate per unit of domain scope. The Convergence Lattice maps every theorem and extension in the program relative to OD-1 along four axes: domain scope, portfolio breadth, adversarial pressure and architectural epoch.

Abstract and Evidence Status

Abstract (verbatim from the Zenodo record)

This paper states Theorem 5 of the Ontological Dominance Papers, the Unified Theorem, which establishes that OD-1 through OD-4 are special cases of a single rate inequality rather than four independently derived frameworks. The unifying invariant is the D-normalized signal construction rate: signal construction rate per unit of domain scope. The theorem introduces the Convergence Lattice, a four-axis map (domain scope, portfolio breadth, adversarial pressure, architectural epoch) locating every theorem and extension in the program relative to OD-1 as origin. Theorem 5 carries the strongest mathematical endorsement in the program — confirmation by three independent mathematical traditions arriving at the same rate condition from distinct starting points — and was classified VERDICT U (Unified) upon adversarial review. Its empirical standing is identical to OD-1 through OD-4: theoretically confirmed, with field confirmation pending execution of the primary falsification test.

Evidence status

Classified VERDICT U (Unified) on adversarial review, with the strongest mathematical endorsement in the program: confirmation by three independent mathematical traditions arriving at the same rate condition. Its empirical standing is identical to OD-1 through OD-4: theoretically confirmed, with field confirmation pending.

Concepts and Related Reading

Keywords

Unified Theorem · D-normalized signal construction rate · Convergence Lattice · domain scope · portfolio breadth · adversarial pressure · architectural epoch · Byrum's Law of Ontological Dominance · The Ontological Dominance Papers

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Cite This Paper

APA

Byrum, J. (2026). The Ontological Dominance Papers Theorem 5: The Unified Theorem [Working paper]. Zenodo. https://doi.org/10.5281/zenodo.21684959

BibTeX

@techreport{byrum2026_od5,
  author       = {Byrum, Joseph},
  title        = {The Ontological Dominance Papers Theorem 5: The Unified Theorem},
  year         = {2026},
  month        = jul,
  type         = {Working paper},
  institution  = {Zenodo},
  doi          = {10.5281/zenodo.21684959},
  url          = {https://doi.org/10.5281/zenodo.21684959}
}

DOI: https://doi.org/10.5281/zenodo.21684959 · Zenodo: https://zenodo.org/records/21684959

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