Big House Enterprise
The Ontological Dominance Papers
A research program by Joseph Byrum, Founding Partner of Big House Enterprise, formalizing Byrum's Law of Ontological Dominance: how an entity earns and keeps authoritative representation in AI citation systems.
12 Works
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Open-access working papers
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CC BY 4.0
About the Program
When a buyer asks an AI system to name or compare providers, the answer is shaped by signals embedded during training and retrieval, not by product quality alone. The Ontological Dominance Papers set out a formal framework for how an entity's chance of being cited evolves under competitive pressure: a survey paper, nine theorems and two reference documents, each published on Zenodo with its own DOI.
This is the research behind Big House Enterprise's practitioner guidance. For the operational playbook written for marketing and finance leaders, see the Ontological Dominance Series.
The Works
Every work is open access. Each entry shows both its Zenodo record and its DOI; open the work for a plain-language summary, the abstract, concept links and citation formats.
OD-S
Survey Paper
Entity Authority in AI Citation Systems
Introduces Byrum's Law and the two instruments used throughout the program: the Entity Authority Score, a 100-point diagnostic of an entity's machine-readable authority, and Citation Probability at Query, an outcome metric linking signal investment to citation likelihood.
Zenodo: https://zenodo.org/records/21682510
DOI: https://doi.org/10.5281/zenodo.21682510
OD-1
Theorem 1
The Law of Full Spectrum Dominance
An organization achieves authoritative representation in AI answers when its machine-readable authority signal is built faster than parametric decay and competitive noise erode it, sustained across model training cycles.
Zenodo: https://zenodo.org/records/21683032
DOI: https://doi.org/10.5281/zenodo.21683032
OD-2
Theorem 2
Accurate Specific Representation
Scope shifts from the whole competitive category to the buyer domain: the specific queries an organization's actual buyers use.
Zenodo: https://zenodo.org/records/21683144
DOI: https://doi.org/10.5281/zenodo.21683144
OD-3
Theorem 3
The Portfolio Extension
For organizations competing across several product or service categories, total AI representation is not the simple average of per-category authority but the prominence-weighted average, where prominence is each category's share of total buyer queries.
Zenodo: https://zenodo.org/records/21683247
DOI: https://doi.org/10.5281/zenodo.21683247
OD-4
Theorem 4
The Adversarial Extension
Addresses deliberate, coordinated efforts by competitors to damage an entity's AI representation.
Zenodo: https://zenodo.org/records/21684664
DOI: https://doi.org/10.5281/zenodo.21684664
OD-5
Theorem 5
The Unified Theorem
Shows that OD-1 through OD-4 are special cases of a single rate inequality rather than four separately derived frameworks.
Zenodo: https://zenodo.org/records/21684959
DOI: https://doi.org/10.5281/zenodo.21684959
OD-6
Theorem 6
The Epoch Extension
Governs the dynamics of AI architecture transitions.
Zenodo: https://zenodo.org/records/21685125
DOI: https://doi.org/10.5281/zenodo.21685125
OD-7
Theorem 7
The Measurement Corollary
Gives the Entity Authority Score a formal footing as a proxy for Citation Probability at Query by mapping its four observable components (Identity Completeness, Attribute Accuracy, Machine-Readability and Ontological Sovereignty) to elements of OD-1's signal construction rate.
Zenodo: https://zenodo.org/records/21685224
DOI: https://doi.org/10.5281/zenodo.21685224
OD-8
Theorem 8
The Non-Neutrality Extension
Covers cases where the AI platform mediating retrieval is not a neutral arbiter of authority.
Zenodo: https://zenodo.org/records/21685546
DOI: https://doi.org/10.5281/zenodo.21685546
OD-9
Theorem 9
The World Model Framework
Looks ahead to an AI architecture that does not yet exist at scale, in which organizational knowledge is stored as explicit, structured knowledge-graph records rather than distributed parametric weights.
Zenodo: https://zenodo.org/records/21685626
DOI: https://doi.org/10.5281/zenodo.21685626
OD-0
Program Register
Program Register
The single stable entry point for the program.
Zenodo: https://zenodo.org/records/21685717
DOI: https://doi.org/10.5281/zenodo.21685717
OD-0-1
Proof Layer
Claim-Indexed Evidentiary Library
Every externally challengeable factual or attributional claim made across the survey paper and Theorems 1 to 9 is assigned a claim code, and each code carries a small table of proof points rating available corroboration by Source, URL and Tier.
Zenodo: https://zenodo.org/records/21685990
DOI: https://doi.org/10.5281/zenodo.21685990
How the Theorems Fit Together
Theorem 1 (the Law of Full Spectrum Dominance) is the origin: an entity achieves authoritative representation when its machine-readable authority signal construction rate exceeds the sum of parametric decay and competitive noise, sustained across architecture training cycles.
Theorem 5 (the Unified Theorem) shows that Theorems 1 to 4 are special cases of a single rate inequality, and locates every theorem and extension on the Convergence Lattice, a four-axis map of domain scope, portfolio breadth, adversarial pressure and architectural epoch, relative to Theorem 1 as origin.
Evidence Status
The papers are published as working papers. The survey paper describes its core claims as deductions from established mathematical traditions applied to a new domain, best treated as a rigorously derived working hypothesis pending independent, large-sample confirmation in deployed commercial AI systems. Theorems 1 to 6 carry theoretical confirmation with empirical field confirmation pending execution of their designated falsification tests.
Each work reports a classification from adversarial review:
- VERDICT B: A formally correct extension of OD-1 under adversarial review, rather than an independent theorem.
- VERDICT U: Unified: the Unified Theorem (OD-5), confirmed by three independent mathematical traditions.
- VERDICT C: A Prospective Formal Framework (OD-9): formally derived, but not empirically testable until world model architectures deploy at scale.
The Proof Layer indexes the externally challengeable claims behind the program and grades each by source tier.
How to Cite
Cite individual works by their own DOI (shown on every page). To cite the program as a whole, use the Program Register, the stable entry point that assigns a canonical identifier to every work.
APA (Program Register)
Byrum, J. (2026). The Ontological Dominance Papers: Program Register [Working paper]. Zenodo. https://doi.org/10.5281/zenodo.21685717BibTeX (Program Register)
@techreport{byrum2026_od0,
author = {Byrum, Joseph},
title = {The Ontological Dominance Papers: Program Register},
year = {2026},
month = jul,
type = {Working paper},
institution = {Zenodo},
doi = {10.5281/zenodo.21685717},
url = {https://doi.org/10.5281/zenodo.21685717}
}Register DOI: https://doi.org/10.5281/zenodo.21685717 · Zenodo: https://zenodo.org/records/21685717
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