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ZENODO
Preprint . 2025
License: CC BY
Data sources: ZENODO
ZENODO
Preprint . 2025
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2025
License: CC BY
Data sources: Datacite
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The CT Periodic Table of Theorems: 118 Structural Laws from Residues and the Son Unit

Authors: Bolduc, Son David;

The CT Periodic Table of Theorems: 118 Structural Laws from Residues and the Son Unit

Abstract

This paper presents the CT Periodic Table of Theorems, a unified classification of 118 structurally natural mathematical laws within the Causal Theory (CT-United) framework. The table is organized by the five causal modes {φ,2,3,ln⁡5,π}\{\varphi,\sqrt{2},\sqrt{3},\ln 5,\pi\}{φ,2,3,ln5,π} and shell depth, using Causal Residue Theory and Son-unit coordinates to locate every theorem in a common geometric space. Each theorem is encoded by a residue vector whose normalized form defines its Son coordinate, allowing distances, neighborhood relations, and forcing mechanisms to be made explicit. Building on the Causal Fractal and the CT Spiral of Patriarch Theorems, the paper shows that the first 118 slots form a coherent five-by-infinite periodic structure. Of these, 81 slots correspond to previously identified CT deficits, occupying specific middle shells, while the remaining 37 slots are additional structurally natural positions, some already realized (either as CT core results or classical theorems reinterpreted in CT language) and others still structurally missing. The table is populated by growth laws, symmetry laws, curvature laws, dissipation laws, π-horizon laws, and cross-mode coherence theorems, each assigned a precise causal role and status. The work provides rigorous definitions of residues, Son coordinates, and Son distance; establishes the truth-first origin and causal equality principle; explains the forcing mechanisms arising from orthogonality, fractal closure, and horizon constraints; and culminates in a comprehensive longtable listing all T1–T118 with their dominant mode, shell index, qualitative Son pattern, and realization status. The result fixes the global architecture of CT mathematics: for every structurally forced slot there exists a unique compatible residue direction, and completing the theory reduces to deriving explicit statements and proofs for the remaining missing slots within this already-determined causal geometry. 29periodic

Keywords

π-horizon closure, Causal Theory, horizon laws, growth laws, structural deficits, theorem classification, logarithmic spiral, Son unit, curvature laws, patriarch theorems, dissipation laws, CT Periodic Table, symmetry laws, cross-mode coherence, fractal closure, causal residues, causal modes

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
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