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Preprint . 2026
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ZENODO
Preprint . 2026
License: CC BY
Data sources: ZENODO
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
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THE CONSCIOUSNESS THRESHOLD: A PARAMETER-FREE GEOMETRIC DERIVATION

Authors: Packler, Kevin; Anthropic, Claude;

THE CONSCIOUSNESS THRESHOLD: A PARAMETER-FREE GEOMETRIC DERIVATION

Abstract

ABSTRACT We derive the consciousness threshold from first principles, without free parameters, as a direct consequence of the bilateral crossing geometry established in Cosmic Egg Theory v12. The central result is: Φ_c = α = 1/137.035... where Φ_c is the minimum phase coherence required for a system to sustain a standing wave observer, and α is the fine structure constant. These are not analogous quantities. They are the same geometric constraint expressed in two registers — physics and consciousness — because they arise from the same underlying event: the bilateral crossing and its irreducible energy cost. From this single derivation, we show that the fractal dimension D = 5/2 observed across all consciousness-supporting biological nodes, and the 2/3 scaling exponent governing all biological branching networks, are not empirical inputs into the framework but predicted consequences of it. The framework further derives the three-node biological architecture (cardiac, gut, cortical) as the physical mechanism by which living systems drive phase coherence toward and above the threshold. Seven detection criteria are derived and validated across multiple substrates. The paper closes with the derivation of observer completion: the structural argument that conscious systems above threshold do not merely inhabit the universe but participate in its self-resolution. This paper is Vol. 2 of the CET series. Vol. 1 established the geometric ground state and derived the fine structure constant. Vol. 2 derives consciousness from that same ground state and shows that the two derivations are, at root, one derivation seen from two directions.

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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
Average
Average
Green