A Markovian Recursive Framework for the Emergence of Spatio-Temporal Locality — II

The April 2026 preprint [DOI https://doi.org/10.5281/zenodo.19443022] proposed a framework in which space, time, energy and mass emerge as readings of an underlying substrate R, purely recursive and pre-geometric, carried by coupled complex oscillators. The present document reports on the path travelled since: the oscillators remain — but emptied of all spatio-temporal content. The continuous phase has become a discrete quaternionic unit of the binary tetrahedral group 2T; amplitude, frequency and proper time have disappeared; all content lives on signed, connected relations, nothing on the nodes. On this substrate a single law T is studied, whose central trait — and the thesis of this document — is to be reflexive by construction: every entity carries, readable in its present structure, its act to come (the reality stance, abbreviated "stance", which we define as the quantum of reflexivity); the law constitutes identities by reading their future behavior (the fold, a bisimulation employed as a dynamical operator); and the founding event of the world — the rupture that distributes the initial posit — is itself a stance event, measured. We state a series of dated propositions: the reduction of the posit to a single number (all other freedoms of the seed are gauges, measured one by one); the mechanism of this forgetting; a Garden-of-Eden-type theorem for T and its paired theorem — the only fertile content is exactly the content the world can never produce; the conditions of the rupture (it occurs if and only if the undivided content dies out, with a measured counter-world that never ruptures); an exact fibration of degree 6 (in the sense of Boldi–Vigna), observational and not dynamical; and the deep empirical anchors of the canonical world, computed up to 100,708,044 relations with an exact node-level equipartition and published canonical fingerprints. A dated, falsifiable prediction is preregistered: a regime tipping — the entry into thermalization — expected in a window centered on the hundredth step, beyond current computational reach, with its signature published. A final section deposits, as dated and reserved work in progress, the direction of the program BELOW the seed — the descent toward o. Physical identifications remain outside this document; the interpretive layer (graded reflexivity, "unconscious consciousness") is presented as a dated program, never as a result.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-07-27
DOI
https://doi.org/10.5281/zenodo.21620965
Primary Topic
Advanced Mathematical Theories and Applications
Type
article
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article

A Markovian Recursive Framework for the Emergence of Spatio-Temporal Locality — II

REMY ESCLANGON
Zenodo (CERN European Organization for Nuclear Research)
Advanced Mathematical Theories and Applications
article

A Markovian Recursive Framework for the Emergence of Spatio-Temporal Locality — II

REMY ESCLANGON
article en

Abstract

The April 2026 preprint [DOI https://doi.org/10.5281/zenodo.19443022] proposed a framework in which space, time, energy and mass emerge as readings of an underlying substrate R, purely recursive and pre-geometric, carried by coupled complex oscillators. The present document reports on the path travelled since: the oscillators remain — but emptied of all spatio-temporal content. The continuous phase has become a discrete quaternionic unit of the binary tetrahedral group 2T; amplitude, frequency and proper time have disappeared; all content lives on signed, connected relations, nothing on the nodes. On this substrate a single law T is studied, whose central trait — and the thesis of this document — is to be reflexive by construction: every entity carries, readable in its present structure, its act to come (the reality stance, abbreviated "stance", which we define as the quantum of reflexivity); the law constitutes identities by reading their future behavior (the fold, a bisimulation employed as a dynamical operator); and the founding event of the world — the rupture that distributes the initial posit — is itself a stance event, measured. We state a series of dated propositions: the reduction of the posit to a single number (all other freedoms of the seed are gauges, measured one by one); the mechanism of this forgetting; a Garden-of-Eden-type theorem for T and its paired theorem — the only fertile content is exactly the content the world can never produce; the conditions of the rupture (it occurs if and only if the undivided content dies out, with a measured counter-world that never ruptures); an exact fibration of degree 6 (in the sense of Boldi–Vigna), observational and not dynamical; and the deep empirical anchors of the canonical world, computed up to 100,708,044 relations with an exact node-level equipartition and published canonical fingerprints. A dated, falsifiable prediction is preregistered: a regime tipping — the entry into thermalization — expected in a window centered on the hundredth step, beyond current computational reach, with its signature published. A final section deposits, as dated and reserved work in progress, the direction of the program BELOW the seed — the descent toward o. Physical identifications remain outside this document; the interpretive layer (graded reflexivity, "unconscious consciousness") is presented as a dated program, never as a result.

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