Grammar of Time GT-02.5: Before the Observable

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Authors: DARVY BORTOLAMEOTTI
Cited by: 6
References: 5

Abstract

GT-02.5 formalizes the methodological move that makes the Grammar of Time (GT) programme scientifically accountable: science has access to stabilized responses, but it cannot legitimately promote either those responses or the structures used to represent them into ontological foundations without a genealogy. The module separates epistemic interface from constitutive dependence and introduces a bidirectional certificate for primitive declassification. Throughout this paper, “primitive elimination” is only technical shorthand for primitive declassification: removing a structure from the primitive-dependency ledger in a declared regime, not denying the existence or empirical utility of the represented entity. The regressive movement begins with a scientifically stabilized response class and reconstructs, by ablation, its necessary conditions. The progressive movement begins with the Mother Cascade and must reconstruct the same operational response class without reintroducing the target primitive or any hidden equivalent. The second part provides a non-trivial mathematical realization in the regime of finite operational processes. Histories are quotiented by predictive equivalence; the quotient is the minimal predictive portato. Under explicit assumptions of regular conditional future laws, stability of predictive equivalence under time translation and update, a finite quotient, well-defined time-homogeneous transition kernels, the semigroup property, and strong continuity at zero, the quotient induces a finite-state Markov generator Q. Under the additional assumptions of irreducibility and a positive stationary law π, the generator splits canonically as Q = S + A. The reversible sector S generates the Dirichlet form, semigroup, return kernel, cost, and reversible diffusion geometry defined in this module. The antisymmetric sector A is equivalent to a divergence-free stationary current supported on cycles and carries affinities and entropy production. A restricted incompleteness theorem follows: any reconstruction that factors only through (π, S) assigns the same (π, S)-derived output to predictively distinct dynamics along a non-trivial current fiber. The contribution is neither a complete theory of nature nor a derivation of fundamental time or probability. It is a methodological certificate and a technical proof of use: state space and the reversible kernel geometry defined here can be conditionally declassified in a declared regime, while hidden reversibility is exposed as the extra assumption required to identify that geometry with complete dynamics.

Fields of Study & Subjects

Nonlinear Dynamics and Pattern Formation Chaos control and synchronization Origins and Evolution of Life

Publication details

Journal / source
Zenodo (CERN European Organization for Nuclear Research)
Publication date
1 July 2026
Document type
Preprint