A Machine-Checkable Operational Standard for Systemic Tau τₛ and the Discrete Extramental Clock (RECD)

We present systemic-tau-formal v0.1.10 as documented in this English preprint (document version 0.1.10-r1): an open monorepository that states the operational core of the Systemic Tau (τₛ) paradigm and the Discrete Extramental Clock (RECD) in a form accepted by a formal verifier. New in this document/software pin: termwise superstable logistic roots (period 1 and 2 unique; period-4 cascade-window existence; secondary residual zero ~3.96); hybrid cascade with geometric tail and δ-limit; free-c operational uniqueness retained. Formal Rolle mono discharge, true termwise SS for all n, and C²-open map-space renorm remain research-scale open. The Lean 4 + Mathlib package encodes regime bands, the gate function g(τₛ), partition and monotonicity lemmas, and a laboratory construction package linked to period-doubling cascade ideas and Feigenbaum's constant δ. Accompanied by a Python reference core, golden rational bridges, continuous integration, and a citable Zenodo software deposit. Source: github.com/johelpadilla/systemic-tau-formal · path papers/preprint-standard-formal/. Software pin: systemic-tau-formal v0.1.10 — DOI 10.5281/zenodo.21537465 (concept 10.5281/zenodo.21516059).

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-07-24
DOI
https://doi.org/10.5281/zenodo.21537484
Primary Topic
Formal Methods in Verification
Type
preprint
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preprint

A Machine-Checkable Operational Standard for Systemic Tau τₛ and the Discrete Extramental Clock (RECD)

Johel Padilla
Zenodo (CERN European Organization for Nuclear Research)
Formal Methods in Verification
preprint

A Machine-Checkable Operational Standard for Systemic Tau τₛ and the Discrete Extramental Clock (RECD)

Johel Padilla
preprint en

Abstract

We present systemic-tau-formal v0.1.10 as documented in this English preprint (document version 0.1.10-r1): an open monorepository that states the operational core of the Systemic Tau (τₛ) paradigm and the Discrete Extramental Clock (RECD) in a form accepted by a formal verifier. New in this document/software pin: termwise superstable logistic roots (period 1 and 2 unique; period-4 cascade-window existence; secondary residual zero ~3.96); hybrid cascade with geometric tail and δ-limit; free-c operational uniqueness retained. Formal Rolle mono discharge, true termwise SS for all n, and C²-open map-space renorm remain research-scale open. The Lean 4 + Mathlib package encodes regime bands, the gate function g(τₛ), partition and monotonicity lemmas, and a laboratory construction package linked to period-doubling cascade ideas and Feigenbaum's constant δ. Accompanied by a Python reference core, golden rational bridges, continuous integration, and a citable Zenodo software deposit. Source: github.com/johelpadilla/systemic-tau-formal · path papers/preprint-standard-formal/. Software pin: systemic-tau-formal v0.1.10 — DOI 10.5281/zenodo.21537465 (concept 10.5281/zenodo.21516059).

Zenodo (CERN European Organization for Nuclear Research)
University of Puerto Rico, Medical Sciences Campus (PR)
Formal Methods in Verification
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