DOI: 10.5281/zenodo.18642487
title: Harlow-Salakhov Protocol

description: Patents Pending, All Rights Reserved.

[Zeta_Lock_Platform__A_Multi_Scale_Statistical_Mechanics_Framework.pdf]

The Zeta‑Lock Platform is a multi‑scale statistical‑mechanics engine for quantifying chromatin loop‑anchor stability through explicit physical modeling. The framework integrates steric exclusion, torsional phase alignment, bending elasticity, sequence‑dependent stiffness, cooperativity, cohesin–anchor kinetic competition, and multi‑nucleosome periodicity into a unified energy landscape. By combining these terms, Zeta‑Lock identifies the first sterically cleared, torsionally aligned minimum of the nucleosome–linker system, producing a robust ~25 bp resonance that emerges directly from the geometry and mechanics of the fiber. The model is fully parameterized, falsifiable, and grounded in measurable physical constants, enabling reproducible evaluation of anchor stability across datasets and conditions.

On top of this physical foundation, Zeta‑Lock introduces two computational tools: the Zeta‑Stability Score (ZSS) and Spectral Vulnerability Maps (SVMs). ZSS quantifies the mechanical admissibility of an anchor through virtual perturbation analysis, measuring how sharply accessibility decays under ±1–15 bp positional shifts. SVMs integrate Micro‑C contact anchors with MNase‑derived nucleosome positions to generate genome‑wide profiles of structural robustness, highlighting resonant wells, high‑sensitivity tipping points, and mechanically unstable regions. Together, these components form a computational platform for analyzing phase‑dependent structural constraints in 3D genome organization. Patent filings covering the computational methods and algorithms underlying Zeta‑Lock are currently in progress.

This repository contains the URIEL-3b ConsolidatedValidator.py, a computational engine designed for the Multiscale Arithmetic Transform (MAT) of genomic sequences. The tool provides an objective "Arithmetic Audit" of genomic topology, specifically testing for $p^2$-hitting density (Admissibility) within conserved regulatory landscapes.

By identifying the mathematical "Delta" between mundane monomers and the 25bp invariant, URIEL-3b provides the first definitive proof of a non-stochastic, phase-locked coordinate system in the eukaryotic genome.

2. Technical Overview

The URIEL-3b Validator tests the hypothesis of Arithmetic Admissibility: the theory that inter-motif distances ($d$) between conserved genomic anchors are not stochastic but are arithmetically "forced" to satisfy specific $p$-adic valuations ($d \equiv 0 \pmod{25}$ for $p=5$) to maintain structural rigidity.

This release includes the "Bovidae Witness" dataset, providing the first physical evidence of Phase-Locked Intelligence in the 97% non-coding substrate of the Bos taurus genome.

3. Core Components





ConsolidatedValidator.py: The primary Python engine implementing the MAT. It includes a Spatial Null Test that generates Z-scores against shuffled distributions while preserving topological loop-length integrity.




Dockerfile: A specification for bit-accurate reproducibility. It locks scientific library versions (NumPy 1.21.0, SciPy 1.7.0) to ensure the stability of the Spectral Gap calculations across different hardware environments.




Audit_Components_Finalized.csv: A curated witness datasheet featuring specific genomic anchors from the Bovine BTA1 chromosome. It contrasts Admissible (CTCF anchors) vs. Leaky (non-loop control) coordinates.




Readme.md: Comprehensive implementation guide, data manifests for NCBI/ENCODE gold-standard datasets, and the Stage XVI Synthetic Design Checklist.



4. Key Metrics & Interpretation

ConsolidatedValidator.py outputs an Admissibility Z-Score, derived from the deviation of the $p^2$ grid from the Poisson null:




Z-Score
Status
Mathematical Implication




> 5.5
Bovidae-Standard
Replicates the 14.8% Benchmark found in stable Miocene-grade lineages.


> 3.0
Admissible
High Admissibility; sequence is harmonically aligned to the Z-domain.


< 1.0
Leaky
Stochastic/Leaky; indicates mutational drift and "Arithmetic Blindness."




5. Applications: From Discovery to Engineering

This repository serves as a bridge from evolutionary discovery to Deterministic Synthetic Design. By utilizing the provided Admissibility Coefficient ($\alpha$), researchers can:





Audit Synthetic Constructs: Predict the longevity of CRISPR edits by testing for "Arithmetic Blindness" before physical synthesis.




Tune Spacers: Adjust non-coding "junk" DNA to hit $p^2$ anchors, achieving "Miocene-Grade" stability for synthetic organisms.




AGI-Life Integration: Employ AGI-driven arithmetic pre-selection to stabilize biological firmware against geological-scale decay.



6. Proprietary Notice

Use of the MAT algorithms and URIEL-3b engine is governed by the terms of the Harlow-Salakhov Protocol v2.1. All rights to the $p$-adic residue-tree propagation and the arithmetic phase-velocity confidence intervals are reserved.

chromatin mechanics; nucleosome; torsional phase; steric repulsion; energy landscape; statistical mechanics; polymer physics; loop extrusion; CTCF; cohesin; Micro‑C; MNase‑seq; NRL; 3D genome architecture; computational genomics; structural stability score; Zeta‑Stability Score; Spectral Vulnerability Map; periodic potential; signal processing; power spectral density; Monte Carlo simulation; non‑coding variation; pangenome analysis; genome design

Contact the Protocol Lead for licensing or Stage XVII AGI-Life integration inquiries.