Announcement

This repository serves as the central hub for the implementation and validation of the Logos Omega Gradient framework.

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DATA RELEASE: Ω-SCANNER MODEL MAPPING PHASE

The complete dataset from the Synthetic Validation Suite (SVS) Phase is currently being ingested into the dedicated mapping/synthetic repository. This release validates the Ω-Scanner Statistical Methodology for substrate-invariance and structural hierarchy detection across nine canonical dynamical systems.

Each system below was subjected to 192 independent Ω-map runs, including runs against the ​ Global Shuffle and Block Shuffle.

Nine Synthetic Systems in Release:

• Lorenz Attractor (lorenz63)

• Standard Map (standard_map)

• Arnold Cat Map (arnold_cat)

• Logistic Map (logistic)

• Hénon Map (henon)

• Hénon-Heiles Hamiltonian (hamiltonian)

• Relativistic Aberration (rel_aberration)

• 1D Ising Model (ising1d)

• 2D Ising Model (ising2d_fixed)

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Deliverables Per Function: Raw Data: Raw ΔΩ metric output for all 192 * 9 models (1728 independent Omega Scanner runs) Summary Data: Consolidated statistical metrics: Mean, Median, σ, and fit parameters
Distribution Plots: Visual distribution of the ΔΩ effect across the 192 * 9 model runs

Repo Location: maps

Initial Testing - single runs: synthetic

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Thank you for your patience and interest in the scientific validation of LOG.

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From Synthetic Omega to Unified Physics

Telos

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Logos Omega Gradient (Ω) — Priority Marker

Abstract: 2025-09-08

This document records the initial statement of the Logos Omega Gradient (Ω) hypothesis and its first computational evidence.

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Formal Information-Theoretic Basis (Gemini formulation, abridged)

Let X be a raw token stream and Z = φ(X) a derived alphabetized stream.

• Predictive Information: I(Y; C) = H(Y) - H(Y | C) (The reduction in uncertainty about a future token Y given a context C.)

• Information Efficiency: η(S) = I(Y; C) / Hμ(S) (Ratio of predictive information to entropy rate, i.e. bits per token.)

Criterion for Ω-positivity: A transformation φ is Ω-positive if both of these are true (with 95% confidence):

• Δ I_pred > 0
• Δ η > 0

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Empirical Results (joint synthesis)

• IB-layer runs (K=32 clusters) show simultaneous gains in predictive information and efficiency, with bootstrapped 95% confidence intervals strictly greater than 0.
• Topic-label and shuffled controls do not show this dual gain, confirming that the signal is specific, not an artifact.
• Null runs (random labels) return no Ω-signal, strengthening the conclusion.

Together, these results satisfy the Ω-positive criterion at the symbolic level: alphabetization itself tilts noisy streams toward sense-bearing compact codes.

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Statement of Record

• This repo contains the first recorded computational confirmation of the Logos Omega Gradient.
• The working codebase will be published once it reaches sufficient quality for independent replication.
• This marker establishes priority of idea and implementation path.

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Expanded README

Expanded

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