Information as Structured Distinction

Information Theory here is not “entropy‑only” or “messages over channels”. It is a distinction‑first, regime‑aware coherence grammar that any student or AI can run as a stable module.

Module identity

Information = structured distinction.
Distinctions are structural units, not symbols, bits, or semantic tokens.
Coherence = distinction stability.
A system is coherent when its distinctions remain identifiable, non‑degenerate, and operator‑stable across regimes.
Signals = operators.
Signals are operators acting on distinction spaces, not “messages” that must be interpreted.

Regimes & scope

R0 → R3 compatible.
From primitive distinctions (R0) to dimensional operators (R3), with coherence preserved across transitions.
Substrate‑neutral.
Not tied to channels, media, or semantics; usable for physics, cognition, computation, and more.

Distinction‑first Coherence‑based Operator‑driven RTT‑aligned Zero drift

Start here

Core orientation for students, operators, and AI agents.

Session context — identity, drift boundaries, audience.
Regimes — R0 → R3 behavior of distinctions.
Operators — 𝓓, 𝓢, 𝓒, 𝓐, 𝓣, 𝓡, 𝓘, 𝓕, 𝓒𝓁.
Operator examples — concrete, student‑ready patterns.

Structure & engine

Files that make the module runnable and cross‑module safe.

Coherence map — how distinction stability is evaluated.
Lineage — historical → structural → RTT arc.
Cross‑module — links to NoS, LDS, RTT, FFT, Resonance Atlas.
Engine notes — internal behavior for AI and compilers.
simulation_hooks.json — distinction‑space and operator hooks.

How to run this canon

Treat this module as a **distinction engine** you can extend:

Define your own distinction spaces using 𝓓.
Model signals as operators with 𝓢 and 𝓣.
Track coherence with 𝓒 and 𝓘.
Use 𝓡 to move across R0 → R3 without drift.