Research-Stack/2-Search-Space/GhostPivot2

Ghost Pivot 2 — Core Theory

This repository is the core theory layer.

Its purpose is to state and eventually prove the substrate-neutral framework:

• invariant-preserving dynamics
• latent load and boundary crossing
• routed multi-subsystem evolution
• bounded resource competition
• bounded memory and switching
• update regimes as general operators

This repo should remain as close as possible to the minimal provable core.

What belongs here

• core definitions
• core theorems and conjectures
• proof-oriented notes
• minimal Lean formalization of the general system
• substrate-neutral math and notation

What does not belong here

• FSC-specific apparatus
• story-derived case studies
• language-specific or biology-specific examples beyond tiny toy examples
• heavy application layers
• experimental manifold adapters that are not needed to state the theory itself

Intended relationship to the extension repo

The extension repo contains refinements, applications, and derived constructions.

Core claim:

the base theory should stand on its own.

Extension claim:

FSC, Stable Islands, domain adapters, and story-derived systems are refinements or instantiations of the core, not the core itself.

Proposed structure

• docs/ — definitions, axioms, theorem statements, proof sketches
• lean/ — minimal formal core
• paper/ — main theory manuscript

Initial split plan

Core

• state / invariant / latent load / resource / routing / update rule / solver
• generic reward shaping and boundary functions
• substrate-neutral adapter interface

Extensions (other repo)

• FSC
• StableIsland
• manifold competition built from FSC steps
• domain adapters
• social / biological / language case studies
• story-derived stress tests

Guiding rule

If removing a module would leave the core theory intact, it belongs in the extension repo. If removing a module would collapse the theory itself, it belongs here.