/collapse

Collapse System Logic — deterministic proof collapse (E→Z→1)

Primary LanguagePythonOtherNOASSERTION

CSL-Core

The Collapse System Logic (CSL) core repository.
This repo contains the operational Python kernel, certified .csl logic modules, and the proof system scaffolding used for CSL compression/expansion.

Core Directories

  • CSL-PyKernel/ — Python kernel and proof driver.
  • .csl files — minimal logic primitives (e.g., mini_or.csl, mini_neq.csl).
  • mathematical_proof_system.py — primary proof orchestrator.

Usage

Proof Compression Flow

Each collapse in the CSL pipeline follows the canonical tri-map:

Stage Operation Description
E Expansion Source code or proof text in its full expressive state.
Z Zipped Canonical Form Structured compression into .cslx (CSL-exchange) format via entropy-minimizing transformation.
1 Terminal Collapse Final certification: a single hash (SHA256/32) validating proof integrity and terminal identity.

Typical Commands

Notes

  • Every .cslx file is verifiable and self-consistent.
  • Collapse certificates are deterministic across systems.
  • CSL aims for entropy → zero under valid proof collapse.

python -m py_compile mathematical_proof_system.py python csl_any_collapse.py mathematical_proof_system.py --info python csl_any_collapse.py mathematical_proof_system.py --pack python csl_any_collapse.py mathematical_proof_system.py.cslx --unpack /usr/bin/time -l python -u mathematical_proof_system.py

CSL Kernel Architecture

The CSL system implements the canonical collapse triad:

Implementation Mapping

Symbol Module / File Functionality
Φ CSL-PyKernel/csl_any_collapse.py Performs entropy-reducing collapse via zlib and canonical hashing.
T mathematical_proof_system.py Transforms proofs from expressive to canonical form (E → Z).
Ψ .csl certified modules Final verification and terminal identity (Z → 1).

Operational Flow

  1. Compile — Validate syntax and structure (E form).
  2. Pack — Collapse to .cslx canonical (Z form).
  3. Unpack — Expand back for verification.
  4. Execute — Run the proof orchestrator; log results and emit terminal hash.

Each phase is deterministic: no randomness, no recursion drift, and total entropy collapse to 0 under valid proofs.

Verification and Certification

Every .cslx file produced by the kernel carries a collapse certificate: This certificate encodes the terminal state of the proof:

  • Canonical Hash (CERT) → irreversible identity of the proof content.
  • Zlib Compression (PACK) → verified entropy reduction.
  • Re-expandable (UNPACK) → structural integrity preserved through collapse.

Double-collapsing (e.g., .cslx → .cslx.cslx) yields identical hashes under valid CSL alignment, confirming deterministic closure.

Validation Rule

A valid proof satisfies: [ \Phi^2 = 0,\quad T^2 = T,\quad \Psi^2 = \Psi,\quad \Psi \circ T = 1 ]

where entropy strictly decreases under Φ.
This is the mathematical guarantee of Collapse Logic Integrity.