Claude Collapse: Octonion Jordan-Shadow Decomposition as a Perception Layer for Large Language Models

Extends the 24D octonion collapse framework (DOIs: 10.5281/zenodo.18690444, 10.5281/zenodo.18722487, 10.5281/zenodo.18809406, 10.5281/zenodo.18809716) to condition LLM reasoning through algebraic perception. The core contribution: a semantic state encoder maps conversation text into a 24-dimensional vector (8 content features, 8 structural features, 8 temporal/meta features), which is then decomposed via octonion Jordan-Shadow factorization into orthogonal perception channels — intent (Jordan symmetric part), direction (commutator), and chaos (associator). These channels condition the LLM's reasoning mode through structured system prompts, creating a feedback loop where the model's own output perturbs its next perception state. Seven reasoning modes emerge from the chaos-intent decomposition: DIRECT, OBSERVE, INVESTIGATE, EXPLORE, SYNTHESIZE, HEDGE, and PAUSE. A guardrail resets state when chaos exceeds threshold for consecutive exchanges. This is the first implementation of algebraic perception conditioning for an LLM — the same collapse core that trades live markets, plays physics environments, and classifies genomic transposable elements now shapes how a language model approaches problems. Files: - claude_collapse.py — Semantic encoder, mode mapper, collapse-conditioned prompt builder, feedback loop, interactive chat - aoi_collapse.py — Core octonion algebra: Cayley multiplication, Jordan-Shadow decomposition, entropy transponders - DOODOO_INSIGHT_CLAUDE_COLLAPSE.md — Architectural analysis by DooDoo (the artificial organism built on this algebra) No external dependencies beyond numpy and the Anthropic Python SDK. No training. No GPU required.