Observer-Centrism

Physics from Three Axioms

Observer-Centrism is a theoretical physics framework that derives the major structures of known physics — quantum mechanics, general relativity, the Standard Model gauge group, thermodynamics, and holographic entropy bounds — from three axioms about what it means to be an observer.

The Three Axioms

1. Coherence Conservation. There exists a primitive quantity — coherence — that is globally conserved. It cannot be created, destroyed, or exported to an external reservoir.

2. Observer Definition. Any structure that maintains at least one invariant quantity across transformations, together with a self/non-self boundary, qualifies as an observer.

3. Loop Closure. Observer dynamics must be closed loops: the internal state returns to its initial configuration after a finite time. Non-closing configurations dissipate.

Project Structure

observer-centrism/
├── observer_centrism.docx     # Original source document (canonical reference)
├── site/                      # Astro website with interactive components
│   ├── src/
│   │   ├── content/
│   │   │   ├── source/        # 15 markdown files from the original document
│   │   │   ├── derivations/   # 61 derivations organized by group
│   │   │   ├── predictions/   # 10 testable predictions
│   │   │   └── guide/         # Narrative walkthrough (9 chapters)
│   │   ├── components/        # Astro layouts + Sygnal interactive components
│   │   ├── data/              # Knowledge database, dependency graph, indexes
│   │   └── pages/             # Astro page routes
│   └── public/                # Static assets
├── lean/                      # Lean 4 formal verification
│   ├── ObserverCentrism/
│   │   ├── Algebra/           # Cayley-Dickson construction, Hurwitz theory
│   │   ├── Gauge/             # Sedenion zero divisors, anomaly cancellation
│   │   ├── Quantum/           # No-cloning theorem, Bell basis completeness
│   │   └── Particles/         # Spin-statistics, generation counting
│   ├── lakefile.toml          # Lake build configuration
│   └── lean-toolchain         # Lean version (v4.29.0-rc6)
├── timestamps/                # OpenTimestamps provenance proofs (.ots files)
└── scripts/
    ├── build-index.mjs        # Regenerates knowledge.db and knowledge-index.json
    ├── lean-status.mjs        # Reports Lean verification status
    └── timestamp.sh           # Creates a timestamped provenance record

Building the Site

The site is built with Astro and uses Sygnal for interactive components (dependency graph, prediction tracker, proof step viewer). Math rendering uses KaTeX via remark-math and rehype-katex.

cd site
npm install
npm run dev       # Development server on http://localhost:4321
npm run build     # Production build to site/dist/
npm run preview   # Preview production build locally

To regenerate the knowledge index (after modifying derivation content):

node scripts/build-index.mjs

Lean 4 Verification

The lean/ directory contains machine-verified proofs of key mathematical claims from the derivation chain. These verify structural results where mechanical verification adds genuine confidence — not arithmetic a human could check at a glance.

Verified results include:

• Cayley-Dickson doubling construction (ℝ → ℂ → ℍ → 𝕆)
• Sedenion zero divisors (the sequence terminates at octonions)
• Anomaly cancellation with Standard Model hypercharges
• No-cloning theorem
• Bell basis completeness
• Spin-statistics core identities
• CKM generation counting

Prerequisites: Lean 4 and elan (Lean version manager).

cd lean
lake exe cache get    # Download precompiled mathlib (required, ~1 GB)
lake build            # Type-check all proofs

A successful lake build with no errors means every theorem statement and proof in the project has been mechanically verified.

Provenance

Key commits are timestamped using OpenTimestamps, anchored to the Bitcoin blockchain. This provides an immutable, independently verifiable proof that the work existed at the recorded date. See TIMESTAMPS.md for the full log and verification instructions.

To create a new timestamp:

./scripts/timestamp.sh "Description of this milestone"

License

This work is licensed under CC BY 4.0 (Creative Commons Attribution 4.0 International).

You are free to share, adapt, and build upon this material for any purpose, including commercially, provided you give appropriate credit. When citing this work:

Troy Presley, Observer-Centrism: Physics from Three Axioms, 2026. https://github.com/tpresley/observer-centrism