How to Contribute

Repository: github.com/tpresley/observer-centrism

Contributions to Observer-Centrism are welcome. You can submit pull requests for new derivations, corrections to existing ones, or additions that strengthen the derivation chain.

What you can contribute

New derivations that extend the framework from its axioms or existing results to new physical consequences
Corrections to existing derivations — errors in proofs, unjustified steps, missing assumptions
Strengthening existing derivations — closing open gaps, tightening bounds, promoting structural postulates to theorems
Lean 4 formalization of derivations that lack mechanical verification

Derivation file structure

Derivations live in site/src/content/derivations/, organized by topic subdirectory:

site/src/content/derivations/
  axioms/             The three axioms + operational coherence
  foundation/         Multiplicity, bootstrap, observer-loop-viability
  minimal-observer/   Minimal observer structure, interactions
  interactions/       Three interaction types, relational invariants
  thermodynamics/     Time, action-planck, entropy, arrow of time
  spacetime/          Speed of light, Lorentz invariance, Einstein eqs
  dimensions/         Three spatial dimensions
  quantum/            Born rule, measurement, entanglement, decoherence
  holography/         Holographic bound, Bekenstein, causal set statistics
  particles/          Spin-statistics, Pauli exclusion, mass hierarchy
  gauge/              Standard Model group, electroweak, strong CP
  flavor/             Three generations, CKM/PMNS, Weinberg angle
  cosmology/          Dark matter, dark energy, baryogenesis, singularity
  thermodynamics-ext/ Extended thermodynamic derivations

Frontmatter

Every derivation file begins with YAML frontmatter:

---
title: "Descriptive Title"
status: "draft"
dependsOn:
  - "axioms/loop-closure"
  - "thermodynamics/action-planck"
enablesDerivation:
  - "spacetime/lorentz-invariance"
tags: ["geometry"]
summary: "One-line summary for navigation and index display"
rigorLevel: "semi-formal"
lastUpdated: 2026-03-15
leanProofs: []
---

Status values

Status	Meaning
● rigorous	All steps formally justified, no unresolved gaps
◐ provisional	Main structure sound but some steps rely on conjectures
○ draft	Argument sketched but significant gaps remain
· stub	Placeholder with direction but little formal content
✗ non-viable	Approach assessed as fundamentally blocked

New contributions should typically start as draft or provisional. Status upgrades happen through review.

Tag values

The tags field determines sidebar grouping:

Tag	Sidebar group	Examples
`axioms`	Axioms	Coherence conservation, observer definition, loop closure
`foundation`	Foundation	Multiplicity, bootstrap, observer-loop-viability
`dynamics`	Dynamics	Minimal observer structure, three interaction types
`geometry`	Geometry	Speed of light, Lorentz invariance, Einstein equations
`quantum`	Quantum	Born rule, measurement, entanglement, decoherence
`particles`	Particles	Spin-statistics, Pauli exclusion, mass hierarchy
`holography`	Holography	Holographic bound, Bekenstein, causal set statistics
`gauge`	Gauge	Standard Model group, electroweak breaking, strong CP
`flavor`	Flavor	Three generations, CKM/PMNS, Weinberg angle
`cosmology`	Cosmology	Dark matter, dark energy, baryogenesis, singularity
`thermo-ext`	Thermo Extensions	Extended thermodynamic derivations

Required sections

Every derivation must include these sections, in this order:

1. Overview

A narrative explanation accessible to physicists who may not follow every line of the proof. Should include:

Bold opening question — what physical question does this derivation answer?
The argument — a plain-language summary of the logical steps
The result — what is derived
Why this matters — connection to known physics
An honest caveat — any structural postulates required, known limitations, or open issues

2. Statement

A formal theorem statement with all variables defined. Begin with **Theorem.** followed by the precise claim in mathematical notation.

3. Derivation

The main proof body, structured as numbered steps:

Structural Postulates (if any) — listed first, before Step 1
Step 1, Step 2, ... — each step contains Definitions, Propositions, and Proofs

Use the standard format:

**Definition N.M.** for new definitions
**Proposition N.M.** or **Theorem N.M.** for claims
*Proof.* followed by the argument, ending with $\square$
**Remark.** for clarifications and context
**Corollary N.M.** for immediate consequences

4. Rigor Assessment

An honest evaluation of the derivation's logical strength. Categorize each major result:

Fully rigorous — complete proofs from stated assumptions
Rigorous given axioms — relies on the framework's axioms being correct
Semi-formal — argument is sound but some steps appeal to physical intuition
Structural — analogies or motivated arguments rather than proofs

5. Open Gaps

A numbered list of specific issues that remain unresolved. Each gap should identify what is missing, what would be needed to close it, and whether it is a straightforward exercise or a deep open problem.

6. Comparison with Other Frameworks (optional)

A table comparing how the result is obtained in standard physics versus the framework.

Citing external papers

Use inline author-date references in the text:

This is the quantum subadditivity theorem [Araki & Lieb, 1970].

For multiple authors, list up to four; beyond that use “et al.”:

[Bennett, Bernstein, Popescu, Schumacher, 1996]
[Lieb & Ruskai, 1973]
[Hawking et al., 1995]

External references are collected in site/src/data/reference-links.json with DOI or arXiv URLs. Add an entry for any new paper you cite:

{
  "araki-lieb-1970": {
    "title": "Entropy Inequalities",
    "url": "https://doi.org/10.1007/BF01646092"
  }
}

The key should be lowercase-author-year format. Prefer DOI links where available; use arXiv URLs for preprints.

Mathematical notation

Inline math: $...$
Display math: $$...$$
KaTeX is the rendering engine — use KaTeX-compatible LaTeX
Cross-reference other derivations with markdown links: [Link Text](/derivations/category/slug)

Dependency graph

The dependsOn and enablesDerivation frontmatter fields automatically integrate new derivations into the dependency graph. Make sure these are accurate — the graph is generated from frontmatter, not from in-text links.

After adding or modifying derivations, regenerate the knowledge index:

node scripts/build-index.mjs

Submitting

Fork tpresley/observer-centrism
Create a branch for your contribution
Add or modify files following the conventions above
Run node scripts/build-index.mjs to regenerate the index
Run cd site && npm run build to verify the site builds cleanly
Submit a pull request with a clear description of what you are contributing and why

For corrections, reference the specific step, proposition, or gap number you are addressing.