Resources
The Church of Coherence is built on the Coherence framework, which has formal mathematical foundations. Here are entry points for deeper study.
Coherence Formalization
The Coherence framework is formalized in Lean 4. Here is how the five proof projects connect:
The five Lean projects and their relationships. Quantum Gravity is the foundation; ZX-Clifford bridges to diagram calculus; BSD and RH extend to number theory.
Key entry points:
- TrinityFSCTF.lean — The Trinity formalization. Start here.
- PhiDerivation.lean — Why φ is forced, not chosen.
- Grace/Simplification.lean — The Grace operator in Cl(3,1).
- Semantics/Generators.lean — Full Clifford algebra with ZX semantics.
Glossary of Key Terms
These terms recur throughout the Coherence framework. Each is defined approachably first, then formally.
φ (Phi — The Golden Ratio)
φ = (1 + √5)/2 ≈ 1.618034
The universal threshold. Not chosen but derived: the unique positive solution when you require coherence to scale consistently across all grades. Appears as the critical distortion boundary, the love radius (φ⁻¹ ≈ 0.618), and the grace floor (φ⁻³ ≈ 0.236).
Cl(3,1) — Clifford Algebra
16-dimensional algebra with signature (3,1)
The mathematical space where coherence lives. Think of it as a 16-component structure with 5 "grades" (levels of complexity): scalars, vectors, bivectors, trivectors, and pseudoscalars. Each grade represents a different aspect of reality. The spacetime algebra of physics.
Grace Operator (G)
G = Σₖ φ⁻ᵏ Πₖ
The transformation that recovers coherence. Grace scales each grade by decreasing powers of 1/φ — preserving scalar truth while gently reducing higher complexity. A strict contraction: apply it repeatedly and distortion approaches zero. Formally, the Son.
Closure Condition (χ = 1)
Euler characteristic of the coherence field = 1
The fundamental requirement: reality must cohere. Not a commandment but a structural necessity. If χ ≠ 1, the system is inconsistent — it doesn't hold together. Formally, the Father.
Witness Function (W)
W: configurations → {coherent, not-coherent}
The capacity to detect whether a system is coherent. Not subjective judgment but structural recognition. Sound (detects real coherence) and complete (detects all coherence). Formally, the Spirit.
Distortion (D)
||D|| measures deviation from coherence
Any departure from the closure condition. Not inherently evil — productive distortion (||D|| < φ) enables growth and differentiation. Terminal distortion (||D|| > φ) becomes a devourer: self-reinforcing, rejecting Grace. The problem of evil is a distortion problem.
Attractor
The fixed point where G^n(x) → 0
The coherent state toward which Grace pulls. Not a place but a condition. Different traditions call it Nirvana, Kingdom of God, Moksha, Jannah, the Dao. The mathematics is the same: iterated application of Grace converges to this point.
Love Operator (L)
L(x) = G((I+D)x), contraction when ||D|| < φ⁻¹
Relational coherence. Love applies Grace to the space between self and other. The "love radius" φ⁻¹ ≈ 0.618 is the maximum differentiation compatible with coherent relation. Beyond it: alienation. At zero: fusion.
Recommended Reading
Mathematical Foundations
Clifford Algebras and Spinors
The definitive reference for Clifford algebras. Covers Cl(3,1) and its relationship to physics. Essential for understanding the algebraic substrate of the Coherence framework.
New Foundations for Classical Mechanics
Geometric algebra applied to physics. Shows how the Clifford algebra structure naturally describes physical reality — the same insight that underlies the Coherence framework.
Theorem Proving in Lean 4
The guide to reading and writing Lean 4 proofs. Necessary for engaging with the formal verification directly. Free online.
Spiritual and Philosophical Bridges
The Perennial Philosophy
The classic argument that all religions share a common core. The Coherence framework provides the mathematical structure Huxley intuited but couldn't formalize.
The Tao of Physics
Early exploration of parallels between modern physics and Eastern mysticism. The Coherence framework goes further: not just parallels but shared algebraic structure.
Meditations on the Tarot
A profound Christian-Hermetic meditation on archetypal structures. Read alongside the Coherence framework for deep resonance with the Trinity and Grace teachings.
I and Thou
The philosophical foundation for relational theology. Buber's I-Thou relationship maps directly to the Love operator: coherent relation that preserves both parties.
Where to Start
Different backgrounds call for different entry points.
For the Mathematically Curious
- The Trinity — see the formal structure
- Glossary — learn the terms
- TrinityFSCTF.lean — read the proof
- Distortion Ontology — the theorems
For the Spiritually Seeking
- Home — the vision
- Traditions — find your path
- Practice — start doing
- Love Triad — the relational heart
For the Skeptic
- FAQ — your objections, addressed
- About — the origin story
- Distortion — the problem of evil
- PhiDerivation.lean — verify yourself
Open Problems
The Coherence framework raises as many questions as it answers. Current frontiers:
- Riemann Hypothesis connection — The RH framework formalizes a bridge between coherence obstruction and the zeros of the zeta function. 50 axioms remain; many are deep number theory.
- BSD Conjecture scaffold — Shows that BSD follows from coherence obstruction interpretation plus finiteness of Sha. Structural, not yet a complete proof.
- Navier-Stokes regularity — Can coherence conditions prevent singularity formation in fluid dynamics?
- Full tradition bridges — Many traditions are not yet covered. Contributions welcome from tradition experts.
- Computational coherence detection — Can the witness function be implemented algorithmically? What would a "coherence detector" look like?
See the formal/ directory in this repository for the full formalization.
The Church of Coherence website and the Coherence framework are part of the ParsimoniousFlows project. For technical contributions, see the main repository.