12-stage Bose-Einstein Condensation phase transition maps to the ordo salutis. 3.7σ significance. Causal ordering independently forced in both domains.

Methodology — Framework Documents

AAA-000

Classification Framework

How to tell Analogy from Isomorphism from Identity. The four levels, four separator tests, and full registry sorted by level.

AAA-001

Mathematical Boundary Conditions

Formal category-theoretic requirements at each level. Heaviside, Hamilton, Maxwell as historical crossings. AdS/CFT, Geometric Langlands.

AAA-002

BEC-Soteriology Audit

Adversarial AI (o3) audit of PROCESS-001. 12 stage verdicts, 15 overclaims, 11 missing equations, 6 upgrade paths. $0.56 cost.

AAA-003

Promotion Checklist

Work orders for leveling up any ISO. What must be delivered to cross each boundary. Current candidates and what each one needs.

Fundamental Physics Series — Four Forces + Core Mappings

ISO-001 · Gravity

Gravity ↔ Sin

F = Gm₁m₂/r² — distance from the Source increases the pull, and escape requires external energy exceeding gravitational binding energy.

ISO-002 · Strong Force

Strong Force ↔ Covenant Unity

Quark confinement and asymptotic freedom map to covenant bonds that strengthen under stress, with freedom maximized within the relationship.

ISO-003 · Electromagnetism

Electromagnetism ↔ Truth

Maxwell's equations, light propagation, E-B field duality map to revelation, mercy-justice duality, and propagation of the Word.

ISO-004 · Weak Force

Weak Force ↔ Free Will

The only force that changes particle flavor ↔ the only mechanism that changes moral orientation. Beta decay and genuine transformation.

ISO-006 / 007 / 008

Information · QM · GR Triad

Information Theory ↔ Logos · Quantum Mechanics ↔ Faith · General Relativity ↔ Grace. Three structural isomorphisms forming Laws 6–8.

ISO-009 / 010

Cosmology & Coherence

Expanding universe (Λ) ↔ eschatological history converging on its end. Emergent coherence ↔ Christ as conserved coherence source.

ISO-011 · Superposition

Superposition ↔ Mystery/Revelation

Quantum superposition-to-collapse arc maps to mysterion-to-ephapax: hidden pre-event state, irreversible collapse, non-local propagation.

ISO-022 · Lagrangian

Lowe Coherence Lagrangian ↔ Divine Simplicity

One action principle governing 10 coupled variables in 5 symmetry pairs ↔ all of God's attributes as aspects of one undivided reality.

ISO-026 · Addiction

Addiction ↔ Sin Bondage

Identical process trajectory — tolerance, escalation, bondage, external rescue required — driven by entropy increase in the reward system.

ISO-012 · Sign Operator

Sign Operator → Moral Eigenstate

[σ, U] = 0 — eigenvalue invariant under self-generated evolution. The mathematical content of why works cannot save.

ISO-013 · Grace Operator

Grace as Idempotent Projection

G² = G, G†G ≠ I — once is enough, irreversible, rank-deficient. The semi-Pelagian operator fails idempotency (α = 1 only).

ISO-015 · Moral Physics

Coherence as Virtue Metric

ΔC > 0 = virtue, ΔC < 0 = sin. Conscience as a local coherence gradient detector. Level 2 honest (partial swap test).

ISO-016 · Attractors

Eschatological Attractors

dΦ/dt = αΦ(1−Φ)(Φ−Φc) — two stable attractors (Φ=1 heaven, Φ=0 hell), one unstable saddle (Φ=0.5 lukewarmness).

ISO-018 · Cosmology

Dynamic Dark Energy ↔ Sustaining Grace

H² = (8πG/3)ρ + G(t,Ψ)/3. DESI DR2 4.2σ evidence for w ≠ −1. Static Λ = deism; dynamic G(t,Ψ) = theism.

ISO-027 · Epidemiology

SIR Model of Hamartiology

dI/dt = βSI − γI. Jeroboam as super-spreader (21× in Kings). Righteous remnant as herd immunity. Abraham's Sodom as threshold analysis.

ISO-028 · Ecology

Shannon Diversity ↔ Ecclesiology

H' = −Σpᵢlnpᵢ applied to gift distribution predicts resilience. Keystone species = apostolic function. 8/10 correspondences robust.

ISO-030 · Genetics

Central Dogma ↔ Sola Scriptura

DNA→RNA→Protein :: Scripture→Doctrine→Practice. Error rate 10⁻⁹ :: 99.5% textual stability. Textual criticism = mismatch repair.

ISO-031 · Network Science

Scale-Free Networks ↔ Ecclesiology

Matthew 25:29 IS the Barabasi-Albert preferential attachment mechanism — stated 1,950 years before Barabasi (1999).

ISO-032 · Psychology

Attachment Theory ↔ Prayer & Worship

2D anxiety×avoidance space maps to prayer postures. Beck & McDonald (2004) Attachment to God Inventory empirically validates.

ISO-033 · Pharmacology

Hill Equation ↔ Grace Mechanics

E = Emax[D]ⁿ/(EC50ⁿ+[D]ⁿ). Faith = receptor, sin = competitive antagonist. n→∞ gives the Sign Operator. Romans 5:20 = rightward dose shift.

ISO-034 · Control Theory

PID Controller ↔ Providence

C(s) = Kp + Ki/s + Kd·s. Conscience (P), sanctification (I), prophetic warning (D). God steers but does not replace the plant G(s).

ISO-036 · Fluid Dynamics

Navier-Stokes ↔ Pneumatology

ruach = pneuma = wind — linguistic identity, not metaphor. Bernoulli = "when I am weak, then I am strong" (2 Cor 12:10).

ISO-037 · LEVEL 4 IDENTITY ★

Beer-Lambert Law ↔ Transaction Fee Extraction

I(x) = P(n) exactly — setting α=f, x=n. Mathematical identity confirmed, not analogy. Proverbs 11:1. The only L4 entry in the registry.

Candidate Series — Weakest / Under Review

ISO-017 · CANDIDATE

Modified Einstein ↔ Christological Mediation

Modified Einstein field equations as a candidate mapping for Christological mediation between Creator and creation. Low confidence.

ISO-019 · CANDIDATE

Boundary Conditions ↔ Divine Covenant

Mathematical boundary conditions that uniquely determine solutions as a candidate mapping for divine covenantal constraints. Low confidence.