Report compiled by the Office of Theoretical Synthesis.

The intellectual history of humanity is characterized by the relentless pursuit of unification. This report provides an exhaustive, expert-level analysis of twelve specific theories identified within the unification corpus. These theories span the ontological spectrum from the behavior of subatomic particles to the metaphysical definitions of divine essence.

For each theory, we rigorously excavate the Established Axioms, identify the Deduced Postulates, and provide direct references to the Seminal Formal Papers. This analysis reveals a striking meta-narrative: a triadic interplay of Information, Relation, and Emergence.

Axiom I: The State Vector (Superposition). Reality allows for simultaneous contradictory states.
Axiom II: Observables as Hermitian Operators.
Axiom III: The Eigenvalue-Eigenstate Link (Quantization).
Axiom IV: The Born Rule (Probability).
Axiom V: Unitary Time Evolution.
Deduced Axiom VI: Wavefunction Collapse.
Deduced Axiom VII: Tensor Product Composition (Entanglement).

Axiom I: The Equivalence Principle. Gravity is a feature of space, not a force in space.
Axiom II: General Covariance. Laws must be invariant under coordinate transformations.
Axiom III: The Geodesic Hypothesis.
Axiom IV: The Einstein Field Equations ().
Deduced Axiom V: Local Conservation of Energy.
Deduced Axiom VI: Gravitational Waves.

Axiom I: Relativistic Invariance.
Axiom II: The Spectral Condition (Stability).
Axiom III: Existence and Uniqueness of the Vacuum.
Axiom IV: Microcausality (Locality).
Deduced Postulate: The Spin-Statistics Theorem.

Axioms: Continuity, Monotonicity, Branching.
Theorem: Entropy ().
Deduced Axiom IV: Noisy Channel Coding Theorem.
Deduced Axiom V: The Irrelevance of Semantics (Explicitly challenged by Theophysics).

Axiom I: Intrinsicality.
Axiom II: Composition.
Axiom III: Information.
Axiom IV: Integration ().
Axiom V: Exclusion.
Deduced Postulate: Cause-Effect Space.

Axiom I: The Triadic Sign (Representamen, Object, Interpretant).
Axiom II: The Pan-Semiotic Axiom ("Life is the action of signs").
Axiom III: The Adapter Hypothesis (Arbitrariness of codes).
Axiom IV: Conservation of Codes.

Axiom I: Abstraction of Connectivity ().
Axiom II: Degree Sum Formula.

Axiom I: Sensitive Dependence on Initial Conditions (Butterfly Effect).
Axiom II: Topological Transitivity (Mixing).
Axiom III: Density of Periodic Points.
Deduced Postulate: The Strange Attractor.

Axioms: Aggregation, Tagging, Nonlinearity, Flows, Diversity, Internal Models, Building Blocks.
Deduced Axioms: Small-World Architecture, Scale-Free Growth (Power Laws).

Axiom I: Monotheism (Unity of Essence).
Axiom II: Consubstantiality (Son is identical essence to Father).
Axiom III: Relational Distinctness (Father Son Spirit).
Deduced Postulate: Perichoresis (Mutual Indwelling).

Axiom I: Historicity of the Fall.
Axiom II: Transmission by Propagation (Inherited state, not learned).
Axiom III: Privation of Grace (Missing signal).
Axiom IV: Universality.

Axiom I: Necessity of Prevenient Grace (External boot sequence).
Axiom II: Cooperation of the Will.
Axiom III: Intrinsic Transformation (Code rewrite, not just label).

Meta-Axiom I: The Primacy of Information
Reality is fundamentally informational. Matter is "frozen" information.

Meta-Axiom II: The Necessity of Relation
Nothing exists in isolation. "To be" is "to be related."

Meta-Axiom III: Emergence through Limitation
Complexity and Redemption require transcending initial linear parameters through non-linear feedback (Grace).

Master Index: The Codex Master Index