IST Axioms (v2)

WARNING: This is a work in progress in need of revision.

These axioms define the foundational rules governing the CD universe.
They express what must be true for:

• coherence
• epochs
• causal axes
• divergence
• cognition
• quantum behavior
• and gravitational curvature
  to exist.

They do not describe physical laws directly; instead, they describe the constraints that make any set of physical laws possible.

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Axiom 1 — The Substrate (Σ) Exists and Is Unbounded

An unbounded informational substrate Σ exists containing all possible informational configurations.

Properties derived from Axiom 1:

• Σ is non-spatial, non-temporal, non-probabilistic.
• Σ contains all potential states; universes are coherent slices through Σ.
• Nothing can “enter” or “leave” Σ; divergence is internal re-slicing, not extrusion.
• Σ does not evolve; evolution is emergent from coherence ordering.

This axiom establishes the ontology: information first; physics second.

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Axiom 2 — Constraints Define What Counts as Physical

A configuration in Σ is physical if and only if it satisfies the active constraint set C.

Consequences:

• Constraints determine what informational configurations cohere.
• Physical laws are the operational form of constraints.
• Universes correspond to stable constraint-satisfying regions inside Σ.
• All physical structure (atoms, fields, observers) is constraint-stabilized information.

This axiom elevates constraints to the fundamental role normally played by “laws of physics.”

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Axiom 3 — Coherence Is Required for Existence

A configuration exists within a universe only if all constraints are satisfied simultaneously.

Formally:

coherent(σ, C) ⇔ ∀ c ∈ C, c(σ) = true

Consequences:

• Coherent regions behave as single causal units.
• Incoherent configurations cannot persist and cannot form epochs.
• Coherence defines objecthood, dynamics, and quantum amplitude structure.
• Quantum provisional branches are internally coherent but not yet globally committed.

This axiom introduces simultaneous constraint-satisfaction as the existence criterion.

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Axiom 4 — Coherent Configurations Must Update

Any coherent configuration must continue generating successor coherent configurations unless divergence prevents synchronization.

Implications:

• Time emerges as the ordering of coherent updates.
• No coherent region can “freeze” unless mismatch forces divergence.
• All physical systems generate local epoch chains.
• Stability (e.g., atoms) means endlessly repeating coherent cycles.

This axiom generalizes conservation of information, quantum evolution, and the impossibility of “stopping” time locally.

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Axiom 5 — Coherent Updates Must Merge If Synchronizable

Local epoch updates must be merged into a global epoch chain if and only if the mismatch between regions is below the coherence window W.

Consequences:

• Universal time = merged epoch ordering.
• Time dilation arises from delayed mergeability (larger τ → slower merge).
• GR curvature is mismatch geometry made macroscopic.
• Differences in cohesion time (Δτ), orientation (Δθ), or constraint structure (ΔC) create gravitational effects.

This axiom introduces synchronizability as the hidden generator of geometry.

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Axiom 6 — Exceeding the Coherence Window Causes Divergence

If the mismatch magnitude exceeds the coherence window W, a region can no longer synchronize and must form an independent epoch chain with a new causal axis.

Formally:

||M(R)|| > W → divergence

Where:

||M|| = √(α Δτ² + β Δθ² + γ ΔC²)

Consequences:

• Divergence = formation of a new universe.
• Black hole horizons are divergence thresholds.
• Causal isolation is absolute: no information can merge across axes.
• Angular momentum influences divergence through Δθ.
• Universes form genealogical trees.

This axiom unifies:

• black holes
• cosmic censorship
• baby universes
• horizon formation
  under a single mismatch principle.

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Axiom 7 — Coherence Filtering Determines Outcome Weights

When a coherent region generates multiple internally consistent provisional branches, each branch receives a coherence weight proportional to its constraint-satisfaction measure.

Commit rule:

w_i = F_coh(ψ_i)
commit selects one branch, weights reproduce |ψ|²

Consequences:

• Born rule emerges from substrate-level filtering.
• Interference patterns arise from overlap of provisional branches.
• Measurement is just a global coherence commit event.
• No collapse, no randomness: only filtering by constraint geometry.

This axiom replaces the measurement postulate of QM.

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Summary of Axioms v2

Axiom	Content	Role
1	Unbounded substrate Σ	Ontological foundation
2	Constraints define physicality	Source of laws
3	Coherence = existence	Defines objecthood
4	Coherent systems must update	Generates time
5	Updates merge if synchronizable	Produces geometry & GR
6	Exceeding W → divergence	Produces horizons & new universes
7	Coherence filtering	Produces QM & Born rule
8	Causality requires coherence
9	Compuation requires causality	An informational constructor. Computation requires information transfer between >1 stable structure

These seven axioms form the fully unified substrate-level description of IST physics.