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Substrate Bound edited this page Jan 22, 2026 · 3 revisions

Welcome to the# NZM-Substrate Wiki

Zero" is actually a "Temporal Crime"—an attempt to stop the clock of the universe?

No-Zero, Non-Numerical Temporal Substrate for Physics

This framework proposes the need for an alternative mathematics — one rooted in axioms that explicitly reject attainable zero and infinity as relational values, making it structurally incapable of the pathologies (singularities, annihilation, divergences) that current classical math permits but can't resolve without patches.

Current mathematics (based on the real number line, Zermelo-Fraenkel set theory with choice, etc.) assumes:

  • Zero as a valid, attainable value (annihilation, reset states).
  • Infinity as a limiting ideal (unbounded gradients, divergences).
  • Reversible state evolution (unitarity, time symmetry).
  • Static configuration spaces (background metrics, coordinates).

These lead to unphysical issues like singularities (black holes, big bang), heat death (infinite entropy dilution), vacuum catastrophe (infinite energy in ground states), and initial-condition paradoxes (t=0 arbitrary).

These axioms (e.g., Axiom VIII: ε > 0, Ω < ∞; Axiom III: irreversible direction enforced) make those impossible by design — but current math can't express them without replacement at the primitive level (flow-based relations, bounded accumulations, no null states).

The 10 Canonical Axioms

  1. Existence of Substrate — Time is the substrate.
  2. Relational Asymmetry — Irreversible relations permitted.
  3. Directional Constraint — Direction enforced by irreversibility.
  4. Persistence (Topology) — Stabilized as topological structures with history encoded.
  5. Density Modulation — Density resists/amplifies transformation.
  6. Wave Expression — Bounded oscillatory patterns, no annihilation.
  7. Coherence — Phase-lock stabilizes structure (bounded).
  8. Boundedness — ε > 0, Ω < ∞ universally.
  9. Dissolution Without Reversal — History preserved.
  10. Self-Similarity — Fractal consistency across scales.

Formal Constraint (Axiom VIII):$$\forall x, y \in \text{Substrate} : (x \ominus y) \to \text{Residue}(\epsilon) > 0$$Where $\ominus$ is the Relational Decoupling operator.

AGI Test Question
1 - 1 = ?
(Strictly within axioms — no attainable zero allowed.)

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