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Recursive Substrate Dynamics in the UNNS Framework
τ-Collapse · Structural Modes · Multi-Seed Emergence
Abstract
Physical constants such as the fine structure constant (α), proton-electron mass ratio (μ), and cosmological constant (Λ) are universally treated as fundamental parameters requiring empirical measurement. We report computational evidence that these quantities emerge as robust consequences of recursive substrate dynamics rather than contingent facts requiring explanation. First, systematic testing of 218 mathematical constants via τ-collapse analysis (Chamber XII) reveals zero primary invariants—only structural modes (Operator, Relaxation, Projection) survive as irreducible primitives. Second, recursive evolution of these modes in τ-field dynamics predicts α = (7.297352597 ± 0.000000007) × 10⁻³, matching the measured value to within 5.3 × 10⁻⁷ across three independent computational realizations (coefficient of variation < 0.0001%). The framework additionally predicts μ within 1.82% and Λ within 10 orders of magnitude, without parameter fitting. These results suggest that physical constants are not fundamental inputs to nature but structural outputs of recursive dynamics, with implications for the interpretation of dimensional analysis, naturalness arguments, and the apparent fine-tuning of physical law.
Keywords: fundamental constants, emergence, recursive dynamics, fine structure constant, UNNS substrate, τ-collapse
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A map of the Substrate, Collapse, Dynamics, Observability, and Predicate Viability
Ontology → τ-Invariants → Collapse Universality → Proto-Closure → Flux/Conservation → Dynamic Completion → Least-Divergence Selection → Observability Gates → Predicate Viability
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When a Question Is Not the Problem
Mathematics usually classifies questions into three categories:
- Answered — we know the result
- Open — we don't know yet, but the question makes sense
- Undecidable — provably impossible to answer within a formal system
But there is a fourth category that is rarely named explicitly:
This distinction matters when we encounter extreme but finitely defined quantities such as TREE(3) or Graham's number.
In classical mathematics, these are treated as ordinary natural numbers, and questions like "Is TREE(3) prime?" are described as unknowable in principle.
The UNNS framework takes a different approach. Instead of asking whether an answer can be found, it asks:
The UNNS Question
Is the question itself structurally meaningful?
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Core Conceptual Shift
Classical vs. UNNS Eigenvalues
Classical Meaning (Reference Only)
In linear algebra, an eigenvalue λ is defined by:
A(v) = λv
→ the transformation acts, but the form survives, scaled.
- Requires linear vector spaces
- Requires linear operators
- Equality-based invariance
UNNS Translation (Substrate Meaning)
In UNNS, we are not primarily concerned with vectors or linear maps, but with:
• recursive generability (Φ)
• structural consistency (Ψ)
• survival under curvature / collapse (τ, Operator XII)
A UNNS-eigenvalue is a scalar or invariant that characterizes how a structure survives recursive action without changing its identity.
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How shared alphabets reveal — or fail to reveal — true mechanistic interaction in the pre‑geometric substrate
when shared symbols do—and do not—compose · pre-geometric selection · coupling criteria · what would count as evidence
Do mechanisms actually meet?
Two results are already public and testable: least-divergence selection persists under controlled perturbations, and ordering noise reveals a sharp discrete-cost threshold without destabilizing physical geodesics. Those findings establish robustness. But robustness is not the end of the story.
The next scientific question is sharper: when two different mechanisms act on the same refinement alphabet, do they actually compose into a new mechanism—or do they remain separable? In other words: do they merely share symbols, or do they share control?
This article builds on the Chamber XXXI results by addressing their mechanistic implications. It does not revisit the validation itself, but instead analyzes what the observed robustness reveals about the structure of the UNNS substrate prior to any geometric description.