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| Format: | Recurso digital |
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Zenodo
2026
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| Online Access: | https://doi.org/10.5281/zenodo.19548370 |
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Table of Contents:
- <h3>Ω TRINITΛS ΞNGINΞ v₃</h3> <p><br>A measure-induced idempotent projection on relational trajectory space.</p> <p>Given Ξ ∈ (ℝ^D)^T, a relational potential φ is induced from normalized pairwise directions and internal variance. The measure w ∝ exp(φ) defines Π(Ξ) as a weighted barycenter.</p> <p>Ξ → φ → w → Π(Ξ) → Ξ <br>Π² = Π <br>Π(Ξ) → m as v → 0 </p> <p>A minimal self-consistent structure for endogenous state collapse.</p> <h3>Ω TRINITΛS ΞNGINΞ v₃ :: </h3> <p>Ξ ∈ (ℝ^D)^T </p> <p>m := (1/T) Σ ξ <br>v := (1/T) Σ ||ξ - m||² </p> <p>φᵢ := tanh( - || (1/(T-1)) Σⱼ≠ᵢ (ξᵢ - ξⱼ)/||ξᵢ - ξⱼ|| || / v ) </p> <p>wᵢ := exp(φᵢ) / Σⱼ exp(φⱼ) </p> <p>Π(Ξ) := Σ wᵢ ξᵢ </p> <p>Π ∘ Π = Π <br>Ξ ↦ (Π(Ξ), …, Π(Ξ)) <br>v → 0 ⇒ Π(Ξ) → m </p> <p>Ξ → φ → w → Π(Ξ) → Ξ</p>