DOI: 10.5281/zenodo.18741704
title: 20.SVRN_OS_L6_Scale-Invariant Percolation Threshold $D_0 = 0.05$ From Semiconductor Netwo

description: [ZENODO DESCRIPTION]

Title (EN): Scale-Invariant Percolation Threshold D₀ = 0.05: From Semiconductor Networks to Cosmological Structure Title (KR): 스케일 불변 퍼콜레이션 임계 D₀ = 0.05: 반도체 네트워크에서 우주 구조 형성까지

Series DOI: 10.5281/zenodo.18325543 Paper DOI: 10.5281/zenodo.18741704 Patent: KR 10-2026-0017941 SHA-256: 05b88ff579c35b4cca90f52e5f876f662ce31b13707aea28387c64772b0d2191



Abstract (4-Section Format)

[ROOT] Percolation theory predicts a dimensionless critical threshold D₀ = (a/ξ)ᵈ at which network connectivity undergoes a phase transition. This paper proposes that D₀ = 0.05 emerges as a scale-invariant structural critical point across two physically distinct domains separated by 28 orders of magnitude in length scale. This is a structural alignment hypothesis, not a universal constant declaration.

[STEM] At the semiconductor nanoscale (L1 domain): three methodologically distinct derivation paths converge on D₀ = 0.05. (1) Percolation theory with a = 45 nm (CPP pitch, IRDS 2024) and ξ = 122 nm yields (45/122)³ = 0.0502. (2) Samsung SF2-to-SF3 area scaling ratio = 0.05 (published). (3) Defect density boundary γ(T) in DOI_17 observes D₀ = 0.05. At the cosmological scale (L6 domain): DESI DR2 BAO data (arXiv:2503.14738, Table IV) reports α_iso = 0.9749 at z = 0.706 (LRG2), yielding Δ = |1 − α| = 0.0251 at 3.75σ. The ratio D_M / D_μ = 0.0251 / 0.05 = 0.502 ≈ 1/2 with 0.4% deviation (A3 alignment, PASS).

[BRANCH] A derived correlation length ξ_eff = 5.43 Mpc is obtained by applying D = (a/ξ)³ with a = 2 Mpc (local clustering cell scale, distinct from BAO sound horizon ~150 Mpc) and D₀ = 0.05. This is explicitly a structurally derived value, not a directly measured r₀. Independent LRG survey literature (Zehavi et al. 2011; Marulli et al. 2013) reports r₀ ~ 5–8 Mpc, which is consistent but not confirmatory. Empirical verification against DESI DR2 density-field data is designated HOLD.

[CROSS] The mapping Δ = |1 − α_iso| → D_M is an interpretative structural mapping, not a formally derived physical equivalence. The ×2 relation (D_M ≈ D₀/2) is an empirical alignment, not a derived projection coefficient. Five HOLD items define the remaining verification roadmap (z_eff=20 cosmic connectivity, ξ_eff vs. measured r₀, density-field F(ρ), ×2 physics mechanism, a=2 Mpc sensitivity). No claim exceeds its evidential basis.



Limits Section






Item
Status




D₀ = 0.05 at semiconductor scale
CONFIRMED — 3-path convergence (LOCKED)


Δ_DESI = 0.0251 at LRG2, z=0.706
CONFIRMED — DESI DR2 Table IV, 3.75σ


D_M ≈ D₀/2 alignment
STRUCTURAL HYPOTHESIS — physics TBD


ξ_eff = 5.43 Mpc
DERIVED VALUE — not measured


D₀ as universal constant
NOT CLAIMED


z_eff = 20 cosmological meaning
HOLD


DESI density-field connectivity
HOLD


a = 2 Mpc justification
HOLD — sensitivity acknowledged







Truth Declaration

This work is an original theoretical proposal by an independent researcher (architect, 25yr; no institutional affiliation). It contains confirmed L1 results (LOCKED), published DESI DR2 data reproduced exactly (no hallucination), structural hypothesis clearly labeled as such, derived values explicitly distinguished from measured values, and open HOLD items with defined verification paths. No universal constant is declared. Published as a structural hypothesis inviting independent verification.



Keywords (20): percolation threshold, scale invariance, D₀=0.05, semiconductor interconnect, BAO, DESI DR2, LRG2, critical threshold, structural alignment hypothesis, cosmological structure formation, GAA, quantum coherence, 2D materials, nuclear shielding, correlation length, percolation theory, dimensionless parameter, 퍼콜레이션, 스케일불변, 반도체