Phase Transition Kinetics and Topological Event Horizons at Extreme omega

Returns to the vertical depth axis to model the extreme-omega 'wind tunnel' of Volume I as phase-transition kinetics. A high-pressure centre N is idealized as a subset of the first 15 primes > 3. For a tuple B with dimension m_B and killer-prime set K_B (primes dividing a member offset: triplet {5}, quadruplet {5,7}, quintuplet {5,7,11}), the per-factor modifier is q/(q-m_B) for non-killers and 0 for killers (an absorbing state: q|N kills a member). The ensemble enrichment <E_B(omega)> = P(avoid all killers) x (geometric enrichment) is evaluated exactly over all C(15,omega) factor subsets. Results: the Twin (no killer) enriches monotonically to the finite primorial value x7.030 at omega=15 (diverging only as omega->infinity). The Event Horizon -- an interior peak omega* where d<E>/domega=0 -- is CONDITIONAL, existing iff the marginal log-enrichment is positive at omega=1: it holds for the triplet (omega*=9) and quadruplet (omega*=4), which peak then collapse to zero measure, but NOT for the quintuplet (three killers), which decays monotonically from omega=1 with no interior horizon. This corrects a naive 'G up, S down implies a unique peak' argument. The construction is a closed-form extrapolation to omega=15 (N>4.7e18), far beyond any sieve, and assumes the local-factor multiplicativity validated only to omega~5-6 persists; it is hypothesis-generating, not an observation of primes, and claims no infinitude.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-06-08
DOI
https://doi.org/10.5281/zenodo.20586919
Primary Topic
High-pressure geophysics and materials
Type
preprint
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preprint

Phase Transition Kinetics and Topological Event Horizons at Extreme omega

Ruqing Chen
Zenodo (CERN European Organization for Nuclear Research)
High-pressure geophysics and materials
preprint

Phase Transition Kinetics and Topological Event Horizons at Extreme omega

Ruqing Chen
preprint en

Abstract

Returns to the vertical depth axis to model the extreme-omega 'wind tunnel' of Volume I as phase-transition kinetics. A high-pressure centre N is idealized as a subset of the first 15 primes > 3. For a tuple B with dimension m_B and killer-prime set K_B (primes dividing a member offset: triplet {5}, quadruplet {5,7}, quintuplet {5,7,11}), the per-factor modifier is q/(q-m_B) for non-killers and 0 for killers (an absorbing state: q|N kills a member). The ensemble enrichment <E_B(omega)> = P(avoid all killers) x (geometric enrichment) is evaluated exactly over all C(15,omega) factor subsets. Results: the Twin (no killer) enriches monotonically to the finite primorial value x7.030 at omega=15 (diverging only as omega->infinity). The Event Horizon -- an interior peak omega* where d<E>/domega=0 -- is CONDITIONAL, existing iff the marginal log-enrichment is positive at omega=1: it holds for the triplet (omega*=9) and quadruplet (omega*=4), which peak then collapse to zero measure, but NOT for the quintuplet (three killers), which decays monotonically from omega=1 with no interior horizon. This corrects a naive 'G up, S down implies a unique peak' argument. The construction is a closed-form extrapolation to omega=15 (N>4.7e18), far beyond any sieve, and assumes the local-factor multiplicativity validated only to omega~5-6 persists; it is hypothesis-generating, not an observation of primes, and claims no infinitude.

Zenodo (CERN European Organization for Nuclear Research)
Energoservis (Czechia) (CZ)
Affordable and clean energy
High-pressure geophysics and materials
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Phase Transition Kinetics and Topological Event Horizons at Extreme omega — Ruqing Chen · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS