{"id":4388,"date":"2026-09-04T03:59:01","date_gmt":"2026-09-04T10:59:01","guid":{"rendered":"https:\/\/coherencegeometry.com\/?p=4388"},"modified":"2026-09-12T08:02:15","modified_gmt":"2026-09-12T15:02:15","slug":"a-minimal-self-organizing-source-model-for-emergent-horizons-and-radiative-scaling","status":"publish","type":"post","link":"https:\/\/coherencegeometry.com\/index.php\/2026\/09\/04\/a-minimal-self-organizing-source-model-for-emergent-horizons-and-radiative-scaling\/","title":{"rendered":"A Minimal Self-Organizing Source Model for Emergent Horizons and Radiative Scaling\u00a0"},"content":{"rendered":"\n

Internal ID:<\/strong> CGI-RSR-000035
Author(s):<\/strong> Barry L. Petersen
Document Type:<\/strong> Research Paper
Publication Date:<\/strong> September 4, 2026
Original Creation Date:<\/strong> September 4, 2026
Revised Document Date:<\/strong> September 4, 2026
Status:<\/strong> Public
Domains:<\/strong> Physics
Sub-Domain:<\/strong> Cosmology, Black Holes and Horizon Structure
Research Topics:<\/strong> Emergent Horizons, Black Holes, Horizon Structure, Quasinormal Modes, Radiative Transport, Scale Covariance, Deterministic Field Dynamics, Source Engineering<\/p>\n\n\n\n

Abstract<\/h3>\n\n\n\n

Horizon calculations ordinarily begin after a horizon-bearing background, flow, or characteristic structure has already been specified. Here we ask an upstream question: can a minimal deterministic source generate its own scale, transition, one-way characteristic surface, intrinsic dynamics, and radiative response?
We construct a scale-covariant two-state variational source possessing an exact stationary transition family. A conserved global source quantity lifts the dilation degeneracy and selects a finite radius \\(R_*\\). Pullback of the projected source metric onto the dilation orbit yields a finite source inertia only for an admissible parameter range, \\(\\lambda>9\/8\\), and generates an intrinsic mode with frequency \\(\\omega\\propto R_*^{-1}\\). A source-dependent coherence flow converts the stationary transition into a one-way characteristic surface, while conservative coupling to the outgoing characteristic channel allows relaxation of the source mode to generate exterior radiation without prescribing either an emitted waveform or phenomenological damping.
The coupled system is verified using conservative finite-volume evolution, boundary-accounted energy transport, retarded detector comparisons, spatial and outer-domain convergence, independent time- and frequency-domain pole extraction, and source-family robustness tests. For the canonical source, the converged dimensionless pole is
\\[
\\hat\\omega
\\simeq
0.894932
3.91\\times10^{-4}i.
\\]
A finite-energy, real-frequency retarded channel normalization partitions the corresponding source-mode loss into an outward fraction
\\[
f_{\\rm out}\\simeq0.537,
\\]
giving
\\[
C_{\\rm loss}\\simeq6.99\\times10^{-4},
\\qquad
C_{\\rm out}\\simeq3.75\\times10^{-4}.
\\]<\/p>\n\n\n\n

For fixed conservative source action, exact scale covariance then gives<\/p>\n\n\n\n

\n
\n
E<\/mi>\u221d<\/mo>R<\/mi>\u2217<\/mo>\u2212<\/mo>1<\/mn><\/mrow><\/msubsup>,<\/mo><\/mspace>P<\/mi><\/mtext>out<\/mi><\/mrow><\/msub>=<\/mo>C<\/mi><\/mtext>out<\/mi><\/mrow><\/msub>\ud835\udcae<\/mi>\u2217<\/mo><\/msub>c<\/mi>q<\/mi>2<\/mn><\/msubsup><\/mrow>R<\/mi>\u2217<\/mo>2<\/mn><\/msubsup><\/mfrac>.<\/mi><\/mrow>E\\propto R_*^{-1}, \\qquad P_{\\rm out} = C_{\\rm out}\\frac{\\mathcal S_*c_q^2}{R_*^2}.<\/annotation><\/semantics><\/math><\/div>\n<\/div>\n<\/div>\n\n\n\n

The construction is not proposed as a microscopic model of an astrophysical black hole or as a derivation of Hawking radiation. It demonstrates that a self-organizing deterministic source can generate, as related outputs, a selected scale, one-way characteristic structure, an intrinsic inverse-radius mode, conserved exterior transport, and inverse-square radiative power.<\/p>\n\n\n\n

Available Document<\/h3>\n\n\n\n

DOI:<\/strong> 10.5281\/zenodo.22282290<\/code><\/p>\n\n\n\n

Citation:<\/strong>
Petersen, B. L. (2026). A Minimal Self-Organizing Source Model for Emergent Horizons and Radiative Scaling (Version 1.0). Zenodo. https:\/\/doi.org\/10.5281\/zenodo.22297099<\/a><\/p>\n\n\n\n

Representative Figure<\/h3>\n\n\n\n
<\/div>\n\n\n