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A Minimal Self-Organizing Source Model for Emergent Horizons and Radiative Scaling 

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

Abstract

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
\[
C_{\rm loss}\simeq6.99\times10^{-4},
\qquad
C_{\rm out}\simeq3.75\times10^{-4}.
\]

For fixed conservative source action, exact scale covariance then gives

E∝R∗−1,Pout=Cout𝒮∗cq2R∗2.E\propto R_*^{-1}, \qquad P_{\rm out} = C_{\rm out}\frac{\mathcal S_*c_q^2}{R_*^2}.

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.

Available Document

DOI: 10.5281/zenodo.22282290

Citation:
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

Representative Figure

Representative radial visualizations of the canonical HorizonSource evolution. The source-generated transition surrounds a central inward-characteristic region, while perturbation of the intrinsic source mode produces organized structure in the exterior propagation channel.

Source Code and Supporting Materials

Computational materials: 
The Zenodo record includes the frozen HorizonSource v0.9 research package used to generate, verify, and reproduce the numerical results reported in Version 1.0.

The package contains the core HorizonSource implementation, automated tests, verification and convergence scripts, stored numerical outputs, example programs, and the figure-generation materials used in the paper. These materials are provided for inspection, transparency, reproducibility, modification, and independent testing. They are not packaged as maintained general-purpose software.

Files included:
1. A_Minimal_Self_Organizing_Source_Model_for_Emergent_Horizons_and_Radiative_Scaling.pdf 

Version 1.0 research paper.

2. HorizonSource_v09.zip 

Frozen HorizonSource v0.9 research package associated with the paper.
The archive includes:

– the core `horizonsource` Python package;
– package and dependency information;
– example scripts;
– automated structural and numerical tests;
– finite-volume transport and convergence tools;
– complex-pole and outer-domain verification;
– outward/inward channel decomposition;
– finite-energy branching normalization;
– source-family robustness tests;
– stored CSV, JSON, and verification-report outputs;
– paper-figure generation scripts and final figure assets; and
– a detailed `ZENODO_README.txt` describing the reproducibility workflow and mapping the numerical results to the corresponding scripts and stored outputs.

Workflow summary:
The package supports a progression from source construction through numerical verification:

HorizonSource model  

→ selected stationary source and scale
→ characteristic structure
→ coupled radiative evolution
→ finite-volume transport verification
→ pole extraction and convergence  
→ finite-energy channel normalization  
→ source-family robustness  
→ scale-covariant reconstruction  
→ paper figures and numerical reports

The principal numerical campaigns can be rerun directly from the included verification scripts.

Reproducibility note:
The stored numerical outputs allow the principal reported coefficients, convergence results, and robustness tests to be inspected without rerunning every calculation.

The radius-family results verify the exact scale-covariant reconstruction of the dimensionless model. They are not five independent dimensional simulations. The reduced equations are formulated in the scaled variables

x=r/R,τ=cqt/R,x=r/R, \qquad \tau=c_qt/R,

and the radius-family reconstruction verifies the resulting relations

ω∝R−1,E∝R−1,P∝R−2.\omega\propto R^{-1}, \qquad E\propto R^{-1}, \qquad P\propto R^{-2}.

Local environment setup may be required before rerunning the package.

Code and data availability:
The Zenodo record includes the executable HorizonSource v0.9 package, automated tests, verification scripts, stored numerical outputs, and figure-generation materials used for the Version 1.0 paper. No public technical support is implied.

Summary and Notes

Scope:
This paper develops a deterministic source-first model of horizon-like organization and radiative response.

Unlike the earlier curvature-bound response study, in which the characteristic radius was supplied to the model, HorizonSource begins upstream. A scale-covariant two-state variational source possesses a continuous stationary family, and a conserved global source quantity selects a definite radius \(R_*\). The selected stationary source then determines both its intrinsic dilation dynamics and its source-dependent characteristic structure.

The resulting logical sequence is

\[
\text{source}
\rightarrow
R_*
\rightarrow
\text{stationary transition}
\rightarrow
\text{one-way characteristics}
\rightarrow
\]
\[
\rightarrow
\text{intrinsic source mode}
\rightarrow
\text{radiative transport}.
\]

The selected scale is therefore not imposed as a horizon location. The one-way characteristic surface, inverse-radius source clock, coupled complex pole, and exterior radiative response all arise downstream of the organized source.

For the canonical model, the converged source pole gives a total loss coefficient
\[
C_{\rm loss}\simeq6.99\times10^{-4},
\]
while the finite-energy retarded channel calculation gives an outward fraction
\[
f_{\rm out}\simeq0.537
\]
and exterior coefficient
\[
C_{\rm out}\simeq3.75\times10^{-4}.
\]
Across the tested source family, changes in source stiffness, flow law, and weak source-radiation coupling alter dimensionless coefficients while preserving the central source-first organization and scale-covariant structure.

Framework context:
The paper belongs to the Physics / Black Holes and Horizon Structure area of the Coherence Geometry research corpus.

Within Coherence Geometry, observable structures are treated as projections of an underlying constrained source. HorizonSource provides a compact scientific example in which source organization, scale selection, intrinsic dynamics, characteristic propagation, diagnostics, and observable radiative projections can all be studied within one executable source model.

The HorizonSource v0.9 package is intended to provide a reusable research implementation that can be inspected, modified, extended, and tested without reconstructing the source model from the paper alone.

Related Work

Related research:
Petersen, B. L. (2026). Horizon-Like Emission from Curvature-Bound Coherence Fields. Zenodo. https://doi.org/10.5281/zenodo.22282290 (v2.0)

Related framework:
Petersen, B. L. (2026). Coherence Geometry Foundations, Part I: Orientation,
Closure, and Algebraic Foundations (Version 0.1). Zenodo.
https://doi.org/10.5281/zenodo.20156531

Petersen, B. L. (2026). Coherence Geometry Foundations, Part II: Physical
Projections (Version 0.2). Zenodo.
https://doi.org/10.5281/zenodo.20156996

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