BIG-B13: Boundary Folding as a Reduced Model of Observation and Self-Measurement

Version 1.1 — source-based figure restoration and methods clarification (15 October 2026).

This version restores all twelve manuscript figure panels from archived B13 numerical results. Eleven panels use the original Colab-generated PNGs; Figure 3 is redrawn from the unchanged 48-condition RMSE table with the tested coordinates labeled explicitly. The original reconstructed illustrations differed from the archived results, particularly in the basin-map domain and the baseline selection-curve shape. Two gradient symbols, printed contents-page numbers and source/fixed-point wording are also corrected. The principal numerical values and original scientific outcomes are retained.

The single ZIP includes the corrected 17-page manuscript, the original PDF, all 37 original result-package files, the recovered original notebook, eighteen unchanged computational function bodies, a portable output adapter, methods clarification and the audit verifier. The saved-data/static-source audit passed 86 groups / 4508 comparison values; no new stochastic trajectory, PDE integration or fixed-point minimization was run. Reproduction is supported in principle; independent rerun auditing is not yet complete.

The audit documents inside the immutable ZIP were frozen before publication. Their provisional publication-status entries are historical snapshots; this Zenodo page supplies the current publication status.

Project repository: https://github.com/Jun-Lucis/BIG-theory

Original research summary:

This paper presents BIG-B13, a reduced structural model of observation-like updating and self-measurement within Boundary Information Geometry (BIG).

In BIG-B13, a system is represented by a boundary field, internal resonance modes, and a hidden-depth memory state. Observation is modeled as a boundary-folding interaction between a system and an observer, where boundary proximity gates a coupling between hidden-depth states. The purpose of this paper is not to derive quantum measurement, the Born rule, consciousness, or AI perception. Rather, it defines a testable reduced mathematical layer for observation-like hidden-depth updating, binary basin selection, Born-like reference comparison, and self-model stability analysis.

Numerical experiments are presented in two parts. First, a spin-like binary observation toy model is tested. The baseline model produces ordinary basin selection rather than Born-rule behavior. However, a low-barrier finite-noise regime reproducibly approaches a Born-like reference curve, with robustness checked across random seeds. Observer coupling is then shown to preserve, bias, or destroy this finite-noise Born-like regime depending on observer-axis symmetry and coupling strength.

Second, a reduced self-observation model is analyzed through fixed points, Hessian spectra, discrete-time stability, and noise-induced basin switching. The model produces a multistable self-observation landscape with four locally stable fixed points. Noise tests show that local Hessian stability is distinct from global noise robustness: lower-energy self-model basins remain more persistent under high noise than higher-energy basins.

BIG-B13 is therefore presented as a reduced, testable model of boundary-folding observation and self-model stability. It does not constitute a theory of quantum measurement or consciousness, but provides a mathematical scaffold for future extensions.