The Emergence of Physical Reality from the Specular Bit Architecture: A Falsifiable Cosmological Hypothesis

This manuscript presents a layered mathematical and computational framework for assessing physical interpretations of Specular Bit Architecture (SBA). Under explicit contracts, the analysis distinguishes strict nonnegative State-11 rewriting, duplicate-plus-adjacency normalization, transactional serialization, and specified mixed-sign algorithms. Results concern reachability and stabilization, legal-history counts, activation spectra, canonical indexing, ensemble-dependent greedy-count laws, ternary residue counts, and resource bounds.

These formal results do not identify physical time, geometry, or statistical ensembles; source-reported updated capacity theorems add exact input-dependent counter bounds. Conditional energy assignments and FLRW dilution identities further constrain possible interpretations but supply no empirical cosmological bridge. Computational studies examine model dynamics, calibration, uncertainty, and sequential risk auditing, including monitoring and predict-before-update adaptation; conclusions remain specific to declared models and observations.

Provenance and claim layer remain separate: bounded local checks, companion-reported results, and unavailable historical artifacts are identified as such. A companion-reported Pantheon+ supernova-only comparison disfavors a frozen SBA bridge surrogate relative to fitted flat-$\Lambda$CDM in-sample; it is neither independently reproduced here nor a rejection of the discrete core. Metric and boundary-reconstruction diagnostics constrain particular candidates but establish no general impossibility theorem. The relation $G_{\mu\nu}=\kappa_{I}T_{\mu\nu}^{(I)}$ remains exploratory, not a derived gravitational field equation.

Physical interpretation requires independently justified clocks, metrics, and observable maps, plus covariance-aware calibration, held-out validation, and multi-probe tests. Two bounded feasibility studies stop before measurement comparison: no usable correspondence is identified for strict parallel relaxation, and the pair-cancellation candidate remains a representation without an emission prediction. No physical confirmation or complete replication bundle is claimed.

Index Terms:

Specular Bit Architecture, Fibonacci rewrite systems, reachability, stabilization, canonical normalization, sequential risk auditing, computational reproducibility, cosmological model testing