# Overview and publication identity

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Identifying Binary Realizations from Intervention Laws: Certificates, Recoding Obstructions, and a Bounded SPC-2/IIT Comparison

 Jeremy Rodgers  
 Independent Researcher  
 Website: [everythingequation.com](https://www.everythingequation.com)  
 DOI: [10.5281/zenodo.23075828](https://doi.org/10.5281/zenodo.23075828)

 30 September 2026  
 Version 1.1-RC1 — release candidate  
 AI-assisted review completed; no independent human mathematical review.  
Public supporting-record identifier pending.



 

**Abstract.**

A constitutive assignment may depend on a system's causal decomposition even when its complete decoded behavior is fixed. We ask what additional response evidence identifies a binary chart without supplied coordinate labels. On a completely distinguished set of $2^n$ states, strictly positive laws that factor in an unknown binary chart identify that chart up to signed permutation when their uniformly centered log-probability matrix has rank $n$. Its row-space projector reconstructs Hamming adjacency, with an explicit sufficient spectral-error certificate. A synthetic five-register demonstration defines independent-flip responses in each implementation's modeled storage chart while withholding that chart from the estimator. Reconstruction, combined with unchanged service and realization contracts, recovers the inherited SPC-2 two-versus-one assignments; it does not validate the perturbation model on a physical device. We also characterize affine transport of product laws, including deterministic and fair coordinates. For the frozen recoding, no fully supported, exactly conjugate native product-kernel family approaches the deterministic endpoint, although sparse common families exist. An official PyPhi search over all matched states, both complete presets, and a frozen spatial pair-macro domain preserves the CCI-1 positive-complex comparison. The response method identifies a candidate microchart, not an intrinsic macrograin, and is potentially usable by different constitutive theories. These are finite specializations and applications within established identifiable-component ideas. Physical conformance of the response model and empirical consciousness attribution remain unestablished.