Answers are grounded in this paper and cite their sources.
Theoretical analysis reveals structural separations in network disclosure and path transport, indicating exact conditions for factorization across reachability quotients.
AbstractThis artifact records two machine-assisted structural probes used to determine whether the network-composition branch of the Identity-Persistence Program required a further theorem owner after Endogenous Interface Synthesis. It is a provenance and commissioning record, not an independent paper. Probe A tests whether joint-sender disclosure separates from collections of bilateral disclosures. Joint disclosure does not enlarge realizability, and its width reduces to the existing pooled-kernel chromatic theory. Nevertheless, a parity witness exhibits a strict revelation separation: within the enumerated class, every bilateral realization incurs epistemic excess relative to the primitive joint realization. The probe further identifies a candidate exact criterion for zero-excess bilateral factorization in terms of meet-decomposition into sender-computable coarsenings, with relays unable to repair a failure. Probe B tests whether the reachability quotient established under fixed-carrier full disclosure survives general transport. Canonicity of the fixed point survives, but bare reachability does not: networks with identical reachability may have different closures when path transports differ, parallel paths may carry additional capability, and cyclic systems require a walk-based rather than simple-path formula. A transport-coherence condition supplies a sufficient intermediate collapse. The two probes therefore separate but converge on one deeper question: when does a network observable factor through the reachability quotient of its path and factorization structure? On that basis the record commissions a single successor owner, The Reachability Quotient: When Network Realization Can Be Forgotten. The later theorem paper discharges the proof obligations transferred by this record.
No takes yet. Share an insight, caveat, or question.
Devin Bostick (2026) studied this question.
Synapse has enriched 8 closely related papers on similar clinical questions. Consider them for comparative context: