Finite-Time Observability and Physical Memory of Hidden Protocol Order

Boundary equivalence, practical detectability and physical memory are different properties of an experiment. We separate them on an exactly reproducible six-vertex reciprocal network. Complete passive boundary data are invariant along an SO(3) family of internal Laplacians. Two closed controls induce non-commuting fibre transports, yet their order is exactly invisible to the passive experiment. An active boundary readout sees the commutator only at fourth order in loop side and linearly in readout-symmetry breaking, so its fixed-noise repeat burden is of order rho^-2 ell^-8. For a known binary alternative, the equal-block-cost optimum is repeated use of the single block with the largest whitened projection; no multi-block protocol can beat this by root-mean-square aggregation. At the reference operating point a Gaussian detector requires 287 blocks and a sign-quantised detector requires 451, reproducing the classical hard-limiter penalty. We then construct a physical observer rather than infer one from sample complexity. A raw sign tape and its 452-state sufficient count have terminal reset entropies of 450.3006 and 6.16795 bits but the same closed-computation ledger: compression moves erasure earlier rather than removing it. A 39-state sequential accumulator reaches error 0.075246 in 244.836 expected blocks. Source-matched finite-time reset protocols obey local detailed balance exactly and yield reproducible work and heat distributions. Finally, finite carrier coherence imposes a threshold correlation time below which the required evidence cannot be accumulated at all, independent of precision. An exactly non-zero, rationally certified interior distinction can therefore be permanently unusable to a finite-coherence observer. The contribution is not the general claim that boundaries underdetermine interiors, which is classical. It is a certified finite example linking non-Abelian quotient geometry, fourth-order readout, eighth-order evidence, finite-state inference, physical reset and a maximal future-decision deficiency, without identifying any two of those levels. This deposit contains the manuscript in PDF and DOCX form together with the complete evidence archive: frozen parent Gate 4 and Gate 5 inputs, production and verification code, all machine-readable tables, 150,000 trajectory records, publication figures, and SHA-256 checksums. The verifier passes 37 numerical and structural checks.