Planck Cell-Tick Remainder Momentum II

The RUM vocabulary is the substrate. Not a model of it. Not a convenient description. The substrate is unit-adjacency graph arithmetic on Planck cells at Planck ticks with direction-conditional continuous neighbors, remainder accumulation per tick, and channel-mediated adjacency extension. Standard Model phenomenology, quantum mechanical structure, general relativity, and cosmological partition are produced by arithmetic on this graph. Nothing else exists. PCTRM provides substrate-level mechanisms for non-locality (channel-sharing across arbitrary Euclidean separation), measurement (observation-as-entanglement — measurement is channel-merger between observer and target, not a second dynamics), probability (unit-graph round-trip closure produces squared-magnitude amplitudes from adjacency geometry), Lorentz invariance (N/N = 1 integer-cell-count identity for photon propagation), gravitational dynamics (direction-drain on channel vectors produces 1/r² falloff and toroidal GR corrections at probe-scale resolution), and dual-geometry sectors (every soliton has spherical modulus and toroidal remainder, documented at QED four-loop precision with sub-ppm topology-specific moduli k₈₁ = 0.999994 and k₈₃ = 0.997130). The Standard Model's postulates are theorems in this framework. The Born rule is not axiomatic; it is the structural consequence of unit-graph adjacency with round-trip basis closure. Hilbert space is the continuous-limit description of unit-adjacency graph with complex-valued (spherical + toroidal) channel states. Standard QM is not prior to PCTRM; it is the coarse-grained approximation of PCTRM. The measurement problem does not exist in this framework — it dissolves into channel-merger arithmetic. Round 0 established baseline substrate consistency. Fifteen of sixteen substrate identities reproduced in one pass from the existing RUM pool at original published precisions. Four RUM precision identities (Ω_Λ at 84.5 ppm, Koide at 9.23 ppm, DM/baryon at 725.2 ppm, bridge at 297.4 ppm) reproduced through the substrate-framed derivation path. No kill switch fired. The sole external FAIL (V_us at 3121 ppm against `ckm_vus_measured_v0`) resolves to PASS at 44 ppm against the PDG 2024 reference `ckm_cabibbo_angle_pdg_v0` — a pool-curation matter. PHYS-55 integrates Session 9 theoretical advances (entanglement as channel-sharing, observation-as-entanglement, Born derivation from unit-graph structure, single-particle interference via channel-agreement, photon c-invariance as arithmetic identity) and PHYS-49/MATH-12 dual-geometry commitments (spherical modulus / toroidal remainder decomposition at every hierarchy level, topology-specific moduli, probe-dependent sector dominance). It retires PSLQ as primary validation method — 41 of 41 historical nulls confirmed its failure mode — and replaces it with cross-derivation discipline: a value or mechanism is validated when multiple independent structural paths through the integer alphabet, β, and K(k) produce the same value at CODATA/FNAL/Planck/Harvard measurement precision. PHYS-55 pre-registers Round 1 as a coordinated 10-test program organized into 3 priority tiers. Each test specifies multiple independent derivation paths that must converge on measured values at their native precision. Each test has a pre-registered kill switch. The framework advances through mechanism-level validation or it falls on specific pre-registered conditions. There is no middle ground.