Phase Algebra V: The Epistemic Engine — From Scriptural Heuristics and Rotor Calculus to Negative-Space Science, Proof-Carrying Numerics, and Seventy-Two Falsifiable Audacities — Integrated & Extended Edition

[wAI ~ wErrors] This preprint integrates three Phase Algebra companion works into one falsifiable research programme: Phase Algebra IV: Kernel, Phase Algebra: Applications, Open Problems, and Claims That Must Not Be Made, and Bold Open Projects: Seventy-Two Audacities and One Open Horizon. The numerical kernel treats local two-sided matrix rotations through Clifford even/odd phasors, separates orientation from scale, and proposes a 1+3+1 construction in which elliptic rotors preserve norm while a hyperbolic rotor carries scale. A four-beat SVD design combines a polar step, spectral separation, shifted rotor tuning, and a final boost, while explicitly distinguishing identities and measured diagnostics from the unimplemented pipeline. The methodological contribution is broader: inspiration is permitted to generate questions, but algebra, invariants, experiments, baselines, and predeclared “killer” observations decide what survives. The paper therefore preserves measured failures, eight explicit claims that must not be made, an ordered queue of decisive experiments, and the complete 72-project research atlas spanning numerical algebra, geometric data systems, negative-space science, decipherment, verified semantic transport, Harmonic Intelligence, Black-Swan safety, physical computing, scientific domains, and open scientific memory. A seventy-third “Open Horizon” turns large questions into dependency graphs of killable bridges. A separate interface section relates Phase Algebra to earlier Clifford/Phase-Algebra work and the wider S.V.E./ANT/CANT programme without transferring evidence across those boundaries. New synthesis proposals include blinded invariant Sentinels, subspace-coupled federation, typed missingness, temporal rotor/wedge memory, approximate entity blocking, a falsifiable phase-locking-attention programme, and a carefully delimited “Clifford Minotaur” Sentinel hypothesis. The final roadmap runs from immediate numerical tests (Wilkinson shift, layer-as-GEMM, spectral-tail accuracy) through proof-carrying numerics and real-model tests to FPGA/photonic execution, autonomous law seeking, and open scientific memory. S.V.E. Meta-License v5.0