M01-M02 (synthesis) RC Hyperoperations and Zeration - A Status-Labelled Synthesis of the Recursive Ladder, Reset Mechanism, Hyper–Shell–Thron Extension, and Loop Closure

M01-M02 is a revised and status-labelled synthesis of the original M01 and M02 materials, combining the earlier right-caterpillar hyperoperation draft and the zeration draft into one corrected document. It also incorporates the M01–M02 repair insert and later corrections, with the explicit aim of separating the proved algebraic core from conditional dynamical results and conjectural high-rank material. The monograph establishes the right-caterpillar hyperoperation ladder, with rank 0 identified as RC zeration: HRC₀ (B, z) = z + 1. It proves that negative RC ranks collapse to the same zerational floor, and that addition differs from zeration only by a shift in initialisation height. In this sense, zeration is not an added convention but the forced floor of the recursive ladder. Its main unconditional chain is: RC recursion → RC zeration → absorbing negative-rank floor → addition as shifted successor → thread points → Base-2 rank neutrality → 4 → 3 ordinal discontinuity → loop closure HRC_ω = HRC₀. So: infinitation closes as zeration. The corrected version is especially valuable because it labels what is proved, what is conditional, and what remains conjectural. The dynamical part studies reset behaviour in the complex parameter plane. It introduces the reset half-plane identity, reset survivor sets, and the reset web; the measure-zero result for reset survivors is explicitly conditional on angular transversality. The document also develops the Hyper–Shell–Thron extension mechanism and the eta-threshold programme, while keeping the full Last Eta statement conjectural. This revised synthesis is intentionally not a complete preservation of all exploratory material from the original drafts. In particular, older dynamical geography material such as cycle-basin geography is represented here in compressed/reset-web form, and some exploratory material — including items such as cycle-polynomial developments — is not treated as part of the corrected core. The corrected document explicitly says its purpose is not to close every dynamical problem, but to separate definitions, unconditional theorems, conditional dynamical theorems, and conjectural high-rank programme. The original M01 and M02 documents are preserved separately as older material: M01 Right Caterpillar Hyperoperations (v0. 9) contains the earlier RC hyperoperation dynamics and tetration-parameter-plane geography, while M02 Zeration (0. 9) preserves the standalone zeration treatment.