The Principle of Non-Contradiction, or Coherence: Written Articulation and Mathematical Ledger of the Residual Process

Working note. Not a journal paper. Not a detection. Not a joint fit. This deposit contains a single PDF with two complementary presentations of the residual process already developed in prior RSIT deposits: (1) an extended axiomatic articulation written so that a reader who knows English but nothing of the subject can follow what is intended, and (2) a compact mathematical ledger that translates the same articulation into an exact symbolic statement. The locks remain parked. Residual class A remains inside the window [0.03, 0.05] centered near 0.040. The geometric dark-energy pair remains frozen at w₀ = −φ/2, wₐ = −1/φ, with crossing at z = 1/√5. No continuous free parameter is introduced. No fourth door is opened. Selective retention, interface sequester, and the discrete activation angles (36° family and 45° pairwise) are unchanged. The language and the ledger are two readings of the same process. The action that holds forms the place. What fails to hold is discarded by the same selective filter. The residual persists. The angles remain. Companion to the existing Principles collection and related RSIT working notes. Locks unmoved.