ANP-09: Scale-Fragmentation Rigidity, Actual Horizon Inverse Limits, Causal-Forest Necessity, and the CN3 Final Audit

Scale-Fragmentation Rigidity, Actual Horizon Inverse Limits, Causal-Forest Necessity, and the CN3 Final Audit

ANP-08 removes D_HTRANS as an independent primitive term. The remaining strong-chain problems concern actual branch persistence, scale/frequency fragmentation, global state/profile escape, spatial fragmentation, and fresh-source/action cascades. Before further compactness work, two semantic corrections are needed: first, a positive high-frequency state does not equal a dangerous-certified state; second, an actual causal forest does not equal a single atomic causal lineage. This round corrects the dangerous-marker semantics of the horizon gate, distinguishing forward causal ancestry from dangerous-certified horizon recurrence. Proves a genuine Horizon Causal-Forest Necessity Theorem: assuming a finite-time singularity, the union of all corrected finite C3 histories terminating at Type-I or non-Type-I certified dangerous horizon seeds is an actual pre-singularity causal DAG in the original solution, with terminals appearing at arbitrarily late times and unbounded singular scales. Using a nonempty compact actual-prefix space plus a continuous surjective truncation map, proves a sufficient theorem for the actual inverse limit of atomic CN3, and shows profile-quotient compactness is not enough to obtain this actual inverse limit. Reclassifies temporal Zeno stagnation as fresh-source renewal (when propagation influence fails at a fixed cut), reclassifies unbounded relative-frequency jumps as balanced high-high downward transfer, and — relative to the DRC dissipation-wavenumber architecture — reclassifies them as viscous absorption or dissipation-span/driver debt. The irreducible atomic-ancestry frontier is a diffuse horizon branch/profile fragmentation: actual dangerous causality may exist in the form of an unbounded horizon forest, without a single atomic infinite branch. Universal causal-forest necessity is therefore proven relative to ANP's own definitions, while strong atomic CN3, finite obstruction, and Navier–Stokes regularity remain OPEN — formally handing off to NS-CFOP.