Generative Structural Theory v1.6: Complete Classification of Event-Flag Non-Implications

Generative Structural Theory v1.6 gives complete realizability classifications for cut-flag states and event-flag states in finite non-negative relation-strength models.

For a strict threshold cut

Eε = {(P,Q) : P ≠ Q and R(P,Q) > ε},

the eight cut flags reduce to four coordinates:

(N4, T0, M, V),

where N4 denotes anchored transitivity, T0 denotes Kolmogorov separation, M records the existence of a mutual pair, and V records the empty cut. The paper proves the complete spectrum

Σcut = {1101, 1100, 1010, 0100, 0010, 0000}.

Thus, exactly six of the sixteen possible cut-flag states are realizable, while the other ten are excluded for every finite model and every non-negative threshold.

The six event flags likewise reduce to three coordinates:

σ(R,c) = ((E2),(E4),(E5)).

The only remaining constraint is

(E5) ⇒ (E2),

giving the complete event-state spectrum

Σev = {111, 110, 101, 100, 010, 000}.

The two impossible event states are therefore 011 and 001. This classification settles the two implication pairs left open in GST v1.3: all four joint assignments of (E4,E5) and all four joint assignments of (E4,E6) are realizable, so neither pair supports an implication in either direction.

The paper also separates strictly positive models from models with a non-empty zero layer. It proves realizability of every cut and event state independently in both classes, introduces lift and descent transformations between them, and establishes positivity invariance of both realizability spectra. The minimum witness complexity is then determined state by state, including the exceptional cut state 1010, for which the strictly positive minimum is smaller.

Finite-model censuses provide bounded computational confirmation of the analytic classifications. The deposit includes the frozen paper, explicit certificate data, table generators, independent verifiers, mutation batteries, a manifest of SHA-256 digests, and an archive sidecar.

Archive SHA-256:

aae07e7c7420bee5937cd5d25dafc83973b383886fd159dd9e56ea4c03af768e

This work builds on GST v1.5, GST v1.4, and GST v1.3.