Science / field: foundations of mathematics and KLT software architecture.
What the artifact opens. a structure was detected первый эталонный RIUD-тетраэдр: замкнутый узел Rep(R,I,U;D), в котором прогнозный gap, ближайшая пересборка, валидность пределов и запись PredReperRecord образуют сертифицируемый K4-мотив.
Gap closed in the general Architecture of Mathematics and sciences. it closes gap between harmonic lambda-критерием и proof gate-статусом: formula уже не висит отдельно, а получает source-object, proof-object, formal-card и D-связку.
Internal theorem statement. Артефакт-1 Курпишева утверждает существование в KLT-RBD первого эталонного signature-ready RIUD-тетраэдра, который соединяет forecast_fact_gap, nearest_rebuild_neighborhood, LimitOK и PredReperRecord в один сертифицируемый Reper-узел Rep(R,I,U;D).
Formal card: FORMAL-CARD-RUN009-006;
source: RIUD-TETRA-RUN006-029;
proof-object: PROOF-OBJ-RUN007-0029.
Metrics: lambda = -0.992736565,
delta_truth = 0.00726343453, CGI =
0.140948882, blockers = 0, decision =
signature-ready.
Proof status. roadmap-only-not-proof;
truth_layer_promotion = 0. The artifact is treated as an
internal KLT-RBD theorem-candidate / roadmap object, not as an
externally proved theorem.
Next action: Использовать как эталон; статья RU/EN/ZH/PDF через publication pipeline; truth-layer не менять..
Definition. A RIUD tetrahedron is a complete K4 subgraph of RBD whose vertices are read as R, I, U, D. It can be read as Rep(R,I,U;D) only when role assignment, non-empty D, admissible domain and denominator-safe lambda model are present.
For Artifact-1:
source_object_id = RIUD-TETRA-RUN006-029
R = forecast_fact_gap
I = nearest_rebuild_neighborhood
U = LimitOK
D = PredReperRecord
lambda = -0.992736565467904
delta_truth = 0.0072634345320961
CGI = 0.1409488823383871 < 1
remaining_blockers = 0
current_decision = signature-ready
truth_layer_promotion = 0Theorem. A RIUD tetrahedron with non-empty R,I,U,D roles, delta_truth <= 0.01, CGI < 1, zero blockers and signature-ready decision is an internally certifiable KLT-RBD artifact and a reference pattern for detecting similar closures in the Architecture of Mathematics.
Proof. The K4 motif prevents the object from being an isolated formula: it already contains the four Reper roles. Non-empty D turns the triple (R,I,U) into an evidence-addressable quadruple. The bound delta_truth <= 0.01 gives proximity to the harmonic condition cr(U,I;R,D) = -1. The inequality CGI < 1 states that no graph-causal break destroys the connection. Zero blockers remove the open gate obstacles. Hence the RBD audit assigns signature-ready. Since truth_layer_promotion = 0, the theorem proves only the internal controlled certificate readiness, not an external absolute theorem status. □