KURPISHEV LOGIC 2 · UNIFIED
RUEN中文DE
Proof obligations

PO-1—PO-12

Current status map after the synchronized closure of PO-9.
PO-1

R⋆R algebra

OPEN

Specify the carrier, field, basis, multiplication/structure constants, unit, involution, norm and domain of the author’s R⋆R.

PN2_theorem_ru_v1.0 §12; PN2_journal_ru_v1.1 §8
PO-2

Consistency

OPEN

Check bilinearity, closure, continuity, zero divisors and the existence of the operators used.

PN2_theorem_ru_v1.0 §12; journal §8
PO-3

Nonzero associator

OPEN

Compute K on explicit triples and classify the associative and nonassociative sectors of R⋆R.

PN2_theorem_ru_v1.0 §12; journal §8
PO-4

Structural coordinate 𝔇

OPEN

Define 𝔇 with Δ_D>0, prove invariance and interpret its unit.

PN2_theorem_ru_v1.0 §12; journal §8
PO-5

Observable S

OPEN

Choose a physically interpretable S and prove c-separation, or use the full-state form.

PN2_theorem_ru_v1.0 §12; journal §8
PO-6

Measurement model

OPEN

Describe hidden b, available data, permitted estimators and the experimental meaning of e_S,e_D,e_R.

PN2_theorem_ru_v1.0 §12; journal §8
PO-7

Uniform constant

OPEN

Choose a normalized Ω for the author’s R⋆R and prove ε_->0; investigate its boundary and degenerate sectors.

PN2_theorem_ru_v1.0 §12; journal §8
PO-8

Dimensional consistency

OPEN

State physical dimensions of S, 𝔇, K, m and κ; introduce calibration maps.

PN2_theorem_ru_v1.0 §12; journal §8
PO-9

Categorical no-go

CLOSED_ABSTRACT_CATEGORY

Specify categories, functors, morphisms and the precise no-go: absence of a natural section, lift or joint estimator.

PN2_theorem_ru_v1.0 §10.3 / §12; PN2_journal_ru_v1.1 §5.3 / §8; synchronized C3.8M 2026-09-01
PO-10

Connection to PN.1

OPEN

Construct a representation ρ in a Hilbert space and define self-adjoint X,P, their domains and the commutator.

PN2_theorem_ru_v1.0 §12, §14; journal §8–§9
PO-11

Examples and counterexamples

CLOSED_ABSTRACTLY

Four constructions: K=0; K≠0 with Δ_S=0; c=1; compact Ω with ε_-=3.

PN2_theorem_ru_v1.0 Appendix A A.1–A.5; journal §6
PO-12

Independent reproducibility

CLOSED_ABSTRACTLY

Certificate PN2-PO12-A2-v1.0, exact code, tests, values.tsv, results.json, SHA-256.

PN2_theorem_ru_v1.0 Appendix B B.0–B.9; journal §8 + Data availability