Statistical PN.2 · rigorous audit
C3.8T: the candidate bound is verified under explicit assumptions. A full proof, sharp examples and counterexamples are available. The canonical patch has not been applied.
Open the rigorous auditC3.8S · CENTRAL PHYSICS–MATHEMATICS EXHIBIT
PN.2 Research Center
An interactive evidence map of Kurpishev’s uncertainty principle: from nonassociative structure to a formal theorem, open physical hypotheses and verification stages.
3PN.2 forms
12PO: 3 abstractly closed
14F: physically open
7stages V0–V6
PN.2 formula workbench
16 PN.2 formulas, lower-bound calculations, a c-separation check and direct links to verified proof pages.
Open the formula workbenchInteractive graph
R⋆R → K → 𝔇 → PN.2 → PO → F → V0–V6
Loading the evidence graph…Select a node to inspect its status, source and dependencies.
Theorem 7.1
Three canonical forms
The formulas are proved in the stated model of a hidden bracketing alternative. Their physical interpretation has separate obligations.
Evidence-status boundary
Closed obligations and open questions
Abstractly closed
PO-9=CLOSED_ABSTRACT_CATEGORYPO-11/PO-12=CLOSED_ABSTRACTLY
Appendix A.1–A.4, Appendix B and the A₂ certificate belong to the closed abstract package.
Open mathematical and bridge obligations
PO-1—PO-8, PO-10=OPEN
The concrete R⋆R, measurement model, units and Hilbert-space bridge remain open.
Physically open
F-1—F-14=OPEN_PHYSICAL_HYPOTHESIS
A software or abstract PASS is not an independent physical test.
Candidate extension
STATISTICAL PN.2=CANDIDATE
The form with (1−τ)² awaits the separate rigorous C3.8T audit.
Direct research links
From the graph to full registers
Proof obligations
Complete statements, anchors, gates and statuses.
Examples and certificate
A.1–A.4 and PN2-PO12-A2-v1.0.
Physical Bridge
Typed specification, measurement contract and blockers.
Unit Ledger
Dimensional discipline: no uncalibrated ‖K‖∼ħ.
Physical hypotheses
Hypotheses, groups and an independent verification program.
Proof Observatory
Blockers of physical conclusions.
Statistical PN.2
TV distinguishability and bounds with (1−τ)².
Public theorem edition
Primary source in the author archive.
Edition boundary. Canonical PN.2-S/R/K and the broader PN.2-A/B/V formulations in the journal branch are different layers of the author’s corpus. They must not be merged automatically into one proved theorem.