PV-PP Scalar Reduction Proof Program

The PV-PP Scalar Reduction Proof Program is the formal mathematical proof effort supporting the Productive Value-Productive Power (PV-PP) framework. Rather than arguing that scalar optimization is generally incorrect, the program identifies the structural conditions under which scalar comparison exactly reproduces a staged decision architecture and establishes formal boundary results describing where that recovery no longer holds.

Repository Status

Current Authority	V3.25 Live Theorem Packet
Status Layer	V3.26
Repository Status	Public Research Repository
Primary Result	Restricted Scalar Containment and Boundary Mathematics

Open GitHub Repository

Repository Organization

01 Scalar Proof Final Reduced Set
Authoritative theorem package containing the Live Theorem Packet and supporting authority documents.
10 Supporting Files
Supporting mathematical work, integration material, and historical development supporting the theorem authority.

Research Scope

The repository currently contains:

Formal theorem packet (V3.25)
Status and boundary layer (V3.26)
Scalar containment results
Non-reduction results
Runtime interpretation
Cross-file verification
Supporting mathematical development

Companion Publications

This repository provides the formal mathematical authority for companion publication papers currently under development. The publication papers summarize and explain the mathematics contained in the theorem packet but do not supersede the theorem authority maintained here.

Project Philosophy

The repository intentionally separates theorem authority, supporting mathematical work, publication material, and historical development. This organization preserves a stable mathematical reference while allowing supporting research to evolve independently.