Hamilton's Principle, Feynman's Path Integral, and the Action Quantum h = 2πℏ as Capacity-Rotor Theorems: A Parameter-Free Derivation from QTT Axioms A1--A7U

Hamilton's Principle, Feynman's Path Integral, and the Action Quantum as QTT Capacity-Rotor Theorems Version: 2.02 First public release: 9 May 2026 Current release: 26 June 2026 Concept DOI: 10.5281/zenodo.20098143 Author: Ali Attar Website: quantumtraction.org This paper develops Hamilton's stationary-action principle, Feynman's path integral, and the action quantum \(h=2π\) as Quantum Traction Theory (QTT) capacity-rotor theorems. The central source claim is that a physical history advances a real \(J\)-dial by \[ dθ=dS/, \] so the laboratory path-integral weight is not introduced as a primitive complex phase. It is the access shadow of a real source rotor: \[ R_J(θ)=cosθ\,I+sinθ\,J, J^2=-I, J^=-J. \] The continuum path integral is written in QTT-native form as \[ K_J(b,a) = ∫_{ HA7U(a,b)} DA6γ\, R_J\!({Sₜₒₜ[γ]}{}). \] The action quantum follows from A4 action-angle transport plus A7/A7U closure: \[ Δ Sone\ revolution = ·2π ≡ h. \] The Planck--Einstein rule \(ET=h\), de Broglie rule \(pλ=h\), Bohr--Sommerfeld loop rule \(∮ p\,dq=nh\), and flux-quantization rule \(qΦ=nh\) are treated as projections of that same dial-closure statement. Version 2.02 does not change the theorem rail of v2.01. It is an onboarding, provenance, and audit release. It adds the corpus-wide QTT Onboarding standard, plain definitions of first-use QTT terms, the first public release date, an early scale-status/no-circularity note for \(/_A\), a familiar recovery route, early falsifiers, an Artian's Universe statement, website deep anchors, a load-bearing axiom/concept map, and concept-DOI-only citation cleanup. Main status labels: GREEN: STATIONARY-ACTION-RECOVERY-IN-LOW-ENERGY-SHADOW GREEN: REAL-J-ROTOR-HISTORY-WEIGHT-DERIVED-FROM-QTT-AXIOM-CHAIN GREEN: ACTION-QUANTUM-CLOSURE-THEOREM-H-EQUALS-2PI-HBAR GREEN: STANDARD-CLOSURE-RULES-RECOVERED-AS-PROJECTIONS YELLOW: SECTOR-SPECIFIC-A7U-RESIDUALS-REQUIRE-PRINTED-BUNDLE-GRAPH Related QTT anchors: Main book: 10.5281/zenodo.17527179 The Artian Hamiltonian Framework: 10.5281/zenodo.20484906 The Artian Lagrangian Framework: 10.5281/zenodo.20657182 Observation as Access: 10.5281/zenodo.20114403 From Rotor to Wavefunction: 10.5281/zenodo.20119662 Corpus Tree: quantumtraction.org/doi-map/ Derivation Atlas: quantumtraction.org/derivation-atlas/ Lexicon: quantumtraction.org/lexicon/ Included files: PDF paper, Version 2.02 Complete reconstruction ZIP containing LaTeX source, local load-bearing style module, Zenodo description HTML, render audit, metadata, and hashes