EQUATION REGISTRY

Area form for a circular loop

Uses the manuscript’s rest radius R and motion-associated radius R′. Comparing with standard Sagnac expressions requires matched area and timing definitions; the area form alone does not establish all-orders agreement.

Theory · DERIVEDEquation version 1.0.0

Based on the final manuscript · Chapter 1

ASD-WEB-LVE-016
t=2πRc,v=R′ω,R′=γRΔt=4πωR′2c2=4ωS′c2,S′=πR′2\begin{aligned}t&=\frac{2\pi R}{c},&v&=R^{\prime}\omega,&R^{\prime}&=\gamma R\\\Delta t&=\frac{4\pi\omega R^{\prime2}}{c^2}=\frac{4\omega S^{\prime}}{c^2},&S^{\prime}&=\pi R^{\prime2}\end{aligned}

Uses the manuscript’s rest radius R and motion-associated radius R′. Comparing with standard Sagnac expressions requires matched area and timing definitions; the area form alone does not establish all-orders agreement.
Chapter reference: Final consolidated manuscript · Chapter 1, Section 3.5, Eqs. (1.39)–(1.43) · ASD-BOOK-ddbade997b45

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Final consolidated manuscript · Chapter 1, Section 3.5, Eqs. (1.39)–(1.43)

Uses the manuscript’s rest radius R and motion-associated radius R′. Comparing with standard Sagnac expressions requires matched area and timing definitions; the area form alone does not establish all-orders agreement.

Conditions retained in this adoption

  • Apparatus, direction and counting conditions remain with each entry
  • Muon inputs are illustrative approximations, not a complete survival fit

Specific unresolved source issues

  • FINAL-CH1-FIZEAU-DIMENSION
  • FINAL-CH1-MUON-OBSERVABLE
  • FINAL-CH1-CLOCK-PROTOCOL

Source locators: p0476 · p0478 · p0480 · p0482 · p0484

Manuscript SHA-256: ddbade997b45913248e588953b1d27ccb9c7c206c3c8d992d3aef2364a64836e

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Previous source, retained as history

CH1-caf38018fc5a · 第一章 §3.5,式(1.39)–(1.43),PDF 第 18 页

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