Project ID: QNFO.RSCH.APH
Status: Phase 0 — Infrastructure & Planning
License: CC-BY 4.0
π, α, and mass are not independent "fundamental constants" but three orthogonal projections of a single geometric structure — a helical/toroidal vortex with the Compton wavelength as its characteristic scale.
| Identity | Meaning |
|---|---|
| α = re / ƛ | Fine-structure constant = classical electron radius ÷ reduced Compton wavelength |
| α = 2π re / λc | Same ratio using full Compton wavelength |
| m = ω | Mass = angular frequency (in Planck units: ħ = c = G = 1) |
| ω_C = mc²/ħ | Compton angular frequency ↔ mass via Planck-Einstein + mass-energy equivalence |
alpha-pi-helix/
├── README.md # This file
├── WBS.md # Work Breakdown Structure (9 phases, 61 tasks)
├── LICENSE # CC-BY 4.0
├── paper/
│ ├── outline.md # Paper structure and section plan
│ └── alpha-pi-helix.md # The full paper (under development)
├── derivations/
│ ├── alpha-re-lambda.tex # α = re/ƛ step-by-step derivation
│ ├── mass-frequency.tex # m = ω in Planck units derivation
│ ├── zb-position.tex # Zitterbewegung position operator
│ └── scaling-chain.tex # re = αƛ = α²a₀ full chain
├── references.bib # BibTeX bibliography
├── figures/ # Diagrams and visualizations
├── appendices/ # Supplementary materials
├── data/
│ └── constants.json # CODATA 2022 values
├── review/
│ ├── red-team.md # Red-team critique
│ └── peer-sim.md # Simulated peer review
├── research-notes/ # Session-by-session provenance notes
└── provenance/ # Zenodo provenance bundle
- Jones (1706): Synopsis Palmariorum Matheseos — first use of π for circle constant
- Hestenes (2008): Zitterbewegung in Quantum Mechanics — electron as lightlike particle with helical ZB (arXiv:0802.2728)
- Hestenes (2019): Zitterbewegung structure in electrons and photons — toroidal vortex model (arXiv:1910.11085)
- Consa (2018): Helical Solenoid Model of the Electron — extends Hestenes' ZB model
- Wikipedia: Attic numerals, Pi, Classical electron radius, Fine-structure constant, Zitterbewegung
- Phase 0: Infrastructure — IN PROGRESS
- Phase 1: Historical Foundations
- Phase 2: Mathematical Foundations (exact identities)
- Phase 3: Physical Foundations (ZB, helical models)
- Phase 4: Synthesis (unification thesis)
- Phase 5: Publication & Dissemination
- Phase 6: Infrastructure & Archive
- Phase 7: Red-Team & Peer Review
- Phase 8: Closeout
See WBS.md for full task breakdown.