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4D RESEARCH — SPECULATIVE EXTENSION TO TIME LEDGER THEORY
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Created: 2026-03-21
Author: Jonathan Shelton
Status: SPECULATIVE — must earn its place

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FOCAL POINT: THE 24-CELL
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The 24-cell (Schlafli symbol {3,4,3}) is an established mathematical object
discovered in the 1850s-1890s. It is the focal point of this entire project.

Key properties:
  - 24 vertices, 96 edges, 96 triangular faces, 24 octahedral cells
  - Self-dual: the dual polytope is another 24-cell
  - The rotation mapping it to its dual is a pi/4 (45 deg) isoclinic
    Clifford rotation in both invariant planes
  - At 45 deg: cos^2(45) = sin^2(45) = 0.5 — exact equal division
  - Unique to 4D — no analog in other dimensions

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RELATIONSHIP TO TLT
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This is an EXTENSION to TLT, NOT part of core TLT.

Core TLT is established and strong. It stands on its own:
  - f|t wave equation (foundational axiom)
  - Euler's formula (topological invariant)
  - 2D/3D lattice tests verified and audited
  - Mathematical framework complete (B1-B6)
  - Cipher validated
  - 17+ audited test entries

The 4D research explores what the 24-cell geometry reveals when subjected
to the same first-principles methodology. Anything discovered here can only
ACT TO CLARIFY the theory — it does not extend, modify, or weaken core TLT.

This project shares TLT's knowledge base but maintains its own:
  - Separate unaudited/audited flow
  - Separate results tracking
  - Own audit protocol (adapted from TLT)
  - Own progression log

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FOLDER STRUCTURE
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4d_research/
  PROJECT.txt              ← this file
  figures/                 ← visualizations, plots, cross-sections
  tests/
    audited/               ← tests that have passed Grok+Gemini external audit
      4d_engine/           ← the FDTD engine (TLT-4D-001, promoted 2026-03-21)
      AUDIT_PROTOCOL.txt   ← audit criteria for 4D tests
    unaudited/             ← new tests pending audit
  results/
    audited/               ← results from audited tests
      TLT-4D-001_4d_engine/
    unaudited/             ← results pending audit
  research/
    24cell_geometry/       ← focal point: 24-cell properties, literature
    theory_mapping/        ← maps connecting 4D observations to domains
    lattice_work/          ← geometric/cipher analysis for 4D
      geometric_mapping/
      cipher_validation/
    research_papers/       ← external literature
    research_studies/       ← internal studies
    curiosities/           ← speculative observations
  notes/
    theory/                ← theory documents relevant to 4D
      mathematical_framework/
      test_descriptions/
    findings_and_progression_log/

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METHODOLOGY
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Identical to TLT methodology:
  - OUTPUT AGNOSTIC: observe what happens, don't prove
  - Pre-register test descriptions BEFORE coding
  - Unaudited first, audit before promotion
  - Claude self-audit → contrarian audit → Grok + Gemini external audit
  - Any scores below 7 trigger investigation
  - ALL bot outputs require Jonathan's approval

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WHAT WOULD CLOSE THIS PROJECT
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This project closes if:
  - The 24-cell geometry produces no meaningful observations beyond noise
  - The 4D wave equation shows no special behavior at geometric vertices
  - Results contradict core TLT rather than clarifying it
  - The speculative nature does not produce testable, falsifiable predictions

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