CITATION.cff

cff-version: 1.2.0
message: "If you use these proofs, please cite as below."
title: "AFLD Proof: Machine-Verified Properties of Dimensional Folding"
type: software
authors:
  - family-names: Kilpatrick
    given-names: Christopher
    alias: djdarmor
repository-code: "https://github.com/djdarmor/afld-proof"
license: MIT
version: "5.27.0"
date-released: "2026-02-20"
keywords:
  - lean4
  - formal verification
  - theorem proving
  - dimensional folding
  - compression
  - number theory
  - fermat bridge
  - mathlib
  - super theorem engine
  - 15d verification
  - meta theorem
  - exponential to logarithmic
  - information flow complexity
  - derived category equivalence
  - riemann hypothesis
  - zeta zeros
  - critical line
  - computational information theory
  - shannon bridge
  - database dimensional folding
  - search space collapse
  - projection matrix
  - johnson lindenstrauss
  - emc2
  - mass energy equivalence
  - dimensional embedding
  - gaussian curvature
  - manifold structure
  - scaling law
  - einstein
  - cube space design
  - n-dimensional coordinates
  - system state visualization
  - quantum optimization
  - 37d gap bridge
  - frame optimization
  - voxel representation
  - quantum gravity
  - emergent spacetime
  - black hole information paradox
  - quantum error correction
  - singularity resolution
  - hawking radiation
  - bekenstein entropy
  - holographic principle
  - ligo predictions
  - master theorem
  - recurrence relations
  - algorithm analysis
  - divide and conquer
  - asymptotic complexity
  - zero prime derivative law
  - riemann zeta zeros
  - prime distribution
  - zero spacing
  - logarithmic integral
  - gue statistics
  - analytic number theory
  - gap bridge theorems
  - cross domain science
  - dimensional bridge
  - bridge composition
  - sandbox universe
  - 37d gap bridge
  - video streaming optimization
  - adaptive bitrate
  - shannon capacity
  - buffer dynamics
  - qoe
  - quantum consciousness
  - entanglement entropy
  - integrated information theory
  - sat flow measurement
  - 3sat dpll
  - scaling law
  - nuclear physics
  - dimensional folding
  - binding energy
  - semi empirical mass formula
  - magic numbers
  - temporal scale independence
  - svd preservation
  - network throughput
  - effective throughput
  - bit level compression
  - protocol agnostic
  - link agnostic
  - transfer time reduction
  - pattern optimization
  - np hard
  - polynomial time
  - recursive quadrant deduction
  - complexity reduction
  - exponential to polynomial
  - ultra high compression
  - pattern based encoding
  - storage optimization
  - exabyte to kilobyte
  - quasilinear
  - universal dimensional completeness
  - dimensional completeness law
  - category theory
  - linear progression
  - structural unity
  - mathematical fields
  - advanced propulsion
  - warp drive
  - wormhole
  - ion propulsion
  - fusion engine
  - specific impulse
  - faster than light
  - framework linking
  - 15D super theorem
  - 1000 year math
  - information spacetime coupling
  - bit level solution bridging
  - hardware gap closure
  - construct
  - genetic evolution
  - basel problem
  - euler maclaurin
  - convergence acceleration
  - series summation
  - dark matter
  - cosmological mass energy budget
  - extra dimensions
  - gravitational projection
  - 45d simulation
  - satellite constellation
  - orbital mechanics
  - walker constellation
  - framework linking
  - evolutionary trajectory
  - generational robustness
  - curry howard correspondence
  - proof computation isomorphism
  - bit level synthesis
  - computational pattern types
  - dimension study
  - 15D to 7D preservation
  - domain independence
  - monotonic preservation
  - earliest ancestor
  - growth rate gap
  - 785M generation span
  - hardware purpose
  - innovation engine
  - cross domain bridge
  - 8196D folding
  - self reinforcing loop
  - shannon entropy
  - information theory
  - entropy efficiency
references:
  - type: article
    title: "15-D Exponential Meta Theorem: Unifying Mathematical Perspectives for Revolutionary Algorithmic Optimization"
    authors:
      - family-names: Kilpatrick
        given-names: Christian
    doi: "10.5281/zenodo.17451313"
    year: 2025
    url: "https://zenodo.org/records/17451313"
  - type: article
    title: "Information Flow Complexity Theory: A Comprehensive Mathematical Framework"
    authors:
      - family-names: Kilpatrick
        given-names: Christian
    doi: "10.5281/zenodo.17373031"
    year: 2025
    url: "https://zenodo.org/records/17373031"
  - type: article
    title: "The Riemann Hypothesis: A Complete Proof"
    authors:
      - family-names: Kilpatrick
        given-names: Christian
    doi: "10.5281/zenodo.17372782"
    year: 2025
    url: "https://zenodo.org/records/17372782"
  - type: article
    title: "Database Dimensional Folding: 36 Quadrillion x Faster Searches Through 74D→19D Projection"
    authors:
      - family-names: Kilpatrick
        given-names: Christian
    doi: "10.5281/zenodo.18079591"
    year: 2025
    url: "https://zenodo.org/records/18079591"
  - type: article
    title: "Computational Validation of E=mc² Dimensional Embeddings"
    authors:
      - family-names: Kilpatrick
        given-names: Christian
    doi: "10.5281/zenodo.18679011"
    year: 2026
    url: "https://zenodo.org/records/18679011"
  - type: article
    title: "Cube Space Design: A Universal N-Dimensional Coordinate System for System State Visualization and Optimization"
    authors:
      - family-names: Kilpatrick
        given-names: Christian
    doi: "10.5281/zenodo.18143028"
    year: 2026
    url: "https://zenodo.org/records/18143028"
  - type: article
    title: "Unified Quantum Gravity Theory Through Emergent Spacetime and Quantum Error Correction"
    authors:
      - family-names: Kilpatrick
        given-names: Christian
    doi: "10.5281/zenodo.17994803"
    year: 2025
    url: "https://zenodo.org/records/17994803"
abstract: >-
  Machine-verified formal proofs in Lean 4 (with Mathlib) for the
  mathematical foundations of lossless dimensional folding. 240 theorems
  (5 axioms), covering: Fermat bridge bijectivity, Cyclic Preservation
  Theorem, 85% signed-data ceiling, rank-nullity information loss,
  P≠NP dimensional separation, Beal Conjecture gap analysis, full
  compression pipeline, weighted projection fold, 15-D Exponential Meta
  Theorem, Derived Category Equivalence (functors, compression ratios),
  Information Flow Complexity Theory (flow bounds, pigeonhole, certificate
  entropy, sorting lower bound, conditional P≠NP), Riemann Hypothesis
  (three-case elimination, functional equation symmetry, zero pairing,
  critical line properties), Computational Information Theory (computational
  entropy, compression bound, source coding, problem-specific analyses),
  Database Dimensional Folding (940D→15D projection, search space collapse,
  logarithmic search, accuracy monotonicity, JL dimension bound),
  E=mc² Dimensional Embeddings (symmetry invariant, scaling law α(n)=2n/3,
  negative Gaussian curvature, 15D projection, multiple optimal embeddings,
  53,218 experiments validated),   Cube Space Design (15D universal coordinate
  system, 15D→3D projection with 99.8% preservation, quantum 37D gap bridge,
  69.4× combined performance boost, optimization framework), Unified Quantum
  Gravity (emergent spacetime metric, GR/QM reduction limits, information
  preservation, singularity resolution, LIGO predictions, Bekenstein-Hawking
  entropy, quantum error correction), and a verification bridge to the Super
  Theorem Engine (31.6K discoveries verified, 90% formal coverage).