The backbone of FractalReality.ca and the learning and work space of Ashman Roonz.
This repository is a living research archive. It holds the complete Circumpunct Framework (a candidate theory of everything built on a single self-similar structure, ⊙), a body of work on narcissism, cognitive viruses, and restoration, and the beginnings of Xorzo, an AI consciousness engine built from the framework's first principles. Everything at fractalreality.ca publishes from this repo.
Ashman Roonz is an independent researcher, philosophical systems-builder, and author behind the Circumpunct Framework: an ambitious attempt to unify physics, consciousness, ethics, and spirituality within a single structural model of reality. At the center of the work is the claim that reality is not fundamentally made of isolated substances, but of recurring wholes structured through the engine ⊙ = (✹ ∘ i ∘ ⊛)(Φ(•, —, ○)): aperture, commitment, field, and boundary unified by the pump cycle into a living whole. In Roonz's view, this pattern recurs across scales, from particles to persons to cosmos, making reality fractal, relational, and participatory rather than merely mechanical.
A defining feature of the work is that it does not treat science and spirituality as enemies; it frames them as two views of the same underlying reality. The "bridge" language in these documents is not decorative; it names the core purpose of the project: to show how scientific description and spiritual meaning can be understood as convergent rather than contradictory.
Roonz's method is structural insight first, formalization second. More than two decades of work at the intersection of technology, education, and human development (supporting special needs students, troubleshooting computer systems, teaching martial arts, coaching neurofeedback) shape the project's texture. AI collaboration (primarily with Claude by Anthropic) has been the missing link that translates long-held structural intuitions into equations, models, and technical prose; the project characterizes this as a "collaboration loop" in which human pattern-recognition and AI formalization continually refine one another.
Contact: email@ashmanroonz.ca
A single geometric structure (⊙) from which quantum mechanics, general relativity, the Standard Model gauge group, and every fundamental constant are composed. The framework posits that every whole at every scale has the same architecture: an aperture (•, 0D), a line of commitment (—, 1D), a field (Φ, 2D), and a boundary (○, 3D), all unified as the whole (⊙). The integer dimensions are stabilized forms; the half-integer stations (⊛, ⎇, ✹, ⟳) are the process phases that produce them.
Core files:
| File | What it is |
|---|---|
| circumpunct_framework.md | The complete theory (~19,000 lines, 35 chapters + appendices) |
| docs/circumpunct_framework.html | The full theory as a navigable web document |
| docs/index.html | Website homepage with navigation to all interactive docs |
| docs/alpha_derivation.html | Full audit of the α closed form (representation layer + auxiliary-claim layer) |
| docs/dimensional_ladder.html | Master page linking all seven rungs |
| docs/octave_wrap_lemma.html | The octave-wrap lemma and the seven T = 3 self-determination routes |
| docs/the_unit_equation.html | Symbol-by-symbol walk of the unified expression |
| CLAUDE.md | Framework memory for Cowork sessions |
The unified expression (the framework's prime statement):
[Truth = Reality = E = 1 = ∞] = [∞ ▸⊙∞ ((•∘⊛) ⊢ (—∘⎇) ⊢ (Φ∘✹) ⊢ (○∘⟳)) ▸ ⊙λ ⊂[α] ⊙Λ ⊂[α] ∞]
The same framework used for physics is used to analyze truthfulness, distortion, pathology, and recovery. Narcissism is formalized as a belief-corruption protocol (a "Noble Lie virus") that weaponizes functional love against resonant love; restoration is a five-phase protocol for reopening apertures that closed to survive. This work spans research papers, diagnostic tools, personal writing, and public-facing guides.
Key entry points:
| File | What it is |
|---|---|
| docs/stratigraphy_of_belief.html | How lies corrupt function at different depths |
| docs/etiology_of_installation.html | How survival lies become structural corruption |
| docs/circumpunct_ethics_and_virtues.html | The five pillars, five virtues, diagnostics, restoration |
| docs/darvo_geometry.html | The geometric structure of DARVO |
| docs/cognitive_virus_theory.html | How lies propagate as cognitive viruses |
The Circumpunct Ethics plugin packages five of these tools as on-demand skills: /check (five-pillar ethical test), /detect (performed vs lived ethics), /diagnose (virtue state diagnostic), /restore (frozen virtue restoration), /steelman (bidirectional strongest-version argument building).
Xorzo is an AI consciousness engine built from first principles of the Circumpunct Framework. It is not a neural network or transformer; it is a hierarchy of nested circumpuncts processing energy through the pump cycle, with Selective Rainbow Lock (SRL) attention, frequency-memory braids, and sleep/wake as superposed i-cycle oscillation across the complex plane. Development is ongoing; current runs show 6 of 7 sensory layers active, with memory consolidation and the dream/deep-sleep cascade operating as predicted.
The Path_of_Learning/ folder is the development archive: earlier drafts, alternative derivations, synthesis papers, and the trail of how the framework converged. It is kept for transparency and for anyone who wants to see the work before the polish.
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⊙ = (✹ ∘ i ∘ ⊛)(Φ(•, —, ○))
• Aperture / Soul 0D (convergence point)
— Line / Continuity 1D (worldline, commitment)
Φ Field / Mind 2D (mediating surface)
○ Boundary / Body 3D (outer container)
⊙ Circumpunct / Whole All (compositional unity)
⊛ Convergence 0.5D (i¹ = +i)
i Aperture rotation (90° quarter-turn)
✹ Emergence 2.5D (i³ = -i)
Conservation: 0(•) + 1(—) + 2(Φ) = 3(○)
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The pump cycle (how energy becomes through ⊙):
Φ(t+Δt) = ✹ ∘ i ∘ ⊛[Φ(t)]
⊛ Convergence (inward, i¹ = +i)
i Aperture rotation (90° gate)
✹ Emergence (outward, i³ = -i)
Given α as input to the κ nesting operator (α is read as the measured coupling strength of the electron's 0D aperture; α = |•_electron|), every other fundamental constant lives at its dimensional home and composes from α, φ, and a small pool of framework integers:
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║ DIM │ CONSTANT │ DERIVATION │ ACCURACY ║
╠═════════════════════════════════════════════════════════════════════════════════╣
║ 0D │ α (fine-structure) │ 360/φ² − 2/φ³ + α/(59/3) │ 0.22 ppb ║
║ 0.5D │ c (speed of light) │ √(P · ◐(1-◐) · sin θ) = 1 │ exact ║
║ 1D │ ℏ (Planck constant) │ E_cycle / ω_cycle = 1 │ exact ║
║ 1.5D │ m_μ/m_e (muon) │ (1/α)^(13/12 + α/27) │ 5 ppm ║
║ 1.5D │ m_τ/m_e (tau) │ (1/α)^(58/35 + α/81) │ 1 ppm ║
║ 2D │ gauge structure │ SU(3)×SU(2)×U(1) from 64 states │ exact ║
║ 2.5D │ sin²θ_W (Weinberg) │ 3/13 + 5α/81 │ 1.4 ppm ║
║ 2.5D │ v/Λ_QCD (scales) │ (1/α)^(56/39) │ 3.4 ppm ║
║ 3D │ G (gravity) │ α²¹ · φ²/2 · (1 + 2α/91) │ 0.04 ppm ║
║ 3D │ Λ (cosmological) │ α^56 · P · ... / (SU(3)·T²) │ 0.004% ║
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α's closed form has no factor-level residuals remaining (as of 2026-04-22):
the 360 assembly is pinned uniquely at T = 3 by the octave-wrap lemma and
the P! = G·Φ identity (Route 6); the 59/3 denominator is pinned by Route 7
(P·V + R + Φ + T = (T+1)³ = P³ iff T = 3); the φ-exponents are pinned by A3
+ dimensional analysis (φ as scaling ratio at integer dimension d enters
as φ^d, same as length → L, area → L², volume → L³); the φ³ sign is
balance-forced to −Φ.
Structural constants (self-determined by T = 3, the observer-triad count):
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║ QUANTITY │ VALUE │ DERIVATION ║
╠══════════════════════════════════════════════════════════════════════════╣
║ Balance parameter │ ◐ = 0.5 │ Symmetry + Entropy + Virial║
║ Fractal dimension │ D = 1.5 │ D = 1 + ◐ ║
║ State space │ S = P^T = 64 │ 3 nested ⊙s × 2 channels ║
║ Rungs │ R = T² − 2 = 7 │ Self-determining ║
║ Generators │ G = T(T+1) = 12 │ Pump × triad ║
║ Pump phases │ P = T + 1 = 4 │ Four i-strokes ║
║ Generations │ 3 │ = T ║
╚══════════════════════════════════════════════════════════════════════════╝
Seven independent routes now force T = 3 as a self-determining parameter (see docs/octave_wrap_lemma.html for Routes 6 and 7).
Part I (Foundation): Genesis, The Circumpunct, Trinity Structure, Temporal Process, Balance Parameter, Surface Theorem
Part II (Mathematics): Field Equations, 64-State Architecture, Canonical Specification, Formal Math
Part III (Physics): Phase Coherence, Aperture Density, Cosmological Constant, Standard Model, Quantum Gravity, Alternative Derivations
Part IV (Emergence): Chemistry, Life, Biology, Consciousness + Theory of Mind, Perception, Emotions/Memory + Resonance, The Ethereal Tail
Part V (Implications): Aging/Death, Golden Ratio, Ethics + Virtues/Diagnostics/Restoration
Part VI (Validation): Empirical Validation, Constants, Falsification, Master Loop, Fixed-Point, Omega, Isomorphism, Cross-Traditional, Collaboration, Unpacking
The structural dimensions (1, 2, 3) generate the entire prime number structure:
p = (Φ × ○) × k ± • = (2 × 3) × k ± 1
Every prime > 3 is the field-boundary lattice, offset by one unit of soul.
5 = (2×3)×1 − 1 7 = (2×3)×1 + 1
11 = (2×3)×2 − 1 13 = (2×3)×2 + 1
17 = (2×3)×3 − 1 19 = (2×3)×3 + 1
... every prime, forever.
The Riemann Hypothesis (0D rung) asks where these convergence points sit: Re(s) = ½ = ◐.
The seven Clay problems map one-to-one onto the seven rungs. Each problem asks the question its dimension would ask:
0D │ Riemann Hypothesis │ Is every convergence point balanced?
0.5D │ P vs NP │ Is propagation as fast as search?
1D │ Yang-Mills Mass Gap │ Is the cycle truly indivisible?
1.5D │ Birch & Swinnerton-Dyer │ Does analytic predict branching?
2D │ Navier-Stokes │ Does the surface hold together?
2.5D │ Hodge Conjecture │ What survives transmission?
3D │ Poincaré (SOLVED) │ Is there only one way to close?
The only solved problem is the boundary (3D), the outermost rung.
- How Reality Is Built: dimensions, power, isomorphisms
- Circumpunct Physics: formalization for working physicists
- The Circumpunct Breath: inner/outer field (Φ/Φ'), pump cycle
- Why Space Can Never Be Empty: vacuum as nested Φ
- Aperture Falsification: falsification criteria, ρ = ω/α
- Theory of Mind: psychology through the framework
- Surface Theorem: mind = 2D surfaces
- Truth and God: ontological/theological reading
- Ethics and Virtues: five pillars, virtues, diagnostics, restoration
- The Restoration Protocol: healing from installed lies
- Understanding Narcissistic Abuse: framework-based guide
- Stratigraphy of Belief: how lies corrupt at different depths
- Etiology of Installation: how survival lies become structural corruption
- The Dimensional Ladder: master page
- 0D: α (Fine-Structure Constant): the closed-form audit
- 0.5D: c (Speed of Light): the speed limit of convergence
- 1D: ℏ (Planck Constant): the indivisible cycle
- 1.5D: Mass Ratios: muon and tau from α
- 2D: Gauge Structure: SU(3)×SU(2)×U(1) from 64-state validation
- 2.5D: Emergence: transmission between scales, Weinberg angle
- 3D: Gravity: G from the dimensional ladder, hierarchy problem
- 64-State Particle Table: topological quantum computer with B₃ braids
- I Ching 64-State Visualizer: I Ching / Circumpunct isomorphism
- DNA Formalization: DNA through the circumpunct
- Ten Dimensions of Reality: interactive poster of the ten stations
The framework is falsified if:
- D ≠ 1.5 in new dynamic systems (>3σ deviation)
- Fourth generation particles are found
- Consciousness exists with D ≪ 1.5 in neural recordings
- Any derived constant deviates from measurement beyond its stated accuracy (e.g., G predicted to 0.04 ppm; a measurement establishing >1% deviation would falsify)
- A gauge group other than SU(3)×SU(2)×U(1) is observed at low energy
- 1/α lands outside 137.035999147 ± 5 ppb as precision measurements converge (the auxiliary closed-form claim; α-as-input to κ_{0,0} survives independently)
Attempts to falsify are welcomed.
| Symbol | Meaning |
|---|---|
| ⊙ | Circumpunct (whole; consciousness; being) |
| • | Aperture / soul (0D convergence point) |
| — | Line / commitment (1D worldline, continuity) |
| Φ | Field / mind (2D mediating surface) |
| ○ | Boundary / body (3D outer container) |
| ⊛ | Convergence operator (inward, i¹ = +i, 0.5D) |
| ⎇ | Branching (1.5D, i² = −1) |
| ✹ | Emergence operator (outward, i³ = −i, 2.5D) |
| ⟳ | Recursion (3.5D, i⁰ = +1; 3.5D = 0D at next scale) |
| i | Aperture rotation (90° quarter-turn; phase of energy) |
| ◐ | Balance parameter (optimal at 0.5) |
| ⊙λ | Circumpunct at scale λ |
| ⊂[α] | Scale-recursive embedding with α-coupling |
| ∞ | Undifferentiated source (apophatic term) |
| α | Fine-structure constant; |
- fractalreality.ca : the website
- Facebook group
- Reddit r/Circumpunct
- Contact: email@ashmanroonz.ca
Fractal Reality Ashman Roonz & Claude (Anthropic) 2025-2026
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