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graph TD
%% Class Definitions
classDef principle fill:#0f172a,stroke:#10b981,stroke-width:2px,color:#f8fafc,rx:8px,ry:8px;
classDef rejected fill:#0f172a,stroke:#ef4444,stroke-width:2px,stroke-dasharray:5 5,color:#cbd5e1,rx:8px,ry:8px;
classDef axiom fill:#0f172a,stroke:#3b82f6,stroke-width:2px,color:#f8fafc,rx:8px,ry:8px;
classDef mechanics fill:#0f172a,stroke:#f59e0b,stroke-width:2px,color:#f8fafc,rx:8px,ry:8px;
classDef complete fill:#164e63,stroke:#22d3ee,stroke-width:2px,color:#f8fafc,rx:8px,ry:8px;
%% LEVEL 1
subgraph L1 [STAGE 1: Methodology Calibration]
direction LR
A["
✔ Principle 1: Epistemic HygieneNothing is assumed. Everything is derived.
No absolute background permitted.
"]:::principle
B["No absolute background permitted.
✖ Standard Model ViolationAssumes empty void as container and
imports 'Dark' entities to fix geometric leaks.
"]:::rejected
A -->|Contrast| B
end
%% LEVEL 1.5 - Distance Justification
subgraph L1_5 [STAGE 2: The Concept of Distance]
DIST["imports 'Dark' entities to fix geometric leaks.
Distance as Relational Tension
"]:::axiom
end
A --> DIST
%% LEVEL 2
subgraph L2 [STAGE 3: Ontological Foundation]
C["Philosophical Justification:
If no absolute background container exists, spatial separation cannot
be 'empty space' between objects. It is an ontological paradox
to assign physical dimensions to nothingness.
Physical Justification:
Distance must be physically derived as the energetic tension required
to transition between different relational states within a closed topology.
If no absolute background container exists, spatial separation cannot
be 'empty space' between objects. It is an ontological paradox
to assign physical dimensions to nothingness.
Physical Justification:
Distance must be physically derived as the energetic tension required
to transition between different relational states within a closed topology.
✔ Principle 2: Spacetime ≡ EnergyTotal rejection of the empty void.
The relational carrier itself is the energetic structure.
"]:::principle
E["The relational carrier itself is the energetic structure.
The Causal Horizon (R_H)We make no metaphysical claims about the 'entire Universe'.
The observer's causal horizon is mathematically and strictly closed.
"]:::axiom
DIST --> C
C --> E
end
%% LEVEL 3
subgraph L3 [STAGE 4: Topological Mechanics]
F["The observer's causal horizon is mathematically and strictly closed.
Global Phase-ClosureIn a closed horizon, dissonant modes self-cancel.
The surviving standing wave forms the Fundamental Tone.
"]:::mechanics
G["The surviving standing wave forms the Fundamental Tone.
Topological Coupling (Ω_pot)Galaxies are continuous S² structural potentials.
Their coupling weight to the horizon is Ω_pot = 2/3.
"]:::mechanics
H["Their coupling weight to the horizon is Ω_pot = 2/3.
Horizon Circumference (C_H)The boundary length of the closed causal system:
C_H = 2π R_H
"]:::mechanics
E --> F
F --> G
E --> H
end
%% LEVEL 4
subgraph L4 [STAGE 5: Horizon Interference]
I["C_H = 2π R_H
Structural Resonance ScaleDerived entirely from geometry, zero fitting:
Ω_pot × (1 / C_H) = (2/3) / (2π R_H) = 1 / 3π R_H
"]:::mechanics
J["Ω_pot × (1 / C_H) = (2/3) / (2π R_H) = 1 / 3π R_H
Geometric InterferenceLocal gravity cannot fall asymptotically into an empty void.
It must physically interfere with the global horizon tension.
"]:::mechanics
G --> I
H --> I
DIST -->|Defines tension limit for| J
I --> J
end
%% LEVEL 5
subgraph L5 [STAGE 6: Algebraic Closure and Observables]
K["It must physically interfere with the global horizon tension.
The Geometric CancellationInterference cross-term: √(β_N² × a_κ × r).
Since local shift β_N² = R_s / 2r, the radial dependence (r) cancels perfectly.
"]:::axiom
L["Since local shift β_N² = R_s / 2r, the radial dependence (r) cancels perfectly.
Final Dimensionless Stateβ_obs = √ [ β_N² + √( R_s / 6π R_H ) ]
Galactic dynamics settle on a flat, universal topological floor.
"]:::complete
J --> K
K --> L
end
Galactic dynamics settle on a flat, universal topological floor.