Logos Map
Derivation of the Energetic Closure Theorem
graph TD
classDef principle fill:#0f172a,stroke:#334155,stroke-width:1px,color:#f8fafc,rx:4px,ry:4px;
classDef lemma fill:#1c1917,stroke:#44403c,stroke-width:1px,color:#f5f5f5,rx:4px,ry:4px;
classDef theorem fill:#171717,stroke:#52525b,stroke-width:1px,color:#fafafa,rx:4px,ry:4px;
classDef final fill:#2e1010,stroke:#991b1b,stroke-width:2px,color:#fee2e2,font-weight:bold,rx:6px,ry:6px;
subgraph Tier1 [STAGE I: THE 4 FOUNDATIONAL METHODOLOGICAL PRINCIPLES]
E1[Principle: Epistemic Hygiene]:::principle
E2[Principle: Relational Origin]:::principle
E3[Principle: Ontological Minimalism]:::principle
E4[Principle: Mathematical Transparency]:::principle
end
style Tier1 fill:transparent,stroke:#334155,stroke-width:1px,stroke-dasharray: 5 5,color:#9ca3af
L1[Lemma: False Separation]:::lemma
P1[Unifying Principle: SPACETIME ≡ ENERGY]:::principle
T1[Theorem: Relational Closure]:::theorem
T2[Theorem: Relational Invariance]:::theorem
T3[Theorem: Relational Isotropy]:::theorem
T4[Theorem: Minimal Relational Carriers S¹ & S²]:::theorem
L2[Lemma: Duality of Relation]:::lemma
T5[Theorem: Conservation of Relation]:::theorem
L3[Lemma: DOF-Indifference]:::lemma
F1[Closure Theorem: κ² = 2β²]:::final
%% Clean downstream routing
E1 --> L1
E2 --> L1
L1 --> P1
E2 --> P1
P1 --> T1
P1 --> T2
P1 --> T3
T1 --> T4
T3 --> T4
E3 --> T4
E4 --> T4
P1 --> L2
E2 --> L2
T4 --> T5
L2 --> T5
T3 --> L3
E3 --> L3
T4 --> F1
T5 --> F1
L3 --> F1
%% Clickable targets
click E1 "https://willrg.com/documents/WILL_RG_I.pdf#pr:epistemic" "Execute proof definition" _blank
click E2 "https://willrg.com/documents/WILL_RG_I.pdf#pr:relational" "Execute proof definition" _blank
click E3 "https://willrg.com/documents/WILL_RG_I.pdf#pr:minimalism" "Execute proof definition" _blank
click E4 "https://willrg.com/documents/WILL_RG_I.pdf#pr:Mathematical" "Execute proof definition" _blank
click L1 "https://willrg.com/documents/WILL_RG_I.pdf#lem:false-separation" "Execute proof definition" _blank
click P1 "https://willrg.com/documents/WILL_RG_I.pdf#pr:unifying" "Execute proof definition" _blank
click T1 "https://willrg.com/documents/WILL_RG_I.pdf#thm:relational_closure" "Execute proof definition" _blank
click T2 "https://willrg.com/documents/WILL_RG_I.pdf#thm:relational_invariance" "Execute proof definition" _blank
click T3 "https://willrg.com/documents/WILL_RG_I.pdf#thm:isotropy" "Execute proof definition" _blank
click T4 "https://willrg.com/documents/WILL_RG_I.pdf#thm:carriers" "Execute proof definition" _blank
click L2 "https://willrg.com/documents/WILL_RG_I.pdf#lem:duality" "Execute proof definition" _blank
click T5 "https://willrg.com/documents/WILL_RG_I.pdf#thm:conservation" "Execute proof definition" _blank
click L3 "https://willrg.com/documents/WILL_RG_I.pdf#lem:dof-indifference" "Execute proof definition" _blank
click F1 "https://willrg.com/documents/WILL_RG_I.pdf#thm:Closure" "Execute proof definition" _blank