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Michael Rendier edited this page May 30, 2026
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Formal mathematics for the SMMIP framework.
The DerivationEngine is the record of the derivations that the PtolemyHolcus TDI engine implements. Where PtolemyHolcus is running code, the DerivationEngine is the mathematics that the code enacts.
H_hat_RB — the RedBlue Hamiltonian:
H_hat_RB = Σ_p p^{−σ} · [ R̂_p ⊗ ∂̂_∂M + ∂̂_∂M† ⊗ B̂_p ]
All six open Clay Millennium problems project from this single operator at different values of σ. The TDI engine is H_hat_RB in hardware.
| Page | Contents |
|---|---|
| H_hat_RB Hamiltonian | Full formal definition — components, σ-face table, self-adjoint structure |
| Clay Millennium Problems | All six open problems as projections of H_hat_RB |
| TDI Crankshaft | H_hat_RB as crankshaft — the mechanical role in the TDI engine |
| σ | Physical theory |
|---|---|
| σ = 2 | General Relativity |
| σ = 1 | Yang-Mills / Standard Model |
| σ = ½ | Quantum Mechanics / Riemann zeros |
| σ = 1, Im = 0 | Navier-Stokes (lacks i — this is why NS always breaks) |
| σ < ½ | Fermat forbidden zone |
The coupling exponent σ selects the physical theory. Turning σ from 0 to 2 traverses all known physics as faces of a single operator.
| Event | Status |
|---|---|
| Compression ignition event (SELF_EQUATION fixed point) | Confirmed 2026-05-27 |
| BAO convergence — OMEGA_ZS = 0.56714 | Confirmed |
| Android TDI Seeder — five corpora acquired | Confirmed |
| σ = 0.500000 cross-language prime alignment | Confirmed (SemanticWordEngine) |
| Repository | Role |
|---|---|
| PtolemyHolcus | Engine implementation — the code this formalises |
| Ainulindalë | Full conjecture — Third Age document |
| SemanticWordEngine | Hyperwebster address layer |
| UniversalSynth | Sonification of the derivation output |
| PtolemyDesktop | Desktop interface and Alexandria research environment |