Papers
The consolidated papers that present the Focospectralics framework in submission-ready form. Each entry below lists what the paper contains, the key values it establishes, and a link to the proofs that support it.
For a portable summary of the framework's invariants, values, and theorems, see the quick reference. A downloadable plain-text version is available as quick-reference.md.
01 · Master Monograph · Thermodynamic Cost of Observation
The primary consolidated paper. Presents the framework's full narrative arc: the embedded observer, the 1/3 : 2/3 conic partition, the thermodynamic bridge, dynamic horizon mechanics, and the cosmological applications. Establishes the four conservation theorems and the machine-precision closure identity as the framework's algebraic backbone.
Key values established
| Quantity | Value | Status tag | Supporting proof |
|---|---|---|---|
| Tetrahedral apex angle θ | 70.5288° | Derived | Tetrahedral solid-angle partition |
| Viewer cone fraction S₊ | 1/3 · 33.333% | Derived | Tetrahedral solid-angle partition |
| Inverse cone fraction S₋ | 2/3 · 66.667% | Derived | Tetrahedral solid-angle partition |
| Boundary partition ratio S₋/S₊ | 2.000000 | Derived | Diffeomorphism invariance |
| Projection factor P_θ | 1.08308 | Derived | Theorem II |
| Effective aperture Ω_eff | 31.73% | Fitted | Theorem III |
| Closure ratio R | 1.0000 | Derived | Closure identity |
Download
Full paper: master-monograph.pdf ↗ — link pending
02 · Step-by-Step Mathematical Derivations
The companion derivations paper. Presents the full algebraic steps behind each of the framework's conservation theorems and the thermodynamic bridge. Structured so that each derivation can be checked independently, with the classical antecedents (Fredholm, Lyapunov–Schmidt, Landauer, Bekenstein–Hawking) cited at each step.
Key values established
| Quantity | Value | Status tag | Supporting proof |
|---|---|---|---|
| Zero-mode fold trajectory | Q±(t) − Q* | Derived | Lyapunov–Schmidt reduction |
| Emission power law P(t) | κ(dQ/dt)² | Derived | Zero-mode power law |
| Landauer bit floor E_bit | 7.155 × 10⁻³⁹ J | Derived | Theorem III |
| Planck area ceiling A_min | 2.159 × 10⁻⁷⁰ m²/bit | Derived | Theorem III |
Download
Full paper: step-by-step-derivations.pdf ↗ — link pending
Quick reference
A one-page summary of the framework's invariants, canonical values, four conservation theorems, status tag taxonomy, and 4-step protocol:
- quick-reference.html — HTML version
- quick-reference.md — plain text, downloadable
Cross-references. The master register is at register.html. Canonical values and resolved drifts are at canonical.html. The full proof set is indexed at proofs/index.html. The applied demonstrations are at experiments/index.html.