Research shelf / AI & machine learning / UCN AIs
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Four fictional AI architectures, written with real theorem statements
These are in-universe technical writeups for AI families inhabiting a fictional setting, and the folder says so at the top. What makes them worth indexing is the register: metric-space definitions, convergence theorems with proof sketches, state-evolution equations and conservation laws — the shape of a foundations paper, applied to systems that do not exist.
Theory or design only. No in-house measurement.
Any Purpose Networks, General Purpose Networks, Signal AI and two learning primitives — worldbuilding artefacts written in the register of a mathematical-foundations paper.
General Purpose Networks are framed over a complete metric space Ω of simulation states, with a model-generation function mapping states to subsets of a hypothesis space and a continuous simulation-evolution operator. Two theorems are stated with proof sketches: simulation convergence via Cauchy sequences in a complete space, and model-generation completeness — that for any concept there exists a simulation path producing a model containing it.
Any Purpose Networks get their own mathematical model and constraint set. Signal AI is presented as a Universal Resonance Learning System with theorems for universal encoding, resonance fields and information preservation. Two further documents cover foundational learning primitives — a linear-congruent learning system and a universal dynamic pattern-verification system.
Each system pairs its mathematical writeup with a design-discussion transcript, so the reasoning that produced the formalism is preserved alongside it. The folder is also unusually careful about its own accuracy: it corrects an earlier README that referenced files and subfolders which are not in it, and points readers to the companion political-system folder for the political-economy material.
Every number, and what stands behind it
A claim is only worth the evidence attached to it. Each row below carries its basis: measured on the author’s own hardware, derived from the construction, measured on synthetic data, projected from literature, or simply cited.
| Claim | Figure | Basis | Context |
|---|---|---|---|
| AI families documented | 3 (APN, GPN, Signal AI) | Derived | Plus two foundational learning primitives |
| GPN state space | complete metric space (Ω, d) | Derived | The completeness assumption that makes the convergence theorem work |
| GPN Theorem 1 | simulation convergence | Derived | Cauchy-sequence argument in a complete space |
| GPN Theorem 2 | model-generation completeness | Derived | Every concept is reachable by some simulation path |
| Signal AI theorems | universal encoding, resonance fields, information preservation | Derived | Stated with proof sketches |
| Documents per system | summary + math model + transcript | Derived | Consistent structure across the folder |
| Setting | fictional (UCN universe) | Derived | Stated by the folder, not inferred |
Measured — author-run experiment on the stated setup. Synthetic — measured, but on synthetic rather than real data. Derived — follows from the stated construction or proof. Projected — paper-stated projection, not an author-run benchmark. Cited — taken from external literature.
How it works
- Metric-space formalisation. Simulation states as points in a complete metric space, so completeness gives convergence.
- State-evolution equations. dS/dt = F(S, M(S), t) with an explicit model-update operator alongside it.
- Conservation and information-flow constraints. Energy functional conserved, information content non-decreasing — constraints stated as properties of the system.
- Transcript preservation. The design conversation kept alongside the formalism, so the reasoning is auditable.
What it does not do
Taken from the folder’s own README. Nothing here has been softened.
- Fiction. These are in-universe writeups for a worldbuilding setting and the folder states that in its first line.
- The theorems are informal statements with proof sketches, not complete proofs. Steps like "show the sequence is Cauchy using the simulation stability property" carry the weight without discharging it.
- The completeness of Ω and the continuity of the evolution operator are assumed, and they are precisely the assumptions that make the results hold.
- No implementation, no experiment, no measurement anywhere in the folder.
- Mathematical register is not mathematical content. These read like foundations papers; they are not.
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