Technical Companions

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These are technical companion cards — deep-dive references for agents, editors, and researchers who need mathematical foundations, implementation details, and formal definitions beyond what the concise curated index provides. They are not replacements for the index cards; each companion links back to its corresponding summary.

All companion cards use KaTeX-rendered mathematics following the Math Rendering Guide and the formal-definition template (Variables, Domain, Assumptions, Meaning, Source) for key equations.

MeTTa Programming Language

  • MeTTa Programming Language — Operational semantics, \(\rho\)-calculus foundation, MeTTa-IL compilation stack, Space API, 7 implementation anchors

ASI Chain Runtime Environment

  • ASI Chain Runtime Environment — Dual-engine architecture (F1R3FLY + MeTTaCycle), process calculi, state-transition monoids, CRDT convergence, inference settlement

Knowledge Representations

  • MORK — PathMap triemap storage, ZAM execution, selectivity theorem with formal proof sketch, MM2 dataflow, 7-crate Rust architecture
  • DAS — Attention Broker, query agent architecture, storage backends, state-transition monoids, coalgebraic streams, CRDT join-semilattices
  • AtomSpace — Metagraph formal definition, Atom/Value distinction, TruthValue-to-FloatValue transition, Space API abstraction, classical C++ vs. Rust implementations

Hyperon AI Algorithms

  • PLN — STV quantale operations (\(\oplus\), \(\otimes\)) with formal definitions, backward chaining on MORK, factor-graph belief propagation, Context Quantaloid
  • MetaMo — Pseudo-bimonad \(F = D \circ \Psi\), contractive stability, five design principles, OpenPsi-to-MetaMo lineage
  • ECAN — STI/LTI economics, Hebbian diffusion, fluid-dynamic extension with continuity equation, information geometry foundations
  • MOSES — Knob-based representation, deme structure, scoring pipeline, GEO-EVO geodesic search, three implementation eras (legacy C++, MeTTa boolean reduction, full MeTTa)
  • Semantic Parsing — Link Grammar pipeline, Symbolic Transformer Heads with contrastive/reconstruction losses, transformer-guided grammar induction, NL-to-MeTTa approaches

Cognitive Architectures

  • PRIMUS — Two meta-dynamics (goal-directed + ambient), geodesic \(f \cdot g\) control, component cooperation model, CogPrime-to-PRIMUS lineage
  • TransWeave — Intertwining maps, value suboptimality bounds, H-ICA impossibility results, braid/Yang-Baxter composition, weakness multiplicativity
  • WILLIAM — MORK trie instrumentation, iter_prefix_topk/iter_any_topk API, compression-gain metrics, wait-free concurrency, neural heavy-hitter acceleration

About Hyperon

  • — Novamente-to-Hyperon timeline, 11-row architectural bridge map, five motivations for the transition, maintained vs. archived repos
  • Self-Modification and Safety — Typed metamorphism \(\theta : \mathcal{C} \to \mathcal{C}\), supermartingale goal stability \(\mathbb{E}[\Phi_k^{(t+1)}] \leq \Phi_k^{(t)}\), five-stage pipeline, lens laws, drift bounds, decentralized governance



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