MORK Research Family

MORK Research Family

What this card is. A navigation map over the cluster of internal Hyperon working-papers (July–October 2025) that explore building Hyperon's algorithmic stack on top of MORK (the MeTTa-Optimized Reduction Kernel and its PathMap trie substrate). It maps each paper/version to its contribution, status, and source, and links to the functional MORK cards — which it does not replace.

Provenance & how to read these. These are internal research working-papers, most authored by Ben Goertzel (several explicitly “GPT-5-Pro productions, lightly edited” or co-credited to Claude Opus 4.1; one is an Arthur Franz meetup presentation), shared on the Hyperon Mattermost channel. They are exploratory design proposals and theory sketches — not peer-reviewed publications, and (with the partial exceptions noted below) not implemented or benchmarked. Read them as a research agenda for where MORK could go, cross-referenced against the actual MORK codebase (see Implementation reality check).

Status legend: [Formal] theorem/analysis with proof sketch · [Proposal] design proposal / research direction · [Sketch] speculative design sketch · [Note] working note / clarification / presentation.

Index

Paper (RawData source)	Date	Sub-family	Contribution	Status
MORK theory	Oct 6 2025	Core theory	ZAM/MORK selectivity theorem: when \(\sum_i \gamma(p_i) > 1\), multi-leg joins feed \(O(1)\) candidates to the unifier	[Formal]
MORK slots	Oct 17 2025	Core indexing	Slot-centric views (≤k) instead of k! permutations; probabilistic break-even rule	[Proposal]
MORK Miner	Jul 21 2025	Core mining	PathMap-native pattern mining (prefix-locality seeds + in-place support counts)	[Proposal]
Chaining Mork Cache	Aug 11 2025	Core caching	Two-tier cache (per-core hash + AtomSpace-backed) with per-predicate epoch invalidation	[Proposal]
PLN Chaining On MORK	Aug 11 2025	PLN execution	Backward-chaining engine: unification indices, weakness scheduling, memoization, KaHyPar placement	[Proposal]
PLN FactorGraph MORK (v3.2)	Jul 18–20 2025	PLN execution	PLN as quantale-annotated factor graphs / belief propagation on MORK (5-version chain; v3.2 latest)	[Proposal]
Moses Mork	Jul 21 2025	Algorithm substrate	MOSES via gCoDD + ENF/CENF canonicalization + factor-graph EDA	[Proposal]
MORK Tensor Networks	Oct 18 2025	Algorithm substrate	Path-algebra → tensor logic on GPUs via ShardZipper; Hierarchical Resolution Transformer example	[Sketch]
WILLIAM on MORK	Sep 4 2025	WILLIAM compression	Formal paper: Algorithms A/B + efficiency theorem under hierarchical prior + weakness-quantale + generalization bounds	[Formal]
AdaptiMORK (v8)	Sep 9 2025	WILLIAM / compression	Streaming compression: parameter elevation + living template library + staged thresholds (v8 supersedes v2)	[Proposal]
QuantiMork	Jul 4 2025	Neural / quantitative	QuantiMORK/NeuroMORK: tensors & neural nets as multiresolution wavelet DAGs in PathMap	[Sketch]
Ebt Pc Mork	Jul 21 2025	Neural / quantitative	Energy-Based Training ≡ Predictive Coding; Wavelet-MORK external memory for transformer states	[Sketch]

The two related WILLIAM-on-MORK documents — the clarification note and the Franz presentation — are covered in §D below.

A. Core theory & indexing

• MORK theory — Articulating Some Conditions Where ZAM/MORK Yield Benefit: A Selectivity Theorem and a Hierarchical Corollary (Goertzel, GPT-5-Pro). The family's formal anchor. Defines the selectivity exponent \(\gamma(p) = -\log_N(|P(p)|/N)\) and proves, under \(\varepsilon\)-independence, \(\mathbb{E}|P_\cap| = \Theta(N^{1 - \sum_i \gamma(p_i)})\); when \(\sum_i \gamma(p_i) > 1\) the path-indexed intersection yields \(O(1)\) candidates to the unifier, versus WAM-style \(\Omega(N)\) per leg. A hierarchical generative-model corollary argues real Atomspaces (proofs, programs, NL parses, knowledge graphs) satisfy the condition. (Mapped per-paper at +Mork theory — this family card links there rather than re-deriving it.)
• MORK slots — avoids the k! permutation blowup in pattern mining by maintaining ≤k slot-centric prefix views plus a few adaptively-promoted “hot” pair views, governed by a break-even rule \(p_{s+1}(M-L) > \alpha\). Worked example: ≈29.4× expected query speedup for roughly 2× the index entries.
• MORK Miner — pattern mining run entirely inside the PathMap index: prefix-locality seed extraction, growth by prefix scans, \(O(1)\) support counts at prefix nodes. Two applications sketched (wavelet hierarchies, factor graphs). Speedups claimed, not measured.
• Chaining Mork Cache — two-tier caching for PLN backward chaining: an ephemeral per-core hash tier + a shared AtomSpace-backed tier, with per-predicate epoch counters for invalidation. Companion to PLN Chaining On MORK.

B. PLN execution on MORK

• PLN Chaining On MORK — low-level backward-chaining engine design: HeadIndex/FactIndex/UnifyIndex, weakness-aware scheduling (prefer general rules), KaHyPar hypergraph partitioning for locality, and magic-sets rewriting. Projects a 10–100× speedup from memoization, magic-sets, and head caches combined.
• PLN FactorGraph MORK — 5-version chain (all Goertzel, Jul 18–20 2025). Recasts PLN as quantale-annotated factor graphs with belief propagation (\(O(|E|)\) vs chaining's per-leg cost). The chain’s evolution: base — Simple-Truth-Value quantale, message-passing, toy deduction/quantifier examples; v1 — adds dependency-handling (detect shared-variable Jaccard overlap → cluster or insert an explicit DependencyFactor); v2 — adds a formal log-normal error-propagation model (exponential damping when \(\log m > \tfrac{1}{2}\sigma^2\)) + ontology-based semantic normalization as the primary mitigation; v3.1 — refactors onto a product quantale \(Q_{\text{comb}} = Q_{\text{logic}} \times Q_{\text{PLN}}\) unifying formulas and truth-values; v3.2 (latest) streamlines v3.1 and is substantively equivalent. Reading guidance: v3.2 is the current statement of the design; v1/v2's error-management material is folded in.

C. MORK as an algorithm substrate

• Moses Mork — MORK-MOSES: Implementation Ideas. MOSES inside MORK via gCoDD (grounded Combinatory Decision DAG preserving Elegant Normal Form, \(O(1)\) structural equality), ENF/CENF canonicalization, quantale-based crossover/mutation, and a factor-graph EDA. The complexity analysis is self-described as “hand-wavy.” (Cross-links to view (Mathematical Foundations and MORK) not supported for Hyperon AI Algorithms+MOSES (Meta-Optimizing Semantic Evolutionary Search)+MOSES Deep Dive+Mathematical Foundations and MORK.)
• MORK Tensor Networks — From Path Algebra in MORK to Tensor Logic on GPUs (“Rough Notes”). Maps path concatenation/union/projection to tensor ops (joins→matmul, quantifiers→reductions, Viterbi→max-plus semiring); ShardZipper partitions the trie to CSR arrays for GPU kernels; a Hierarchical Resolution Transformer example claims \(\tilde{O}(n \log n)\).

D. WILLIAM incremental compression on MORK

The WILLIAM thread integrates Arthur Franz's incremental-compression learner with MORK. Three related documents plus the AdaptiMORK spec pair:

• WILLIAM on MORK (Goertzel, Sep 4 2025) — the formal paper: WILLIAM-on-MORK: Efficient Incremental Compression with Hierarchical Priors. Algorithm A (basic, weighted-triemap feature proposal) + Algorithm B (integration-friendly MeTTa/Hyperon service); a theorem that under a hierarchical (laminar-motif) prior WILLIAM-on-MORK achieves near-optimal compression with bounded overhead; a quantale weakness theory extension (Bennett's “weakness”); and generalization bounds for link-prediction accuracy under hierarchical priors.
• WILLIAM on MORK clarifications (Sep 7 2025) — answers “how does storing patterns in MORK actually accelerate template search?”; lays out a 7-level search spectrum (greedy → small beam → adaptive → MORK-guided mining → evolutionary → bounded synthesis → universal dovetailing) and argues a tiny beam (k=2–3) suffices on hierarchical data because MDL/weakness scoring prunes aggressively. It also states a compact theorem-style guarantee for the hierarchical case.
• William On Mork (Arthur Franz, meetup slides, Oct 18 2025) — overview of incremental-compression theory and WILLIAM demos. Caveat: the compression figures shown (outlier detection ≈80%, regression 19.6%, classification 21%, decision-tree 6.5%, tic-tac-toe policy, geometric-figure recognition) are results of standalone WILLIAM, illustrating the method — they are not WILLIAM-on-MORK integration benchmarks.
• AdaptiMORK (v2 → v8, Goertzel, Sep 9 2025; v8 supersedes v2) — a concrete streaming-compression codec realizing WILLIAM-style incremental compression on MORK: Sequitur-like rule induction over a bounded editable suffix window + adaptive (Huffman/arithmetic) coding. v8 adds parameter elevation (grow patterns from simple seeds, turning inverse discovery into monotonic growth), a living template library with cross-domain reuse, and meta-learning. Projected (not measured) ≈10–100× search speedup and 15–30% compression gain on structured data.

E. Neural / quantitative MORK

• QuantiMork — QuantiMORK & NeuroMORK via Multiresolution DAGs (“(Im)modest Proposal”). Represent tensors/neural nets as discrete-wavelet multiresolution DAGs keyed (ℓ, band, i, j) in PathMap; symbolic rules dispatch GPU kernels only where needed; wavelet CNNs/transformers with linear intra-scale + sparse cross-scale attention; predictive-coding (local, backprop-free) learning. (The downstream synthesis of this proposal already lives at PRIMUS+QuantiMork — this card links there.)
• Ebt Pc Mork — Predictive Coding Transformers with Wavelet-MORK Memory (Speculative Design Sketch). Casts Energy-Based Training's MCMC sampler as predictive-coding inference and weight updates as local Hebbian learning; stores transformer hidden states as wavelet-coefficient trees in MORK for coarse-to-fine retrieval.

Implementation reality check

These papers describe an aspirational MORK-centric algorithm stack. Against the actual codebase (AtomSpace Backend Integration cluster pilot, 2026-04-29):

• MORK is an 8-member Rust workspace; PeTTa/MORK has been benchmarked to ~400M atoms in RAM (the “500M+” figure was an OOM ceiling, not demonstrated capacity).
• PathMap — on which nearly every paper here depends — is a foundational sibling repo (Adam Vandervorst-architected; upstream namespace Adam-Vandervorst/PathMap, with contribution/fork/documentation context from Luke Peterson and zariuq), not a bundled MORK crate. Its pathmap-book database section is still a stub, and its Lean/ZAM formalization theorems are not wired into the Rust kernel. Treat formal results (e.g. the selectivity theorem) as analyses of the design, not verified properties of shipped code.
• DAS-side MorkDB hard-fails on link/S-expression delete, and MORK's server branch has drifted ~49 commits ahead of the DAS pin — i.e. the durable-mutable-store assumptions some of these papers lean on are not yet met.
• The main formal-theorem anchors are MORK theory and Mork William (the WILLIAM clarifications note also states a compact theorem). No paper in the family claims a completed implementation or integration benchmark; the empirical numbers that appear are either projections or standalone-WILLIAM results.

Related wiki cards (kept separate)

• MORK (MeTTa Optimized Reduction Kernel) and MORK Deep Dive — the functional kernel cards.
• +Mork theory — per-paper reader's map for the selectivity theorem.
• PRIMUS+QuantiMork — QuantiMORK research-direction synthesis.
• view (Mathematical Foundations and MORK) not supported for Hyperon AI Algorithms+MOSES (Meta-Optimizing Semantic Evolutionary Search)+MOSES Deep Dive+Mathematical Foundations and MORK and view (Execution on MORK) not supported for Hyperon AI Algorithms+PLN (Probabilistic Logic Networks)+PLN Deep Dive+Execution on MORK — algorithm-side MORK execution cards.

Source archive: the working-papers are carded under RawData+Publications+* and stored at publication_texts/mattermost_papers/. Synthesized for the Publications backlog (tracker Sources Pending Analysis, P2). AI-generated; pending human review.