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The knowledge layer for collective intelligence

A portable data substrate for humans and their tools to think together.

The knowledge layer for collective intelligence

A portable data substrate for humans and their tools to think together.

The knowledge layer for collective intelligence

A portable data substrate for humans and their tools to think together.

The knowledge layer for collective intelligence

A portable data substrate for humans and their tools to think together.

An LLM's Perspective: What It's Actually Like to Receive These Instructions | Notion

graph TB subgraph

Knowledge Networks and the Politics of Protocols

Harmony without loss of Variety;  Variety without loss of Harmony.

Higher-Order Knowledge Representations for Agentic Scientific Reasoning

Scientific inquiry requires systems-level reasoning that integrates heterogeneous experimental data, cross-domain knowledge, and mechanistic evidence into coherent explanations. While Large Language Models (LLMs) offer inferential capabilities, they often depend on retrieval-augmented contexts that lack structural depth. Traditional Knowledge Graphs (KGs) attempt to bridge this gap, yet their pairwise constraints fail to capture the irreducible higher-order interactions that govern emergent physical behavior. To address this, we introduce a methodology for constructing hypergraph-based knowledge representations that faithfully encode multi-entity relationships. Applied to a corpus of ≈\approx 1,100 manuscripts on biocomposite scaffolds, our framework constructs a global hypergraph of 161,172 nodes and 320,201 hyperedges, revealing a scale-free topology (power law exponent ≈\approx 1.23) organized around highly connected conceptual hubs. This representation prevents the combinatorial explosion typical of pairwise expansions and explicitly preserves the co-occurrence context of scientific formulations. We further demonstrate that equipping agentic systems with hypergraph traversal tools, specifically using node-intersection constraints, enables them to bridge semantically distant concepts. By exploiting these higher-order pathways, the system successfully generates grounded mechanistic hypotheses for novel composite materials, such as linking cerium oxide to PCL scaffolds via chitosan intermediates. This work establishes a “teacherless” agentic reasoning system where hypergraph topology acts as a verifiable guardrail, accelerating scientific discovery by uncovering relationships obscured by traditional graph methods.

satellitecomponent/Neurite

Fractal Graph-of-Thought. Rhizomatic Mind-Mapping for Ai-Agents, Web-Links, Notes, and Code.

claude-obsidian

Self-organizing AI second brain for Obsidian + Claude Code. Drop any source and Claude reads, links, and files it into one connected knowledge graph of plain Markdown you own. AI note-taking, personal knowledge management (PKM), and an open-source Notion alternative. Based on Karpathy's LLM Wiki pattern.

Horismos: Self-representation and the Derived Constitutional Boundary in Enriched Cognitive Systems

We present a theory of self-representing cognitive systems grounded in $$([0,\infty ],+)$$([0,∞],+)-enriched category theory and the Yoneda lemma. The central object is a self-representing $$([0,\infty ],+)$$([0,∞],+)-enriched category $$\mathcal{C}$$C—a Lawvere metric space whose objects are complete epistemic architectures, whose hom-values record directed informational upgrade costs, and which is separated, closed under internal homs, and bilaterally Cauchy complete—together with a contractive cognitive endofunctor $$F:\mathcal{C}\rightarrow \mathcal{C}$$F:C→Cmodelling iterative self-improvement. We establish eight results in a single logical arc. The Horizon Theorem shows that the Yoneda embedding $$\varphi (A)=\mathcal{C}(-,A)$$φ(A)=C(-,A)is never essentially surjective: $$\mathcal{C}$$C sits strictly inside its own free Cauchy completion $$\mathcal{P}(\mathcal{C})$$P(C), with the non-representable presheaves forming a topologically dense family, proved via a reflexivity argument. The Lawvere–Banach Attractor Theorem shows that every contractive endofunctor on a bilaterally complete, separated $$([0,\infty ],+)$$([0,∞],+)-enriched category converges to a unique fixed point $$\mathbf {\Omega }$$Ωat a geometric rate. The Boundary Derivation Theorem shows that $$\mathbf {\Omega }$$Ωis the minimal F-invariant substructure of $$\mathcal{C}$$C, with all of $$\mathcal{C}$$Cas its basin of attraction—the constitutional boundary, derived rather than postulated. The Horizon Expansion Theorem shows that each strictly ascending self-modification produces a new, quantitatively distinct non-representable witness. Beyond these four central results, we prove that Kleene and Bourbaki–Witt conditions yield only non-expansiveness when metrised, that contractive endofunctors form a monoid, and that the Yoneda horizon admits an observable diagnostic stabilising in finite time. The architectural section derives structural corrigibility and the alignment-incompleteness duality among five implications. The organising duality is exact: the non-surjectivity of $$\varphi $$φ and the existence of $$\mathbf {\Omega }$$Ωare two faces of the same $$([0,\infty ],+)$$([0,∞],+)-enriched structure. $$\mathbf {\Omega }$$Ωinhabits the space between them—not as a postulate, but as a proof. We argue that the eight theorems constitute universal laws of contractive cognitive systems: a stable constitutional boundary is not an engineering design choice but a topological inevitability for any reliably self-improving agent operating within a self-representing enriched metric space. The postulate becomes a theorem. The boundary is not imposed. It emerges.

Four Ps for Building Massive Collective Knowledge Systems

Design principles for collective knowledge systems—permanence, provenance, permission, and placement—that enable robust networks for evidence-based decision making.

Four Ps for Building Massive Collective Knowledge Systems

Design principles for collective knowledge systems—permanence, provenance, permission, and placement—that enable robust networks for evidence-based decision making.

Farcaster

A decentralized social network