Case packet
Neutral case identifier: case-394ae9372bce28
The possible directed relationship from Artifact A to Artifact B is under review.
Artifact A
Short composable notes maximize combinatorial discovery
The library layer (kb/notes/) exists for co-loading. [Discovery] — seeing shared structure across particulars — requires co-presence: you can't find that three notes share unnamed structure if only one fits in context. Under [bounded context], the number of notes that fit determines the surface area for cross-cutting connections. Short, atomic notes maximize that surface area.
The gain is probabilistic, not mechanical — not every pair yields a discovery. What matters is breadth of independent perspectives. Notes from distant domains are more likely to reveal shared structure than additional notes within the same topic. The library should be optimized for this: many small, independently authored claims that can be loaded together in varied combinations.
[Resolution-switching] complements this. Claim titles and descriptions give broad surface-level pairing without loading full bodies; full notes are loaded selectively where depth is needed. Short notes make both modes cheaper.
Prior work
Atomic, composable units are a recurring design principle:
- Zettelkasten (Luhmann) — one idea per note, connections between notes. "One claim, one note" is Luhmann's atomicity principle. The most direct ancestor.
- Modular design (Parnas, 1972) — modules hide design decisions and expose interfaces. The Unix philosophy ("do one thing well, compose through pipes") is the same principle applied to programs.
- Faceted classification (Ranganathan, 1933) — describe items along independent combinable facets rather than a single hierarchy. Composable notes are facets.
What's specific to our context is the bounded-context motivation: atomicity here is driven by a hard token limit that makes co-loading capacity the scarce resource, not by filing convenience or code maintainability.
TODO: This survey is from the agent's training data, not systematic. Zettelkasten methodology in particular has extensive practitioner literature on atomicity trade-offs worth ingesting.
The design rule
One claim, one note. The title states the claim, the body supports it, the footer connects it. If a note has multiple ## sections making independent claims, that's a signal to decompose.
Longer synthesized views belong in workshops or are generated. Theory overviews, campaign understanding, multi-note summaries — these are consumers of library notes, not library notes themselves. They live in kb/work/ as workshop artifacts with lifecycles, or are generated (like indexes). When the purpose is served, the workshop artifact expires but the library notes remain available for recombination.
Evidence
The improvement log provides examples. Entries tagged ABSTRACTION and SYNTHESIS are discoveries made by co-loading notes and recognizing shared structure:
- "shared unnamed structure: execution-boundary compression" — found across five notes from different theoretical angles
- "two independent decompositions of agent memory from different traditions that together predict a two-axis taxonomy" — found by co-loading notes grounded in cognitive science alongside notes grounded in computer architecture
The structure emerged from the juxtaposition of independent perspectives. A single long note synthesizing all of memory theory would have contained the same information but wouldn't have surfaced the cross-cutting structure — it would have pre-committed to one narrative instead of leaving the connections available for discovery.
Tension with argument coherence
Some arguments genuinely need space — the reasoning from premises to conclusion loses force when atomized. [Evolving understanding needs holistic rewrite, not composition] — when a consumer needs the whole picture, reconciling into a single narrative beats composing fragments.
The resolution: coherent narratives are workshop artifacts, not library artifacts. The library stores premises and conclusions as separate composable notes. The workshop assembles them into narratives for a specific purpose. When the narrative expires, the atomic notes remain.
Relevant Notes:
Artifact B
Conjecture is seeing the particular as an instance of the general
Conjecture — the phase of the [discovery lifecycle] where a claim not entailed by the evidence gets posited — has a dual structure, whether in mathematics, science, or a knowledge base:
- You posit something general that didn't previously exist as a named concept
- You recognize that things you already knew are instances of it
How tightly the two halves bind depends on depth. At the shallow end, the instances are legible as a group before anyone posits the rule — repeated failures already look similar; the conjecture names what they share. At the deep end the two halves cannot be separated: the general doesn't exist until you see the particular as an instance of it, and the particular wasn't legible as an instance until you posited the general. They co-arise. A mathematician extracting a shared lemma from two theorems, Darwin seeing four unremarkable observations as axioms of a single theorem — the creative act is the same: recognizing that things from different contexts are instances of a structure that nobody had named yet.
Three depths of abstraction
Similarity-based connections vary not by kind (topical vs mechanistic) but by depth. This hierarchy draws on [Alexander's levels of concreteness] — from structural templates through generative processes to mutual reinforcement:
| Depth | Operation | Power |
|---|---|---|
| Shared feature | Name a surface similarity | Descriptive — organizes but doesn't explain |
| Shared structure | Extract a common pattern | Structural — reveals form but not cause |
| Generative model | Propose an abstract machine that produces both phenomena | Explanatory — explains why the similarity exists and predicts new instances |
Each level subsumes the previous. But they're increasingly powerful, increasingly hard to reach, and increasingly epistemically risky — a generative model can be compellingly wrong (phlogiston, caloric theory) precisely because it explains so much. This table is the conjecture's internal grading, and it aligns with the [discovery lifecycle]'s polation axis: shared structure extends along dimensions the cases already have (extrapolation), while a generative model posits a new dimension (hyperpolation). The dual structure above tightens along the same axis — full co-arising is the deep end's signature.
(This hierarchy covers similarity-based connections. Knowledge systems also need contrastive links (contradicts, supersedes), causal links (caused, enabled), and temporal links (preceded) — those aren't similarity at any depth.)
Recognition is the hard problem
The hard problem in knowledge systems is not linking (once you see a connection, articulating it is straightforward) but recognition — seeing that two things share structure at some level of abstraction.
Recognition cost scales with depth: - Surface similarity: cheap. Embeddings, keywords, filenames get you there. - Structural similarity: expensive. Requires understanding what a note is really about, then comparing across notes. - Generative similarity: very expensive. Requires inventing the dimension along which the comparison becomes visible.
The mathematical tradition offers a partial solution: develop vocabulary for naming structures. Once a structure has a name, recognizing new instances becomes cheap. The naming amortizes the cost of the conjecture that produced it. In a knowledge system, this means the highest-value act isn't linking two notes that share a mechanism — it's creating a new note that names the mechanism.
Worked examples
Mathematical lemma extraction is the clean case. A mathematician notices that two apparently unrelated proofs make the same move and extracts that common structure as a lemma. The lemma becomes a new graph node; both theorems can now link to it, and later theorems can recognize the same structure cheaply. Category theory pushes the same move further: it makes deep structural similarity nameable across domains that looked unrelated at the surface.
Darwin's theory of natural selection shows the generative-model depth. Variation, overproduction, heritability, and environmental pressure were separately familiar observations. Darwin's conjecture was seeing them as premises of one abstract machine: any population with those properties adapts over time. The empirical work identified the right axioms; the creative act was positing the general model that made multiple particulars instances of the same process — the decades of subsequent evidence-gathering were the lifecycle's test phase.
Fleming's penicillin discovery shows the conjecture handing off to the rest of the lifecycle. A mold-contaminated plate with a bacterial inhibition zone suggested a shared-feature conjecture: this substance kills bacteria. The broader antimicrobial general did not arrive in that act; it stabilized through the later phases — extraction, purification, clinical development — that turned the conjecture into an accepted discovery. The particular opens a direction; the general is earned by the phases that follow.
Luhmann-style linking clarifies the KB implication. The important distinction is not topical versus mechanistic linking. Topic and mechanism are both similarity judgments at different abstraction depths. Luhmann's stronger move was judgment-based linking instead of category filing: this note connects to that note for this articulated reason. That reason may be topical, structural, analogical, contrastive, or causal; the value comes from recognizing and naming the connection rather than filing both notes under a preexisting bucket.
Relevant Notes:
- [constraining] — suggestive parallel: constraining and conjecture depth are both gradients where each step trades generality for power, though on different axes
Operationalized into:
- [/connect skill] — the recognition claim is operationalized as the skill's articulation test for a specific connection reason
Under-review context phrase
discovery requires co-presence of multiple particulars