Case packet

Neutral case identifier: case-26b9c135a0d7e2

The possible directed relationship from Artifact A to Artifact B is under review.

Artifact A

Linking theory

We have link practices — relationship types ([ADR 009]), title-as-claim, context phrases, position conventions — but no theory explaining why these practices work and when they break down. This note collects the grounding claims and builds toward one.

Established claims about linking

Seven notes across the KB argue what makes links work. They cluster into three groups.

[Agents navigate by deciding what to read next] models every link encounter as a decision: follow or skip? The decision is always probabilistic — the agent can't know what the target contains until loading it. What makes it tractable is context: information surrounding the pointer that hints at what the target contains. The more context a pointer carries, the cheaper the navigation decision.

When the title carries the argument, the pointer itself becomes the hint — every link text, every search result, every index entry does navigation work without additional context. Title-as-claim is the shortcut that works across all pointer types.

[Instruction specificity should match loading frequency] adds the progressive-disclosure constraint: the title layer is the cheapest disclosure layer. If titles are claims, agents decide what to load from the title alone. If titles are topics, agents must load notes to discover what they argue — the disclosure layer fails.

Links as argument structure

[Title as claim enables traversal as reasoning] — when titles are claims, following links reads as a reasoning chain. "since [structure enables navigation]" composes grammatically; "since [navigation notes]" doesn't. The note graph becomes scannable arguments. Link semantics ("since", "because", "but") encode relationship types — Toulmin warrants connecting grounds to claims.

[Claim notes should use Toulmin-derived sections for structured argument] — title-as-claim is the Toulmin claim; "since"/"because" link semantics encode warrants. Not all claim-titled notes need the full Toulmin scaffold, but the scaffold reveals what claim titles are doing implicitly.

[Link strength is encoded in position and prose] — an inline "since [X]" that uses a note as a premise carries more weight than a footer entry. Position and prose encode commitment level, creating a weighted graph orthogonal to relationship type.

Links as maintenance surface

[Title as claim exposes commitments, enabling Popperian maintenance] — claim titles expose what each note commits to, so reviewing the KB becomes scanning hypotheses: "do I still believe this?" Maintenance cost scales with doubtful claims, not total notes. Topic titles hide commitments behind labels that require opening every file.

[Title as claim makes overlap between notes visible] — two claim titles arguing the same thing are obviously redundant at the index level. Two topical titles covering the same territory are invisible until you read both. Overlap detection becomes a scanning task rather than a reading task, and the benefit compounds with KB size.

Candidate theory: links as decision-cost reducers

The claims above share a common mechanism: links are decision points, and link quality is the reduction of navigation uncertainty per unit of context consumed.

Every interaction with the knowledge graph involves a decision under bounded context: follow this link? Load this note? Open this search result? Each decision has a cost — context consumed to make it — and a value — probability of reaching task-relevant information. Link quality is the efficiency of that exchange: how much uncertainty about the target does the link context eliminate, relative to the context budget it consumes?

Each practice instantiates this principle:

Typed relationships (extends, contradicts, grounds) beat "related" because they carry more decision-relevant information per word. "Related" eliminates zero uncertainty about what following the link will do for the reader's task.
Claim titles beat topical titles because they compress the note's commitment into the pointer. A claim title is a one-line summary of what you'll get; a topical title says only what territory you'll enter.
Position encodes strength because inline links pay for their context with the surrounding argument — the prose advances the argument while hinting at the target, making the marginal context cost near zero. Footer links must pay for their context out-of-band.
"Related" is not a relationship — it carries zero bits of decision-relevant information, the linking equivalent of a null description.

Content registers constrain link direction

The decision-cost model needs one more axis: the content layer of the source and target. [A knowledge base holds theories, descriptions, and prescriptions with asymmetric linking] argues that theory, description, and prescription have different quality goals and maintenance directions. Those differences constrain which links are load-bearing.

A theory can cite a description as evidence while remaining generally stated; a description can cite theory as rationale for why the system is shaped that way; a prescription can cite both theory and system description because procedures must be justified and executable against the current system. Reversing those relationships changes the maintenance contract. If a theory depends on a specific description for its formulation, the link reveals that the artifact has not yet been abstracted into theory. If an instruction omits the descriptive system target it acts on, executability suffers.

So relationship vocabulary is not enough by itself. A grounds or rests-on edge has different consequences depending on whether it stays within theory or crosses into description, prescription, or system-definition content. Link review should check both the local relationship phrase and the collection-crossing contract.

What the theory predicts

If link quality is decision-cost reduction, the theory predicts:

Vocabulary size is a trade-off. Too few relationship types and you can't discriminate; too many and authoring cost exceeds the discrimination benefit. Our five types — extends, grounds, contradicts, enables, exemplifies — should be evaluated against common agent tasks.
Different tasks need different link types. An agent verifying a claim should prioritize "grounds" and "contradicts" links. An agent looking for examples should prioritize "exemplifies". The vocabulary is useful to the extent that agent tasks decompose along the same axes.
Untyped links work in small KBs but fail at scale. With few notes, every link target is roughly equally likely to be useful — decision cost is low regardless. As the note count grows, untyped links provide no discrimination.
Link density has diminishing returns. Each additional link adds decision points. If the marginal link carries less decision-relevant information than the context cost of processing it, it hurts navigation rather than helping it.
Maintenance cost scales with exposed commitments. Popperian maintenance works because claim titles externalize decision-relevant information. Any practice exposing commitments at low context cost — claim titles, typed relationships, context phrases — will reduce maintenance effort.

Open questions

How do relationship type and position interact? A "contradicts" link in a footer is arguably more important than an "exemplifies" link inline. Do type and position compose additively, or does one dominate?
Is the vocabulary the right one? Our five types were borrowed from arscontexta and adapted. Are there common agent navigation patterns that need a type we don't have? Are there types we never use in practice?
Can we measure decision cost? The theory is only testable if we can observe agents making navigation decisions and measure whether typed links lead to better choices. Agent trace analysis might provide this.

Relevant Notes:

Artifact B

Title as claim enables traversal as reasoning

Don't name notes like topics ("thoughts on memory"). Name them like claims ("structure enables navigation without reading everything").

When you link to a claim-titled note, the link becomes part of your argument:

"because approvals guard against LLM mistakes not active attacks, we can separate the security boundary from the approval UX"

The title IS the reasoning. Traversal IS thinking. The title functions as a typed signature — you know what you're getting before you load the full note. A topic label like "memory notes" is an undocumented function; a claim like "structure enables navigation" tells you the return value. This connects to how [types applied to documents mark affordances] — a claim title is an affordance declaration.

Prior work

Propositional titles are established practice in several fields:

Academic writing — thesis statements and paper titles that state the conclusion. The abstract leads with the claim.
Journalism — headlines state the finding ("Scientists discover X"), not the topic ("Research about Y").
Evergreen notes (Matuschak) — explicitly advocates for note titles as complete propositions rather than topic labels.
Zettelkasten practice — Luhmann used precise descriptive titles; the community has extensive discussion of atomicity and title quality.

The traversal-as-reasoning consequence — when titles are claims, link-following reads as argument — came to us via [arscontexta], which likely drew on these same traditions. The [Toulmin argumentation model] provides the formal structure behind the "since/because" link semantics this enables.

TODO: This survey is from the agent's training data, not systematic. Matuschak's writing on evergreen notes and Zettelkasten community resources on title conventions are worth ingesting.

Why it works

Inline links carry richer relationship data than metadata fields. The prose surrounding a link encodes WHY the linked note matters here — "because [X]" is a causal claim, "since [Y]" is a foundation claim, "but [Z]" is a tension. Claim-as-title makes these constructions possible, because topic labels don't compose grammatically. You can write "since [claims must be specific enough to be wrong]" but not "since [specificity notes]." Our [link relationship semantics] formalize this — argumentative links ("since", "because") and referential links ("see", "as defined in") are different intents that require different anchor context.

Progressive disclosure depends on this. The first disclosure layer is titles. If titles are claims, agents can curate what to load based on what each note argues. If titles are topics, agents must load notes to discover what they argue — the disclosure layer fails. This is why [instruction specificity should match loading frequency] — the loading hierarchy assumes that titles and descriptions carry enough signal for agents to decide what to load next.

Practical benefits: - scanning file tree = scanning arguments - following links = following reasoning chains - the vault becomes readable without opening files

Where it breaks: multi-claim documents

The pattern works best for ideas that ARE single claims. It breaks for compositional documents — specs, frameworks, classification systems — that embody multiple independent design choices.

[Document classification] is a clear example. It contains several distinct claims: "types assert structure not subject matter," "status is orthogonal to type," "a document has exactly one base type but zero or more traits," "text is the root type." Each could be a standalone claim note. But no single claim subsumes them all — any attempt produces something so abstract it's useless ("documents should be classified").

The traversal-as-reasoning framing explains why. A claim-titled note can serve as a premise: "since [X], therefore Y." A multi-claim document can't serve as a single premise because it IS multiple premises. When you write "see document classification," you're not invoking a reasoning step — you're pointing to a reference. The link semantics shift from argumentative ("since," "because") to referential ("see," "as defined in").

Document kind	Title convention	Link semantics	Role in traversal
Single-claim (insight, rationale)	Claim title	"since [X]", "because [X]"	Premise in reasoning chain
Multi-claim (spec, framework)	Topical title	"see [X]", "as defined in [X]"	Reference, not premise
Definitional (term pinning)	The term itself	"see [X]", "[X] means..."	Reference, not premise

Definitional notes are a second exception. Notes like [codification], [constraining], and [context engineering] pin down how a technical term is used in this project. Their titles are the terms they define — topical by nature. They function as reference entries: you link to them for precision ("as defined in [codification]"), not as premises in reasoning chains. Like specs, they can link TO claim-notes for justification while carrying topical titles themselves.

The two layers coexist. Specs link TO their constituent claim-notes for justification ([document types should be verifiable] is the rationale extracted from the classification spec). Claim-notes link TO specs as the system they support. But they have different title conventions because they play different roles in traversal.

This maps onto the existing type system: notes with claim titles may be promoted to type: structured-claim when the argument matures; spec, index, and other structural types carry topical titles. The title convention (claim vs topical) is independent of the type — any note can use a claim title.

The shadow side

Not every idea decomposes into a single declarative sentence — some are relational, procedural, emergent, or compositional. When reformulation feels forced, the question is whether the insight isn't ready or the format can't accommodate it. The type system makes this explicit: if you can't write a claim title, the note stays type: note with a topical title, and that's fine.