spec/objects.md

Frozen experimental objects

This file is normative for the v4.33.0 reproduction. Code and prose must be changed together whenever one of these choices changes.

Raw corpus

The Lean extractor imports the umbrella module Mathlib at the pinned commit and visits kernel declarations whose defining module is Mathlib or begins with Mathlib.. For every such declaration it records:

• fully qualified name, defining module, namespace and declaration kind;
• whether the name satisfies Lean's Name.isInternal predicate;
• whether Lean classifies the name as automatically generated or private;
• direct constants occurring in the elaborated type;
• direct constants occurring in the retained value, when one exists;
• the number of structurally distinct Expr subterms in the type and value.

The raw export is not filtered into a research graph. In particular, a reference to a constant outside the Mathlib-module corpus remains present as provenance even though it cannot become an internal graph edge.

Primary theorem view

A vertex is a raw declaration satisfying all of the following:

1. its kind is theorem (ConstantInfo.thmInfo);
2. is_auto_or_private is false;
3. it belongs to a Mathlib module by the raw-corpus rule above.

For every retained theorem T, intersect its value_refs with this vertex set. If the intersection is nonempty it yields one directed hyperedge

{retained theorem constants in T's stored proof} -> T.

Inputs are a set and are serialized in name order. Their occurrence order, multiplicity, inference rules, intermediate proof terms and alternative proofs are not represented. A theorem with no retained in-view premise remains an isolated root and contributes no hyperedge.

The diagnostic sensitivity view changes only condition 2: it excludes names for which Name.isInternal is true, reproducing the old extractor's narrower filter on the same v4.33.0 corpus. It is not the paper's primary object.

Depth and reuse

• Edge direction is premise to conclusion.
• Recorded depth is the longest directed path ending at a vertex, with roots at depth zero.
• Direct reuse is the number of retained hyperedges in which a theorem occurs as an input; repeated occurrences within one proof count once.

These are properties of the induced view. A root may have dependencies that were outside the view.

Expression-size proxy

Statement size is the number of structurally distinct Expr subterms in the elaborated theorem type. Proof-term size is the same count for its retained proof value. Referenced declarations remain leaf constants: their bodies are not unfolded. The Section 3.3 ratio is

proof_term_dag_size / statement_dag_size.

It is therefore an elaborated-term proxy, not an expanded proof length and not the length of a shortest proof.

Declaration view for Section 4

Section 4 is a parallel graph, not a projection of the primary theorem hypergraph. Its exact inclusion rule, edge rule and frozen Ahlfors mapping are versioned separately in navigation.md before the v4.33.0 result is promoted.