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

```text
{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

```text
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.