File size: 3,113 Bytes
e4dca97 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 | # 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.
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