# Iter-3 Integrity Audit

**Graph file:** `/Users/primetrce/Documents/maths/knowledge_graph.json` (4.8 MB)

## Node counts

- Total nodes: 6225
- Axioms     : 1571
- States     : 2925
- Theorems   : 1667
- Techniques : 62
- Total edges: 10556

## Duplicate id check

- Duplicate ids: 0

## Orphan nodes (no incident edges)

- Total orphans: 5
  - axiom: 5

## Connected components

- Components: 7
- Giant component size: 6219 / 6225 = 99.90%
- Singletons (size 1): 5
- Other small components (size 2–10): 1

## Theorems with no incoming edge (no derivation recorded)

- Count: 0

## Axioms with no outgoing edge (unused)

- Count: 5
  - `s_divisor_on_curve`
  - `s_closed_ball_D_n`
  - `s_elliptic_operator_D`
  - `s_jacobian_variety`
  - `s_unit_balls_sphere_packing`

## Low-fan techniques (fan-in + fan-out < 3)

- Count: 3 of 62
  - `t_ricci_flow_with_surgery` : in=1, out=1
  - `t_urysohn_lemma_application` : in=2, out=0
  - `t_riemann_mapping_application` : in=2, out=0