Pith Number

pith:JWP2HF7H

pith:2009:JWP2HF7HBM2GUCH6FUYP7T3AIJ

not attested not anchored not stored refs pending

On Leighton's graph covering theorem

Walter D. Neumann

arxiv:0906.2496 v2 · 2009-06-13 · math.GR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JWP2HF7HBM2GUCH6FUYP7T3AIJ}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T04:16:42.466227Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4d9fa397e70b346a08fe2d30ffcf6042409fea86a4396d23f0bca54b5402ec7a

Aliases

arxiv: 0906.2496 · arxiv_version: 0906.2496v2 · doi: 10.48550/arxiv.0906.2496 · pith_short_12: JWP2HF7HBM2G · pith_short_16: JWP2HF7HBM2GUCH6 · pith_short_8: JWP2HF7H

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/JWP2HF7HBM2GUCH6FUYP7T3AIJ \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 4d9fa397e70b346a08fe2d30ffcf6042409fea86a4396d23f0bca54b5402ec7a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "28240b6e1e98eef34839433a06703d411fe5d83af4ac90e624b85d77f4dbfeee",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2009-06-13T19:10:16Z",
    "title_canon_sha256": "6cbcfbc9da10e74409fa0c06a883e8bbad3cbbb59b29353fba31f93c85c9fe7f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0906.2496",
    "kind": "arxiv",
    "version": 2
  }
}