Pith Number

pith:MJ5K2NEX

pith:2013:MJ5K2NEXYVP3O42ZDF66GHOG4R

not attested not anchored not stored refs pending

Explicit bounds for graph minors

Jim Geelen, R. Bruce Richter, Tony Huynh

arxiv:1305.1451 v2 · 2013-05-07 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MJ5K2NEXYVP3O42ZDF66GHOG4R}

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	2026-05-18T01:15:59.365049Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

627aad3497c55fb77359197de31dc6e4740848e3a73d2ce6ab7f88287f8f8b71

Aliases

arxiv: 1305.1451 · arxiv_version: 1305.1451v2 · doi: 10.48550/arxiv.1305.1451 · pith_short_12: MJ5K2NEXYVP3 · pith_short_16: MJ5K2NEXYVP3O42Z · pith_short_8: MJ5K2NEX

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/MJ5K2NEXYVP3O42ZDF66GHOG4R \
  | 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: 627aad3497c55fb77359197de31dc6e4740848e3a73d2ce6ab7f88287f8f8b71

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c70228ea59b809fca525e1d89a8018aa3026ffc63285edc5ee3599d36ecea2c0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-05-07T09:49:52Z",
    "title_canon_sha256": "205e0535c8d2bf8fb2acb6b35326edbdec36da9110465f0f0d7e1c9c5437ec81"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1305.1451",
    "kind": "arxiv",
    "version": 2
  }
}