Pith Number

pith:3FRIZAFW

pith:2009:3FRIZAFWTKNKWGPVEQAEI3YP7I

not attested not anchored not stored refs pending

Face-width of Pfaffian Braces and Polyhex Graphs on Surfaces

Dong Ye, Heping Zhang

arxiv:0908.1506 v2 · 2009-08-11 · 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{3FRIZAFWTKNKWGPVEQAEI3YP7I}

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	2026-05-18T03:16:17.885215Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d9628c80b69a9aab19f52400446f0ffa1cfe946a3f266b0a5bbd6860fcd702d4

Aliases

arxiv: 0908.1506 · arxiv_version: 0908.1506v2 · doi: 10.48550/arxiv.0908.1506 · pith_short_12: 3FRIZAFWTKNK · pith_short_16: 3FRIZAFWTKNKWGPV · pith_short_8: 3FRIZAFW

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/3FRIZAFWTKNKWGPVEQAEI3YP7I \
  | 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: d9628c80b69a9aab19f52400446f0ffa1cfe946a3f266b0a5bbd6860fcd702d4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "708282aaf7162515279d4e0e7cd94f8a079955470fb847a805b26d71059b51f2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2009-08-11T12:38:47Z",
    "title_canon_sha256": "7f7c02e10a071b5e4763cec7b091481854d098303032c48f91b56d086c93e254"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0908.1506",
    "kind": "arxiv",
    "version": 2
  }
}