Pith Number

pith:FK2Y3FV3

pith:2013:FK2Y3FV3RR7BNWWOKE47VII4YO

not attested not anchored not stored refs pending

$r$-fundamental groups of graphs

Takahiro Matsushita

arxiv:1301.7217 v3 · 2013-01-30 · math.CO · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FK2Y3FV3RR7BNWWOKE47VII4YO}

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	2026-05-18T01:33:16.993311Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2ab58d96bb8c7e16dace5139faa11cc3a79cfd7fe8b8594248a9550f45aa70d1

Aliases

arxiv: 1301.7217 · arxiv_version: 1301.7217v3 · doi: 10.48550/arxiv.1301.7217 · pith_short_12: FK2Y3FV3RR7B · pith_short_16: FK2Y3FV3RR7BNWWO · pith_short_8: FK2Y3FV3

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/FK2Y3FV3RR7BNWWOKE47VII4YO \
  | 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: 2ab58d96bb8c7e16dace5139faa11cc3a79cfd7fe8b8594248a9550f45aa70d1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "03007b7ad940dbeb5fdfc0b39dec2c75a251105e97e9b9e7bb407fbe3c5f5f23",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-01-30T13:32:59Z",
    "title_canon_sha256": "c0b19837470226eb46eb86d16c60f8e1e109d47443ddba62de81640480811be2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.7217",
    "kind": "arxiv",
    "version": 3
  }
}