Pith Number

pith:GU5M6QYY

pith:2019:GU5M6QYYYERPC5FSLZ6SPLK3SV

not attested not anchored not stored refs pending

The Hopf monoid and the basic invariant of directed graphs

Keiju Kato

arxiv:1907.10825 v1 · 2019-07-24 · math.CO · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GU5M6QYYYERPC5FSLZ6SPLK3SV}

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	2026-05-17T23:39:29.809004Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

353acf4318c122f174b25e7d27ad5b95726914f64f7da87cb08b08a4ca7734d5

Aliases

arxiv: 1907.10825 · arxiv_version: 1907.10825v1 · doi: 10.48550/arxiv.1907.10825 · pith_short_12: GU5M6QYYYERP · pith_short_16: GU5M6QYYYERPC5FS · pith_short_8: GU5M6QYY

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/GU5M6QYYYERPC5FSLZ6SPLK3SV \
  | 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: 353acf4318c122f174b25e7d27ad5b95726914f64f7da87cb08b08a4ca7734d5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5efa7d27384c90318302f4a04fceda0532a26dfcd66f4985256ae7dab7818893",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2019-07-24T06:35:49Z",
    "title_canon_sha256": "428e16529590b7412cf9395863026a243abc4966cda97b386d9c83ad3a3e91cb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1907.10825",
    "kind": "arxiv",
    "version": 1
  }
}