Pith Number

pith:IZCOP5TO

pith:2018:IZCOP5TO3FOHI2A43IAXAMTN6W

not attested not anchored not stored refs pending

A signature invariant for knotted Klein graphs

Catherine Gille, Louis-Hadrien Robert

arxiv:1803.08025 v2 · 2018-03-21 · 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{IZCOP5TO3FOHI2A43IAXAMTN6W}

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	2026-05-18T00:02:35.381934Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4644e7f66ed95c74681cda0170326df59fdc80f32e712b23d94b9634b9720090

Aliases

arxiv: 1803.08025 · arxiv_version: 1803.08025v2 · doi: 10.48550/arxiv.1803.08025 · pith_short_12: IZCOP5TO3FOH · pith_short_16: IZCOP5TO3FOHI2A4 · pith_short_8: IZCOP5TO

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/IZCOP5TO3FOHI2A43IAXAMTN6W \
  | 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: 4644e7f66ed95c74681cda0170326df59fdc80f32e712b23d94b9634b9720090

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b077298e064fb4e09697b9fd907464549df0edbcf0d636c58cfe7d42eb9ffbe7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2018-03-21T17:24:36Z",
    "title_canon_sha256": "9045f7809f7c9ed692c8f94a60bf3cc0d435b6055bfee91e5cfed99d7eac3c20"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1803.08025",
    "kind": "arxiv",
    "version": 2
  }
}