Pith Number

pith:CCZFIYF2

pith:2011:CCZFIYF2CVIAPY73IK7ZIUY4EC

not attested not anchored not stored refs pending

Total Curvature of Graphs after Milnor and Euler

Robert Gulliver, Sumio Yamada

arxiv:1101.2305 v1 · 2011-01-12 · math.DG · 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{CCZFIYF2CVIAPY73IK7ZIUY4EC}

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	2026-05-18T04:31:43.199092Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

10b25460ba155007e3fb42bf94531c209d9389b377e8a3d65166f24d82a2fb34

Aliases

arxiv: 1101.2305 · arxiv_version: 1101.2305v1 · doi: 10.48550/arxiv.1101.2305 · pith_short_12: CCZFIYF2CVIA · pith_short_16: CCZFIYF2CVIAPY73 · pith_short_8: CCZFIYF2

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/CCZFIYF2CVIAPY73IK7ZIUY4EC \
  | 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: 10b25460ba155007e3fb42bf94531c209d9389b377e8a3d65166f24d82a2fb34

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5f9595bb352a50c1b81eb39037720e8db2cb7ff4549d8d6af551470e02d4f62c",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2011-01-12T09:33:45Z",
    "title_canon_sha256": "a1ec8fc44ceaacab8a0d427cf0dd749fddddad9eeaed888427843e19215735f8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.2305",
    "kind": "arxiv",
    "version": 1
  }
}