Pith Number

pith:ZCWT7GV3

pith:2013:ZCWT7GV3ADSU3UC46CCZWB27UL

not attested not anchored not stored refs pending

The Euler characteristic of an even-dimensional graph

Oliver Knill

arxiv:1307.3809 v1 · 2013-07-15 · math.GT · cs.DM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZCWT7GV3ADSU3UC46CCZWB27UL}

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	2026-05-18T03:18:27.850579Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c8ad3f9abb00e54dd05cf0859b075fa2c932151b43263f4325b5595897134457

Aliases

arxiv: 1307.3809 · arxiv_version: 1307.3809v1 · doi: 10.48550/arxiv.1307.3809 · pith_short_12: ZCWT7GV3ADSU · pith_short_16: ZCWT7GV3ADSU3UC4 · pith_short_8: ZCWT7GV3

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/ZCWT7GV3ADSU3UC46CCZWB27UL \
  | 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: c8ad3f9abb00e54dd05cf0859b075fa2c932151b43263f4325b5595897134457

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "71e8c4deb87f0edaee2d6a9590d5dc80dc7c1351caffb8bdb8717a01069bb0fb",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2013-07-15T02:37:47Z",
    "title_canon_sha256": "5c51b386a61e29cea91892e36aad8ab15febeb425fecb99aad65ca800634e0e3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.3809",
    "kind": "arxiv",
    "version": 1
  }
}