Pith Number

pith:BZKHGD7W

pith:2015:BZKHGD7WP35HDVEDJHTFAA63FN

not attested not anchored not stored refs pending

The Jordan-Brouwer theorem for graphs

Oliver Knill

arxiv:1506.06440 v1 · 2015-06-22 · cs.DM · cs.CG · 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{BZKHGD7WP35HDVEDJHTFAA63FN}

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	2026-05-18T01:41:45.226490Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0e54730ff67efa71d48349e65003db2b721d659f10b69beb08aee046a09e3e08

Aliases

arxiv: 1506.06440 · arxiv_version: 1506.06440v1 · doi: 10.48550/arxiv.1506.06440 · pith_short_12: BZKHGD7WP35H · pith_short_16: BZKHGD7WP35HDVED · pith_short_8: BZKHGD7W

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/BZKHGD7WP35HDVEDJHTFAA63FN \
  | 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: 0e54730ff67efa71d48349e65003db2b721d659f10b69beb08aee046a09e3e08

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "30d537d71cd471572e9b8f52d5899c0977b063c239e332df64d827a4dc46013b",
    "cross_cats_sorted": [
      "cs.CG",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DM",
    "submitted_at": "2015-06-22T01:52:45Z",
    "title_canon_sha256": "c5b92dbc4f1ee7791cc44da6d9959075463dc940dce3b9cc03c97ecab39bda81"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.06440",
    "kind": "arxiv",
    "version": 1
  }
}