Pith Number

pith:U4P32SKZ

pith:2020:U4P32SKZDPGABCV7KDJDNHSTQE

not attested not anchored not stored refs pending

Criteria for integer and modulo 2 embeddability of graphs to surfaces

Arthur Bikeev

arxiv:2012.12070 v2 · 2020-12-22 · math.CO · cs.CG · cs.DM · 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{U4P32SKZDPGABCV7KDJDNHSTQE}

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	2026-07-05T03:31:56.168654Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a71fbd49591bcc008abf50d2369e53811c20064f302148152b9710f6f371fc22

Aliases

arxiv: 2012.12070 · arxiv_version: 2012.12070v2 · doi: 10.48550/arxiv.2012.12070 · pith_short_12: U4P32SKZDPGA · pith_short_16: U4P32SKZDPGABCV7 · pith_short_8: U4P32SKZ

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/U4P32SKZDPGABCV7KDJDNHSTQE \
  | 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: a71fbd49591bcc008abf50d2369e53811c20064f302148152b9710f6f371fc22

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "49c25c637d18add47d32042b36d832136704bbfbf4c6565cec9ccb490ea8436b",
    "cross_cats_sorted": [
      "cs.CG",
      "cs.DM",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2020-12-22T15:09:03Z",
    "title_canon_sha256": "612d8f6b32f703c6743cc9771d2ebbfb279969076ccd6cc7ec95a54b46f75643"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2012.12070",
    "kind": "arxiv",
    "version": 2
  }
}