Pith Number

pith:BG7ODCRI

pith:2011:BG7ODCRIWGPEB2QQSS3TKOASO2

not attested not anchored not stored refs pending

Many, many more intrinsically knotted graphs

Noam Goldberg, Ramin Naimi, Thomas W. Mattman

arxiv:1109.1632 v4 · 2011-09-08 · 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{BG7ODCRIWGPEB2QQSS3TKOASO2}

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	2026-05-18T02:25:11.819900Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

09bee18a28b19e40ea1094b7353812769477d19f8b258db97628696016cd3f36

Aliases

arxiv: 1109.1632 · arxiv_version: 1109.1632v4 · doi: 10.48550/arxiv.1109.1632 · pith_short_12: BG7ODCRIWGPE · pith_short_16: BG7ODCRIWGPEB2QQ · pith_short_8: BG7ODCRI

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/BG7ODCRIWGPEB2QQSS3TKOASO2 \
  | 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: 09bee18a28b19e40ea1094b7353812769477d19f8b258db97628696016cd3f36

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "82c91d20fefb7c957f3c8d698d698533c411b8bf1fdc3b2e08b854d0cd82d9c1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-09-08T06:01:10Z",
    "title_canon_sha256": "e506b8388a12f6a8f4cad72be7deb11e01a1751790891c74dc9dd65bcb9a5d7c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.1632",
    "kind": "arxiv",
    "version": 4
  }
}