Pith Number

pith:423R7XQL

pith:2016:423R7XQLPGAUPWQV3QXXIPQKJT

not attested not anchored not stored refs pending

Thin position for knots, links, and graphs in 3-manifolds

Maggy Tomova, Scott A. Taylor

arxiv:1606.03331 v2 · 2016-06-10 · 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{423R7XQLPGAUPWQV3QXXIPQKJT}

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	2026-05-18T00:18:54.199621Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e6b71fde0b798147da15dc2f743e0a4cd19ac8b296ae3d9a93ea164383b83102

Aliases

arxiv: 1606.03331 · arxiv_version: 1606.03331v2 · doi: 10.48550/arxiv.1606.03331 · pith_short_12: 423R7XQLPGAU · pith_short_16: 423R7XQLPGAUPWQV · pith_short_8: 423R7XQL

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/423R7XQLPGAUPWQV3QXXIPQKJT \
  | 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: e6b71fde0b798147da15dc2f743e0a4cd19ac8b296ae3d9a93ea164383b83102

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1e909d152167889061740328ce1da755f1ae832bd5f10a6c63ae187d4d449003",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2016-06-10T14:05:00Z",
    "title_canon_sha256": "c2c70ceb50b73942d860b9b48d41e1bfc23a4a6e53eb23feb4cf0ae87bb93ff2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.03331",
    "kind": "arxiv",
    "version": 2
  }
}