Pith Number

pith:Y4U5OZXZ

pith:2011:Y4U5OZXZIZ6C7MC3SVKYZ7ZQZC

not attested not anchored not stored refs pending

Pretzel Knots with Unknotting Number One

Dorothy Buck, Eric Staron, Julian Gibbons

arxiv:1109.4560 v3 · 2011-09-21 · 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{Y4U5OZXZIZ6C7MC3SVKYZ7ZQZC}

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	2026-05-18T03:38:14.416960Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c729d766f9467c2fb05b95558cff30c8b836b9f30d03145d3f9cf31f83414cad

Aliases

arxiv: 1109.4560 · arxiv_version: 1109.4560v3 · doi: 10.48550/arxiv.1109.4560 · pith_short_12: Y4U5OZXZIZ6C · pith_short_16: Y4U5OZXZIZ6C7MC3 · pith_short_8: Y4U5OZXZ

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/Y4U5OZXZIZ6C7MC3SVKYZ7ZQZC \
  | 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: c729d766f9467c2fb05b95558cff30c8b836b9f30d03145d3f9cf31f83414cad

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "629697a680240026b3d216e32dc7787f5d2321bbaf69f8f445fea7ea7f617183",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-09-21T15:40:00Z",
    "title_canon_sha256": "5a546a2ee99d8b207960327b415cc1d44ab5a7a1a823110ad8f0f765b6d32b4e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.4560",
    "kind": "arxiv",
    "version": 3
  }
}