Pith Number

pith:MZC4LH3U

pith:2009:MZC4LH3UNNMZZKXUC7RKFVNW4T

not attested not anchored not stored refs pending

The Khovanov homology of (p,-p,q) pretzel knots

Laura Starkston

arxiv:0909.1853 v3 · 2009-09-10 · 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{MZC4LH3UNNMZZKXUC7RKFVNW4T}

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	2026-05-18T04:04:15.536697Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6645c59f746b599caaf417e2a2d5b6e4c806e308646aacfb285ca3442ee52ba8

Aliases

arxiv: 0909.1853 · arxiv_version: 0909.1853v3 · doi: 10.48550/arxiv.0909.1853 · pith_short_12: MZC4LH3UNNMZ · pith_short_16: MZC4LH3UNNMZZKXU · pith_short_8: MZC4LH3U

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/MZC4LH3UNNMZZKXUC7RKFVNW4T \
  | 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: 6645c59f746b599caaf417e2a2d5b6e4c806e308646aacfb285ca3442ee52ba8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7fea7513e8c554dfac3a833986dcff54e345ab9a908b6194eb62b1ee641fccf6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2009-09-10T01:15:13Z",
    "title_canon_sha256": "7fbfe89cb63dcce00a3362db647eff38df6a7198aee3167facb901497b90b0b5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0909.1853",
    "kind": "arxiv",
    "version": 3
  }
}