Pith Number

pith:I7BK27EG

pith:2008:I7BK27EG67XKF2M7NGGFZ5JMGV

not attested not anchored not stored refs pending

The crossing number of composite knots

Marc Lackenby

arxiv:0805.4706 v2 · 2008-05-30 · 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{I7BK27EG67XKF2M7NGGFZ5JMGV}

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	2026-05-18T02:58:11.481297Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

47c2ad7c86f7eea2e99f698c5cf52c3545dbba3088efd4b55461b3e5fe53598b

Aliases

arxiv: 0805.4706 · arxiv_version: 0805.4706v2 · doi: 10.48550/arxiv.0805.4706 · pith_short_12: I7BK27EG67XK · pith_short_16: I7BK27EG67XKF2M7 · pith_short_8: I7BK27EG

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/I7BK27EG67XKF2M7NGGFZ5JMGV \
  | 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: 47c2ad7c86f7eea2e99f698c5cf52c3545dbba3088efd4b55461b3e5fe53598b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ee211b86636b6a7df676614abb35cd22173100d7835edcdaea89b919ffa6ac6d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2008-05-30T09:49:11Z",
    "title_canon_sha256": "5c2690182662a4286e83e268b20e76004c447b342d3908745fb87d665502f497"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0805.4706",
    "kind": "arxiv",
    "version": 2
  }
}