Pith Number

pith:TNRWQEC6

pith:2011:TNRWQEC6EQVW2JMFZSRC6BHXWX

not attested not anchored not stored refs pending

The crossing number of satellite knots

Marc Lackenby

arxiv:1106.3095 v2 · 2011-06-15 · 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{TNRWQEC6EQVW2JMFZSRC6BHXWX}

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	2026-05-18T02:38:18.108273Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9b6368105e242b6d2585cca22f04f7b5db13f3dccad60b7eeb3163f56071022d

Aliases

arxiv: 1106.3095 · arxiv_version: 1106.3095v2 · doi: 10.48550/arxiv.1106.3095 · pith_short_12: TNRWQEC6EQVW · pith_short_16: TNRWQEC6EQVW2JMF · pith_short_8: TNRWQEC6

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/TNRWQEC6EQVW2JMFZSRC6BHXWX \
  | 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: 9b6368105e242b6d2585cca22f04f7b5db13f3dccad60b7eeb3163f56071022d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bb1dbcb7bfb9734eda6e4f3ab1331b1f500981f9542e27d99f15f18146d61363",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-06-15T20:31:26Z",
    "title_canon_sha256": "772017242c0fe48da26823e27d4365e90cfdb319f6bb78a8c7d074f19b6f3872"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.3095",
    "kind": "arxiv",
    "version": 2
  }
}