Pith Number

pith:XL3VVDP7

pith:2019:XL3VVDP7SFAUOLAFJOFAH57GGF

not attested not anchored not stored refs pending

The tunnel number of all 11 and 12 crossing alternating knots

Felipe Castellano-Mac\'ias, Nicholas Owad

arxiv:1908.01693 v2 · 2019-08-05 · 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{XL3VVDP7SFAUOLAFJOFAH57GGF}

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	2026-07-05T04:07:20.271592Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

baf75a8dff9141472c054b8a03f7e6315c6986234c7a325a6bc8784bc5fb1287

Aliases

arxiv: 1908.01693 · arxiv_version: 1908.01693v2 · doi: 10.48550/arxiv.1908.01693 · pith_short_12: XL3VVDP7SFAU · pith_short_16: XL3VVDP7SFAUOLAF · pith_short_8: XL3VVDP7

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/XL3VVDP7SFAUOLAFJOFAH57GGF \
  | 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: baf75a8dff9141472c054b8a03f7e6315c6986234c7a325a6bc8784bc5fb1287

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ad15cdb1a9aa4feaf624e357cf1ca1fca9fbc7522604346656191b8e120d0cc4",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2019-08-05T15:38:49Z",
    "title_canon_sha256": "1361fc1245df2b4258098ffb19efac4aae1d4194724b0360ded7a6999d3a14e7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.01693",
    "kind": "arxiv",
    "version": 2
  }
}