Pith Number

pith:XFAP7FZ3

pith:2016:XFAP7FZ3MCF7RX2HEIGS4PNXRQ

not attested not anchored not stored refs pending

The efficient certification of knottedness and Thurston norm

Marc Lackenby

arxiv:1604.00290 v3 · 2016-04-01 · 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{XFAP7FZ3MCF7RX2HEIGS4PNXRQ}

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.

Cited by

1 paper in Pith

Link Crossing Number is NP-hard

Receipt and verification

First computed	2026-07-05T02:30:53.613021Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b940ff973b608bf8df47220d2e3db78c2cbc2fb548de6cc22be7e90c27487989

Aliases

arxiv: 1604.00290 · arxiv_version: 1604.00290v3 · doi: 10.48550/arxiv.1604.00290 · pith_short_12: XFAP7FZ3MCF7 · pith_short_16: XFAP7FZ3MCF7RX2H · pith_short_8: XFAP7FZ3

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/XFAP7FZ3MCF7RX2HEIGS4PNXRQ \
  | 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: b940ff973b608bf8df47220d2e3db78c2cbc2fb548de6cc22be7e90c27487989

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "db95afd6b6c8288df0c6f204f1c2d2356c3808081120bebeaa8ea1da3edcfd9c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2016-04-01T15:38:16Z",
    "title_canon_sha256": "9e24411d98944fd58ae1770a26bfb7377a87182147ebc5917b5c9513b6724421"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1604.00290",
    "kind": "arxiv",
    "version": 3
  }
}