Pith Number

pith:45LP76RZ

pith:2012:45LP76RZPQGQXTPDKUM4CZUPMK

not attested not anchored not stored refs pending

Upper bound on lattice stick number of knots

Kyungpyo Hong, Seungsang Oh, Sungjong No

arxiv:1209.0048 v1 · 2012-09-01 · math.GT

Open paper page JSON Open Graph Bundle Merged state What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{45LP76RZPQGQXTPDKUM4CZUPMK}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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	2026-05-18T00:44:30.284724Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e756fffa397c0d0bcde35519c1668f62bd1bd3803ecba9d376438c02b6d26da4

Aliases

arxiv: 1209.0048 · arxiv_version: 1209.0048v1 · doi: 10.48550/arxiv.1209.0048 · pith_short_12: 45LP76RZPQGQ · pith_short_16: 45LP76RZPQGQXTPD · pith_short_8: 45LP76RZ

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/45LP76RZPQGQXTPDKUM4CZUPMK \
  | 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: e756fffa397c0d0bcde35519c1668f62bd1bd3803ecba9d376438c02b6d26da4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e4f88f095b8faab9c85e616ae6bffe6401e8db48cc6228d74b895318da1506bb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2012-09-01T02:40:40Z",
    "title_canon_sha256": "d733993c05a4ba99fc6827d438b53386cd0bff345334a7bf49ec2666519ff927"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.0048",
    "kind": "arxiv",
    "version": 1
  }
}