Pith Number

pith:PKBDF4BZ

pith:2010:PKBDF4BZGCPHCGLETJX7CYIWEU

not attested not anchored not stored refs pending

The Least Spanning Area of a Knot and the Optimal Bounding Chain Problem

Anil N. Hirani, Nathan M. Dunfield

arxiv:1012.3030 v3 · 2010-12-13 · cs.CG · cs.DS · math.DG · 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{PKBDF4BZGCPHCGLETJX7CYIWEU}

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	2026-05-18T04:26:02.303685Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7a8232f039309e7119649a6ff161162503b42740f1fe0b54312b120fa4d4c54f

Aliases

arxiv: 1012.3030 · arxiv_version: 1012.3030v3 · doi: 10.48550/arxiv.1012.3030 · pith_short_12: PKBDF4BZGCPH · pith_short_16: PKBDF4BZGCPHCGLE · pith_short_8: PKBDF4BZ

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/PKBDF4BZGCPHCGLETJX7CYIWEU \
  | 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: 7a8232f039309e7119649a6ff161162503b42740f1fe0b54312b120fa4d4c54f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "749293d938fd0532b192328e5231e73f6e6e7e03ff6851817fd01530b620270c",
    "cross_cats_sorted": [
      "cs.DS",
      "math.DG",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CG",
    "submitted_at": "2010-12-13T16:18:16Z",
    "title_canon_sha256": "51ae75acd95309013650d54bc92bd880f49f42392ab317795a7117f487bf8597"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.3030",
    "kind": "arxiv",
    "version": 3
  }
}