Pith Number

pith:T4L3GMLH

pith:2011:T4L3GMLHPRGTNW5FNL2KPR233K

not attested not anchored not stored refs pending

On intersections of closed curves on surfaces

Elena A. Kudryavtseva, Heiner Zieschang, Semeon A. Bogatyi

arxiv:1111.5277 v1 · 2011-11-22 · math.AT · math.DG · math.GN

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{T4L3GMLHPRGTNW5FNL2KPR233K}

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	2026-05-18T01:23:10.758070Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9f17b331677c4d36dba56af4a7c75bda91ce97b28f07ea592d272c7400e8faac

Aliases

arxiv: 1111.5277 · arxiv_version: 1111.5277v1 · doi: 10.48550/arxiv.1111.5277 · pith_short_12: T4L3GMLHPRGT · pith_short_16: T4L3GMLHPRGTNW5F · pith_short_8: T4L3GMLH

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/T4L3GMLHPRGTNW5FNL2KPR233K \
  | 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: 9f17b331677c4d36dba56af4a7c75bda91ce97b28f07ea592d272c7400e8faac

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "21232c857bf3a66f5dffeaef436668f8979275f4babae7206bbdc9fa39935f8d",
    "cross_cats_sorted": [
      "math.DG",
      "math.GN"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2011-11-22T18:36:50Z",
    "title_canon_sha256": "41a6b0479a2af6cbb0d2c5deef3d197bb85c52a0b2ec4e314cc7067da6c9338b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.5277",
    "kind": "arxiv",
    "version": 1
  }
}