Pith Number

pith:B4DLLYOM

pith:2016:B4DLLYOMNWMJW5NZHPETAIX65A

not attested not anchored not stored refs pending

Typical representatives of free homotopy classes in a multi-punctured plane

Maxim Arnold, Yuliy Baryshnikov, Yuriy Mileyko

arxiv:1601.04224 v1 · 2016-01-16 · math.PR · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{B4DLLYOMNWMJW5NZHPETAIX65A}

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	2026-05-18T01:22:45.600020Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0f06b5e1cc6d989b75b93bc93022fee8076e3be5069c6ca77df07fb6d1a30600

Aliases

arxiv: 1601.04224 · arxiv_version: 1601.04224v1 · doi: 10.48550/arxiv.1601.04224 · pith_short_12: B4DLLYOMNWMJ · pith_short_16: B4DLLYOMNWMJW5NZ · pith_short_8: B4DLLYOM

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/B4DLLYOMNWMJW5NZHPETAIX65A \
  | 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: 0f06b5e1cc6d989b75b93bc93022fee8076e3be5069c6ca77df07fb6d1a30600

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7dd1b2db28825549d0970021276558610e54b91ed6c36accb34b9fb13b3aaf09",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-01-16T22:44:09Z",
    "title_canon_sha256": "aa4521416c615b5b3f0b4773de6ed79a3b22f38b51bc06ff189725b1f0ea68c2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.04224",
    "kind": "arxiv",
    "version": 1
  }
}