Pith Number

pith:GBZLRCRO

pith:2019:GBZLRCRO627MONWFQQYCHZNKJM

not attested not anchored not stored refs pending

First Betti numbers of orbits of Morse functions on surfaces

Iryna Kuznietsova, Yuliia Soroka

arxiv:1908.03014 v1 · 2019-08-08 · math.GR · math.AT · math.GT · math.KT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GBZLRCRO627MONWFQQYCHZNKJM}

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	2026-07-04T23:52:25.557787Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3072b88a2ef6bec736c5843023e5aa4b2450b3bdaba4d51f9de5052f71bfd029

Aliases

arxiv: 1908.03014 · arxiv_version: 1908.03014v1 · doi: 10.48550/arxiv.1908.03014 · pith_short_12: GBZLRCRO627M · pith_short_16: GBZLRCRO627MONWF · pith_short_8: GBZLRCRO

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/GBZLRCRO627MONWFQQYCHZNKJM \
  | 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: 3072b88a2ef6bec736c5843023e5aa4b2450b3bdaba4d51f9de5052f71bfd029

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1460c7e8550e70fc26e81a29498b4dbf01ea6ae7c1f9041abecfe4e0aec14ccd",
    "cross_cats_sorted": [
      "math.AT",
      "math.GT",
      "math.KT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2019-08-08T10:59:58Z",
    "title_canon_sha256": "7c390eaeaf93087ee84ca252ad2f8f5556e8a5782b6f066e6e6d72aabe44c5c5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.03014",
    "kind": "arxiv",
    "version": 1
  }
}