Pith Number

pith:CBKZU26A

pith:2019:CBKZU26A5HABJ5OB6B4NTKEQWM

not attested not anchored not stored refs pending

A note on Lefschetz spheres and their relatives

Afshin Goodarzi

arxiv:1906.04134 v2 · 2019-06-10 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CBKZU26A5HABJ5OB6B4NTKEQWM}

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	2026-05-17T23:42:58.047042Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

10559a6bc0e9c014f5c1f078d9a890b3008bbe211290bb7969ed5d65c1be2b8a

Aliases

arxiv: 1906.04134 · arxiv_version: 1906.04134v2 · doi: 10.48550/arxiv.1906.04134 · pith_short_12: CBKZU26A5HAB · pith_short_16: CBKZU26A5HABJ5OB · pith_short_8: CBKZU26A

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/CBKZU26A5HABJ5OB6B4NTKEQWM \
  | 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: 10559a6bc0e9c014f5c1f078d9a890b3008bbe211290bb7969ed5d65c1be2b8a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bc1ac787a678569130cd58840505e68c57e31ab77c4829c84d3dc40a515c2555",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2019-06-10T17:11:25Z",
    "title_canon_sha256": "57612fc76b0dbb92e800035409a27decd24e33df668e2eef2d9de9ada0c31d7a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1906.04134",
    "kind": "arxiv",
    "version": 2
  }
}