Pith Number

pith:P45UK3SJ

pith:2024:P45UK3SJCOF4QW6HEUBGTWCCUM

not attested not anchored not stored refs pending

Arrangements of small circles for Morse-Bott functions

Naoki Kitazawa

arxiv:2412.03846 v3 · 2024-12-05 · math.AG · math.CO · math.GN · 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{P45UK3SJCOF4QW6HEUBGTWCCUM}

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	2026-07-05T10:02:55.643545Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7f3b456e49138bc85bc7250269d842a31cab95bc8000391d217bc967f18d3f48

Aliases

arxiv: 2412.03846 · arxiv_version: 2412.03846v3 · doi: 10.48550/arxiv.2412.03846 · pith_short_12: P45UK3SJCOF4 · pith_short_16: P45UK3SJCOF4QW6H · pith_short_8: P45UK3SJ

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/P45UK3SJCOF4QW6HEUBGTWCCUM \
  | 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: 7f3b456e49138bc85bc7250269d842a31cab95bc8000391d217bc967f18d3f48

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9b664260f77edbfc8c71387ae23fe08a44bde8de2fd499e876fd098fe6293e74",
    "cross_cats_sorted": [
      "math.CO",
      "math.GN",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2024-12-05T03:23:58Z",
    "title_canon_sha256": "afee1bfaf879c73e1abf022ead694de8d70be8c016157bcded35159ca76e76a8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.03846",
    "kind": "arxiv",
    "version": 3
  }
}