Pith Number

pith:25UCUQM2

pith:2013:25UCUQM2YUHEACZSD2K7U623OW

not attested not anchored not stored refs pending

Tachibana, Killing and planarity numbers of compact Riemannian manifolds

Josef Mike\v{s}, Sergey E. Stepanov

arxiv:1301.0470 v1 · 2013-01-03 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{25UCUQM2YUHEACZSD2K7U623OW}

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	2026-05-18T03:37:19.540148Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d7682a419ac50e400b321e95fa7b5b758a79054f0a03b291112ee97441b02c86

Aliases

arxiv: 1301.0470 · arxiv_version: 1301.0470v1 · doi: 10.48550/arxiv.1301.0470 · pith_short_12: 25UCUQM2YUHE · pith_short_16: 25UCUQM2YUHEACZS · pith_short_8: 25UCUQM2

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/25UCUQM2YUHEACZSD2K7U623OW \
  | 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: d7682a419ac50e400b321e95fa7b5b758a79054f0a03b291112ee97441b02c86

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a9ee5f898c4a2d85fdc14a0ecbf7b615e7cb95a6165e0d3fcc08cb8327d1a3cf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2013-01-03T14:45:29Z",
    "title_canon_sha256": "bfd05eef02f5f0bf6330f8441a8b60b98033c68043e8016c0fb14621b7f56c9f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.0470",
    "kind": "arxiv",
    "version": 1
  }
}