Pith Number

pith:W7M5MP3I

pith:2015:W7M5MP3IYYPPWHYVPNWMVJ4A2M

not attested not anchored not stored refs pending

Curvature properties of some class of warped product manifolds

Georges Zafindratafa, Jan Je{\l}owicki, Ma{\l}gorzata G{\l}ogowska, Ryszard Deszcz

arxiv:1507.02915 v1 · 2015-07-10 · 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{W7M5MP3IYYPPWHYVPNWMVJ4A2M}

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	2026-05-18T01:22:20.788042Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b7d9d63f68c61efb1f157b6ccaa780d308dafe5290b836eaf7ac2ed62ac8fe67

Aliases

arxiv: 1507.02915 · arxiv_version: 1507.02915v1 · doi: 10.48550/arxiv.1507.02915 · pith_short_12: W7M5MP3IYYPP · pith_short_16: W7M5MP3IYYPPWHYV · pith_short_8: W7M5MP3I

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/W7M5MP3IYYPPWHYVPNWMVJ4A2M \
  | 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: b7d9d63f68c61efb1f157b6ccaa780d308dafe5290b836eaf7ac2ed62ac8fe67

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6766a6fd3612772550137e0b1a2802b6cbae39a27d3ab4160cd61c375ee006ec",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2015-07-10T14:21:06Z",
    "title_canon_sha256": "8a9b062a85c0d6f8680cfb5843a62170e51dab1f06decc28f9a9ee3fae4af1e3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.02915",
    "kind": "arxiv",
    "version": 1
  }
}