Pith Number

pith:4TZY74PR

pith:2010:4TZY74PRAL3NXP72EHI74H3YL2

not attested not anchored not stored refs pending

On a new definition of Ricci curvature on Alexandrov spaces

Hui-Chun Zhang, Xi-Ping Zhu

arxiv:1007.4042 v2 · 2010-07-23 · math.DG · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4TZY74PRAL3NXP72EHI74H3YL2}

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	2026-05-18T04:42:21.926545Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e4f38ff1f102f6dbbffa21d1fe1f785ebe4926c9164a3384a6c5339eb0c0b219

Aliases

arxiv: 1007.4042 · arxiv_version: 1007.4042v2 · doi: 10.48550/arxiv.1007.4042 · pith_short_12: 4TZY74PRAL3N · pith_short_16: 4TZY74PRAL3NXP72 · pith_short_8: 4TZY74PR

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/4TZY74PRAL3NXP72EHI74H3YL2 \
  | 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: e4f38ff1f102f6dbbffa21d1fe1f785ebe4926c9164a3384a6c5339eb0c0b219

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "201638c9983197e38dd736f63f51291c362526eeb0a289c9031a4d77b36e964c",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2010-07-23T05:18:16Z",
    "title_canon_sha256": "ffc5792b18b72b6e3eef2a020073b3fa73587890f85b783f3920d82d9d8d2ae6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1007.4042",
    "kind": "arxiv",
    "version": 2
  }
}