Pith Number

pith:VW23VSUG

pith:2010:VW23VSUGO6ZNLVGSAF6DNJZK3I

not attested not anchored not stored refs pending

Yau's gradient estimates on Alexandrov spaces

Hui-Chun Zhang, Xi-Ping Zhu

arxiv:1012.4233 v3 · 2010-12-20 · 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{VW23VSUGO6ZNLVGSAF6DNJZK3I}

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	2026-05-18T04:00:59.934213Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

adb5baca8677b2d5d4d2017c36a72ada20337d17425f7101b9c718e8206dcb37

Aliases

arxiv: 1012.4233 · arxiv_version: 1012.4233v3 · doi: 10.48550/arxiv.1012.4233 · pith_short_12: VW23VSUGO6ZN · pith_short_16: VW23VSUGO6ZNLVGS · pith_short_8: VW23VSUG

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/VW23VSUGO6ZNLVGSAF6DNJZK3I \
  | 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: adb5baca8677b2d5d4d2017c36a72ada20337d17425f7101b9c718e8206dcb37

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "618d74f5f69f4640fc93d3bf70ba0f58547abd6903dde70b572be165d96ea1c8",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2010-12-20T03:15:56Z",
    "title_canon_sha256": "86855485a31f0380876f92b3c967c2c5ce81eda7ffa0279ac91ceaf33d617155"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.4233",
    "kind": "arxiv",
    "version": 3
  }
}