Pith Number

pith:ADMUQXR4

pith:2011:ADMUQXR44FF3MUEC3BYE67JIO5

not attested not anchored not stored refs pending

Sharp Spectral Gap and Li-Yau's Estimate on Alexandrov Spaces

Hui-Chun Zhang, Xi-Ping Zhu, Zhongmin Qian

arxiv:1102.4159 v2 · 2011-02-21 · math.DG · math.AP · 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{ADMUQXR44FF3MUEC3BYE67JIO5}

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	2026-05-18T03:54:49.502112Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

00d9485e3ce14bb65082d8704f7d28774d3f50ff624f969079df603703c45ed8

Aliases

arxiv: 1102.4159 · arxiv_version: 1102.4159v2 · doi: 10.48550/arxiv.1102.4159 · pith_short_12: ADMUQXR44FF3 · pith_short_16: ADMUQXR44FF3MUEC · pith_short_8: ADMUQXR4

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/ADMUQXR44FF3MUEC3BYE67JIO5 \
  | 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: 00d9485e3ce14bb65082d8704f7d28774d3f50ff624f969079df603703c45ed8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dbb90753fd112d44f33b4826ca18a4c80129aadc7168c0a130b7cfeb91c568d5",
    "cross_cats_sorted": [
      "math.AP",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2011-02-21T08:29:53Z",
    "title_canon_sha256": "c767a7d43acd85f9fb2d9fcbe8b8b525ae7e03c7d6f8fea61f0fa78ef08692b3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.4159",
    "kind": "arxiv",
    "version": 2
  }
}