Pith Number

pith:6UHR7C4O

pith:2018:6UHR7C4OB2BQV2B54BVIKMROCD

not attested not anchored not stored refs pending

Buser's inequality on infinite graphs

Shuang Liu

arxiv:1810.12003 v1 · 2018-10-29 · math.DG · math.AP · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6UHR7C4OB2BQV2B54BVIKMROCD}

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	2026-05-18T00:02:06.724159Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f50f1f8b8e0e830ae83de06a85322e10ed1cdebf0b20ef402ca4149c0ee315bc

Aliases

arxiv: 1810.12003 · arxiv_version: 1810.12003v1 · doi: 10.48550/arxiv.1810.12003 · pith_short_12: 6UHR7C4OB2BQ · pith_short_16: 6UHR7C4OB2BQV2B5 · pith_short_8: 6UHR7C4O

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/6UHR7C4OB2BQV2B54BVIKMROCD \
  | 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: f50f1f8b8e0e830ae83de06a85322e10ed1cdebf0b20ef402ca4149c0ee315bc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7f734957a737fc9c22ddeada294c782b434d01af20715940f2e028dd64bcbeac",
    "cross_cats_sorted": [
      "math.AP",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2018-10-29T08:54:29Z",
    "title_canon_sha256": "ebc6bab66ee99c391e3153917ae4d0713b1012d1795608b6e757ab4f9eb65d35"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1810.12003",
    "kind": "arxiv",
    "version": 1
  }
}