Pith Number

pith:LSGDCFCB

pith:2011:LSGDCFCBGU42DCQY6NLB6AXP33

not attested not anchored not stored refs pending

Kato's inequality and Liouville theorems on locally finite graphs

Li Ma, Xiangyang Wang

arxiv:1104.2697 v1 · 2011-04-14 · math.AP · math.CA · math.DG · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LSGDCFCBGU42DCQY6NLB6AXP33}

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	2026-05-18T04:24:27.034538Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5c8c3114413539a18a18f3561f02efdec73cf7c7bb07587c012ae144866e5eb6

Aliases

arxiv: 1104.2697 · arxiv_version: 1104.2697v1 · doi: 10.48550/arxiv.1104.2697 · pith_short_12: LSGDCFCBGU42 · pith_short_16: LSGDCFCBGU42DCQY · pith_short_8: LSGDCFCB

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/LSGDCFCBGU42DCQY6NLB6AXP33 \
  | 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: 5c8c3114413539a18a18f3561f02efdec73cf7c7bb07587c012ae144866e5eb6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "31a86bcdcf54dd18f6f8b64b894cca0a5617953e3e28e6b541ca93beee5bbd82",
    "cross_cats_sorted": [
      "math.CA",
      "math.DG",
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-04-14T08:44:43Z",
    "title_canon_sha256": "a2eafdcc7abfc572890e695d89395ff86314386bd84cdc7e206197922a9d8f85"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1104.2697",
    "kind": "arxiv",
    "version": 1
  }
}