Pith Number

pith:54PLS6CP

pith:2013:54PLS6CPMUKRRK5TMJWQEKDXPC

not attested not anchored not stored refs pending

Bochner formula and Bernstein type estimates on locally finite graphs

Li Ma

arxiv:1304.0290 v2 · 2013-04-01 · math.DG · math.AP · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{54PLS6CPMUKRRK5TMJWQEKDXPC}

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	2026-05-18T03:12:22.264588Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ef1eb9784f651518abb3626d02287778a670f2b0be335e57c4934cf3fe997716

Aliases

arxiv: 1304.0290 · arxiv_version: 1304.0290v2 · doi: 10.48550/arxiv.1304.0290 · pith_short_12: 54PLS6CPMUKR · pith_short_16: 54PLS6CPMUKRRK5T · pith_short_8: 54PLS6CP

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/54PLS6CPMUKRRK5TMJWQEKDXPC \
  | 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: ef1eb9784f651518abb3626d02287778a670f2b0be335e57c4934cf3fe997716

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "19f4d58ef0c9f3dbe2cc75a87984f0cc03c3b52ae37799213fd9a9e3a450ea5e",
    "cross_cats_sorted": [
      "math.AP",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2013-04-01T03:35:02Z",
    "title_canon_sha256": "da7d902ceffb61d7b740a9e94109cb95827595b352cac3330c2c427296530dfc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.0290",
    "kind": "arxiv",
    "version": 2
  }
}