Pith Number

pith:YZZPTTTN

pith:2010:YZZPTTTNM7E22BHWQJP6LKYG3Y

not attested not anchored not stored refs pending

A theorem of do Carmo-Zhou type: oscillations and estimates for the first eigenvalue of the p-Laplacian

Barnabe Pessoa Lima, Newton Luis Santos

arxiv:1008.2214 v1 · 2010-08-12 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YZZPTTTNM7E22BHWQJP6LKYG3Y}

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	2026-05-18T04:42:14.389568Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c672f9ce6d67c9ad04f6825fe5ab06de192a1fd143be81d85916c83b1a5a6dd8

Aliases

arxiv: 1008.2214 · arxiv_version: 1008.2214v1 · doi: 10.48550/arxiv.1008.2214 · pith_short_12: YZZPTTTNM7E2 · pith_short_16: YZZPTTTNM7E22BHW · pith_short_8: YZZPTTTN

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/YZZPTTTNM7E22BHWQJP6LKYG3Y \
  | 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: c672f9ce6d67c9ad04f6825fe5ab06de192a1fd143be81d85916c83b1a5a6dd8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0d40e167e47e916802cef8b9b3a71a050d09624f6fd33dc2ba49fc3021cc0a7e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2010-08-12T20:53:27Z",
    "title_canon_sha256": "4c2b730578ecab39d659b1f84b0be554aeefd9385b7315fac3c7e21944c12651"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1008.2214",
    "kind": "arxiv",
    "version": 1
  }
}