Pith Number

pith:JIK54YJ4

pith:2010:JIK54YJ4XJ5K2BQOU3KX2ZYDER

not attested not anchored not stored refs pending

Keller-Osserman type conditions for differential inequalities with gradient terms on the Heisenberg group

Luciano Mari, Marco Magliaro, Marco Rigoli, Paolo Mastrolia

arxiv:1003.5780 v1 · 2010-03-30 · math.DG · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JIK54YJ4XJ5K2BQOU3KX2ZYDER}

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	2026-05-18T04:18:04.713853Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4a15de613cba7aad060ea6d57d67032470f6151070480fcfe836ddc6c3e7de90

Aliases

arxiv: 1003.5780 · arxiv_version: 1003.5780v1 · doi: 10.48550/arxiv.1003.5780 · pith_short_12: JIK54YJ4XJ5K · pith_short_16: JIK54YJ4XJ5K2BQO · pith_short_8: JIK54YJ4

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/JIK54YJ4XJ5K2BQOU3KX2ZYDER \
  | 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: 4a15de613cba7aad060ea6d57d67032470f6151070480fcfe836ddc6c3e7de90

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4f088bad8473dd7471e3071b29afa6af6526a84acb91518f2e45d6373ed36234",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2010-03-30T10:17:11Z",
    "title_canon_sha256": "a1d8ca20195351f84adb8b2413d63bc61c356293e960c01382063c3593ba2b22"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1003.5780",
    "kind": "arxiv",
    "version": 1
  }
}