Pith Number

pith:MJ2B24DS

pith:2012:MJ2B24DSJMDLG44V3IGJFDLWPL

not attested not anchored not stored refs pending

Harnack inequality for fractional sub-Laplacians in Carnot groups

Bruno Franchi, Fausto Ferrari

arxiv:1206.0885 v4 · 2012-06-05 · 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{MJ2B24DSJMDLG44V3IGJFDLWPL}

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	2026-05-18T02:42:37.593951Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

62741d70724b06b37395da0c928d767afb0d76ceda08aa459586c4428cd98644

Aliases

arxiv: 1206.0885 · arxiv_version: 1206.0885v4 · doi: 10.48550/arxiv.1206.0885 · pith_short_12: MJ2B24DSJMDL · pith_short_16: MJ2B24DSJMDLG44V · pith_short_8: MJ2B24DS

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/MJ2B24DSJMDLG44V3IGJFDLWPL \
  | 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: 62741d70724b06b37395da0c928d767afb0d76ceda08aa459586c4428cd98644

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2359fa28e45e74023b366db60b136cfbee4ca5de9bac3a9416d38f7ce6d932d6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-06-05T11:39:09Z",
    "title_canon_sha256": "7cf1a3b0bcdec72fa19a250615b695d382bad9ff75a2ef5535c2880dbb08c678"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.0885",
    "kind": "arxiv",
    "version": 4
  }
}