Pith Number

pith:HVQN7W2U

pith:2011:HVQN7W2UBHIHFKBT4OCHSZJ37B

not attested not anchored not stored refs pending

On the $L^{1}$-Liouville property of stochastically incomplete manifolds

Alberto G. Setti, G. Pacelli Bessa, Stefano Pigola

arxiv:1111.4074 v1 · 2011-11-17 · 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{HVQN7W2UBHIHFKBT4OCHSZJ37B}

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	2026-05-18T04:08:12.028154Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3d60dfdb5409d072a833e38479653bf87ff23caf99450d49dd69cf0d3afba174

Aliases

arxiv: 1111.4074 · arxiv_version: 1111.4074v1 · doi: 10.48550/arxiv.1111.4074 · pith_short_12: HVQN7W2UBHIH · pith_short_16: HVQN7W2UBHIHFKBT · pith_short_8: HVQN7W2U

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/HVQN7W2UBHIHFKBT4OCHSZJ37B \
  | 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: 3d60dfdb5409d072a833e38479653bf87ff23caf99450d49dd69cf0d3afba174

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a9481820085e4854fe1a6ab854f4547f7679dc8a44579b44425c86b441253e31",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2011-11-17T12:32:12Z",
    "title_canon_sha256": "38b1c35c375182a9d6b08f2f4e47bd32dc482faca50e6b444f45958995c5ec40"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.4074",
    "kind": "arxiv",
    "version": 1
  }
}