Pith Number

pith:JNYCJY7H

pith:2008:JNYCJY7HUTUCUJDW5EJWIGRNME

not attested not anchored not stored refs pending

Basic properties of nonsmooth Hormander's vector fields and Poincare's inequality

Luca Brandolini, Marco Bramanti, Marco Pedroni

arxiv:0809.2872 v2 · 2008-09-17 · 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{JNYCJY7HUTUCUJDW5EJWIGRNME}

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	2026-05-18T03:17:57.829593Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4b7024e3e7a4e82a2476e913641a2d613ae9f6c190f128331616c5f8c1785c69

Aliases

arxiv: 0809.2872 · arxiv_version: 0809.2872v2 · doi: 10.48550/arxiv.0809.2872 · pith_short_12: JNYCJY7HUTUC · pith_short_16: JNYCJY7HUTUCUJDW · pith_short_8: JNYCJY7H

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/JNYCJY7HUTUCUJDW5EJWIGRNME \
  | 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: 4b7024e3e7a4e82a2476e913641a2d613ae9f6c190f128331616c5f8c1785c69

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cbf4aee71696fa1eea7e8732c993fbc70fc6ca0437252c58fdf1d2f86d06357b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2008-09-17T08:04:45Z",
    "title_canon_sha256": "a51491277197df13a0736d8022671e6a7ad63fdef604e3c0e9de276ed0fa3a51"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0809.2872",
    "kind": "arxiv",
    "version": 2
  }
}