Pith Number

pith:XLKJNJ7R

pith:2010:XLKJNJ7RXSHFDEZPQMJDSFJCPU

not attested not anchored not stored refs pending

Higher-order multilinear Poincar\'e and Sobolev inequalities in Carnot groups

Kabe Moen, Virginia Naibo

arxiv:1008.0414 v2 · 2010-08-02 · math.CA · 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{XLKJNJ7RXSHFDEZPQMJDSFJCPU}

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	2026-05-18T03:25:44.163634Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bad496a7f1bc8e51932f83123915227d0dc1cb2ee91718bc9951bf031ea9a8e7

Aliases

arxiv: 1008.0414 · arxiv_version: 1008.0414v2 · doi: 10.48550/arxiv.1008.0414 · pith_short_12: XLKJNJ7RXSHF · pith_short_16: XLKJNJ7RXSHFDEZP · pith_short_8: XLKJNJ7R

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/XLKJNJ7RXSHFDEZPQMJDSFJCPU \
  | 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: bad496a7f1bc8e51932f83123915227d0dc1cb2ee91718bc9951bf031ea9a8e7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3c0fbb48197afc1090b54a70fbc2d655116a3b88945d444bdc1cb9af1a0c6f6e",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2010-08-02T21:25:36Z",
    "title_canon_sha256": "abe26a50f074f50e11ab820eca853825627b0333288569865329f7c2a58cce34"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1008.0414",
    "kind": "arxiv",
    "version": 2
  }
}