Pith Number

pith:VPJ7MN7F

pith:2013:VPJ7MN7FQYPQUCKLG3DPMVAS4M

not attested not anchored not stored refs pending

Refined Sobolev inequalities on manifolds with ends

Jean-Marc Bouclet, Yannick Sire

arxiv:1308.0853 v2 · 2013-08-04 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VPJ7MN7FQYPQUCKLG3DPMVAS4M}

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	2026-05-18T03:05:01.265608Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

abd3f637e5861f0a094b36c6f65412e3318744cc7bf73b2644019837d2206ed5

Aliases

arxiv: 1308.0853 · arxiv_version: 1308.0853v2 · doi: 10.48550/arxiv.1308.0853 · pith_short_12: VPJ7MN7FQYPQ · pith_short_16: VPJ7MN7FQYPQUCKL · pith_short_8: VPJ7MN7F

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/VPJ7MN7FQYPQUCKLG3DPMVAS4M \
  | 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: abd3f637e5861f0a094b36c6f65412e3318744cc7bf73b2644019837d2206ed5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5c54a0801212939a087f3740e2e64125fb2117f5d06040b84b8b03b00969dc62",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2013-08-04T22:11:07Z",
    "title_canon_sha256": "9e6119f7af9cfee78345bb0e2d7faf3fb15f654618d9cc7044360cf8aaab661b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.0853",
    "kind": "arxiv",
    "version": 2
  }
}