Pith Number

pith:F2WXLID2

pith:2011:F2WXLID2Q74Y3YCVXI7VDTUFOJ

not attested not anchored not stored refs pending

Injections de Sobolev probabilistes et applications

Gilles Lebeau (JAD), Nicolas Burq (LM-Orsay)

arxiv:1111.7310 v1 · 2011-11-30 · 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{F2WXLID2Q74Y3YCVXI7VDTUFOJ}

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	2026-05-18T04:07:18.135666Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2ead75a07a87f98de055ba3f51ce85726190dac8786644b15eec90ca72204bbf

Aliases

arxiv: 1111.7310 · arxiv_version: 1111.7310v1 · doi: 10.48550/arxiv.1111.7310 · pith_short_12: F2WXLID2Q74Y · pith_short_16: F2WXLID2Q74Y3YCV · pith_short_8: F2WXLID2

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/F2WXLID2Q74Y3YCVXI7VDTUFOJ \
  | 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: 2ead75a07a87f98de055ba3f51ce85726190dac8786644b15eec90ca72204bbf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "980353a8df15aa2cf5ce6c795196d0da8752d1636b1138a45f4845e52bc191fb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-11-30T20:37:46Z",
    "title_canon_sha256": "b1555183bd2caa929197a99196fc89beca69849a260ae3c4531143fb00363911"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.7310",
    "kind": "arxiv",
    "version": 1
  }
}