Pith Number

pith:OU24FIMJ

pith:2012:OU24FIMJ2AVDMYADODW3O2C2GL

not attested not anchored not stored refs pending

Optimal limiting embeddings for $\Delta$-reduced Sobolev spaces in $L^1$

Carlo Morpurgo, Luigi Fontana

arxiv:1202.1133 v3 · 2012-02-06 · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OU24FIMJ2AVDMYADODW3O2C2GL}

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	2026-05-18T03:30:02.963598Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7535c2a189d02a36600370edb7685a32ca6164bb7bd10357d880266a4098859c

Aliases

arxiv: 1202.1133 · arxiv_version: 1202.1133v3 · doi: 10.48550/arxiv.1202.1133 · pith_short_12: OU24FIMJ2AVD · pith_short_16: OU24FIMJ2AVDMYAD · pith_short_8: OU24FIMJ

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/OU24FIMJ2AVDMYADODW3O2C2GL \
  | 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: 7535c2a189d02a36600370edb7685a32ca6164bb7bd10357d880266a4098859c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "08c95a2ab89900876446e58c276fcc895627eff1ab774f82eac195e654af9273",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-02-06T13:25:59Z",
    "title_canon_sha256": "5a74f09e8b6328578b7922099b09a6556e0d0558b7c8b44e4aec10fceb5649d9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1202.1133",
    "kind": "arxiv",
    "version": 3
  }
}