Pith Number

pith:F3N7PJ6D

pith:2011:F3N7PJ6DD7QXMBWH4H3ZOIHJY2

not attested not anchored not stored refs pending

Factoring Sobolev inequalities through classes of functions

David Alonso-Guti\'errez, Jes\'us Bastero, Julio Bernu\'es

arxiv:1107.2139 v1 · 2011-07-11 · 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{F3N7PJ6DD7QXMBWH4H3ZOIHJY2}

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	2026-05-18T04:18:32.836755Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2edbf7a7c31fe17606c7e1f79720e9c68f3b27f130563f497ad80dd5b2e4b7f9

Aliases

arxiv: 1107.2139 · arxiv_version: 1107.2139v1 · doi: 10.48550/arxiv.1107.2139 · pith_short_12: F3N7PJ6DD7QX · pith_short_16: F3N7PJ6DD7QXMBWH · pith_short_8: F3N7PJ6D

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/F3N7PJ6DD7QXMBWH4H3ZOIHJY2 \
  | 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: 2edbf7a7c31fe17606c7e1f79720e9c68f3b27f130563f497ad80dd5b2e4b7f9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "96aed0b6581cdf468becb355dc576687bb6c27c9edff8375470ac80bff964f4a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2011-07-11T20:38:39Z",
    "title_canon_sha256": "0464b853a9453ce624c6078c28d2613a9742e8d24973ce8d3688c6eae92e5e56"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.2139",
    "kind": "arxiv",
    "version": 1
  }
}