Pith Number

pith:LK2AOCYW

pith:2013:LK2AOCYWTE5FBTZVY23EWJIMJ4

not attested not anchored not stored refs pending

Improved interpolation inequalities on the sphere

Jean Dolbeault (CEREMADE), Maria J. Esteban (CEREMADE), Michael Loss, Michal Kowalczyk (DIM)

arxiv:1309.7931 v2 · 2013-09-30 · 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{LK2AOCYWTE5FBTZVY23EWJIMJ4}

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	2026-05-18T03:00:49.184161Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5ab4070b16993a50cf35c6b64b250c4f3a3acc7a1aaa2717747977b59f6d542a

Aliases

arxiv: 1309.7931 · arxiv_version: 1309.7931v2 · doi: 10.48550/arxiv.1309.7931 · pith_short_12: LK2AOCYWTE5F · pith_short_16: LK2AOCYWTE5FBTZV · pith_short_8: LK2AOCYW

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/LK2AOCYWTE5FBTZVY23EWJIMJ4 \
  | 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: 5ab4070b16993a50cf35c6b64b250c4f3a3acc7a1aaa2717747977b59f6d542a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "33f5f4211d549ab4fc476867a33e326c9e29025efd926262ae0a327d588e5dce",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-09-30T17:32:26Z",
    "title_canon_sha256": "046aa0b80740a63de84756c3d4d6b466c221896b39cb927434c99164e8260e84"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.7931",
    "kind": "arxiv",
    "version": 2
  }
}