Pith Number

pith:LJ5TH3NV

pith:2013:LJ5TH3NVKC2IOODZFD6YHGOSYP

not attested not anchored not stored refs pending

Optimal Rellich-Sobolev constants and their extremals

Roberta Musina

arxiv:1307.7394 v3 · 2013-07-28 · 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{LJ5TH3NVKC2IOODZFD6YHGOSYP}

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	2026-05-18T03:01:10.387673Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5a7b33edb550b487387928fd8399d2c3ec279edad1dd2c086c8f6a0148b8ee04

Aliases

arxiv: 1307.7394 · arxiv_version: 1307.7394v3 · doi: 10.48550/arxiv.1307.7394 · pith_short_12: LJ5TH3NVKC2I · pith_short_16: LJ5TH3NVKC2IOODZ · pith_short_8: LJ5TH3NV

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/LJ5TH3NVKC2IOODZFD6YHGOSYP \
  | 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: 5a7b33edb550b487387928fd8399d2c3ec279edad1dd2c086c8f6a0148b8ee04

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "210e9144ca7859bd6177f3533ca1f277c00846e63d3370554885059e469f4320",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-07-28T19:40:03Z",
    "title_canon_sha256": "0e8734d9eecebdf9b66f30d035aeb41d398616069d07db01c3dc966ff50e12e1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.7394",
    "kind": "arxiv",
    "version": 3
  }
}