Pith Number

pith:J77WZK3R

pith:2014:J77WZK3RG5IAVTZ5I57AUBQDUJ

not attested not anchored not stored refs pending

Equivalence between Poly\'a-Szeg\H{o} and relative capacity inequalities under rearrangement

Jean Van Schaftingen

arxiv:1401.2780 v1 · 2014-01-13 · math.FA · 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{J77WZK3RG5IAVTZ5I57AUBQDUJ}

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	2026-05-18T02:38:10.401219Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4fff6cab7137500acf3d477e0a0603a2705a9d4f1ed79a64d4743c5e307ea4de

Aliases

arxiv: 1401.2780 · arxiv_version: 1401.2780v1 · doi: 10.48550/arxiv.1401.2780 · pith_short_12: J77WZK3RG5IA · pith_short_16: J77WZK3RG5IAVTZ5 · pith_short_8: J77WZK3R

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/J77WZK3RG5IAVTZ5I57AUBQDUJ \
  | 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: 4fff6cab7137500acf3d477e0a0603a2705a9d4f1ed79a64d4743c5e307ea4de

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9fbbaaea498c9d2cdf32470fc4462d952aa1328b27de4a8d7fde7afde28a5355",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2014-01-13T10:48:36Z",
    "title_canon_sha256": "6107ca32c73f527b64f042ba0f88f1ce3c0e466dd41d8e350944cb53a3afedad"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1401.2780",
    "kind": "arxiv",
    "version": 1
  }
}