Pith Number

pith:V5VZSH37

pith:2012:V5VZSH37QROU2537H4DEXLG6TP

not attested not anchored not stored refs pending

Fractional Sobolev Inequalities: Symmetrization, Isoperimetry and Interpolation

Joaquim Martin, Mario Milman

arxiv:1205.1231 v4 · 2012-05-06 · math.FA · math.AP · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{V5VZSH37QROU2537H4DEXLG6TP}

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	2026-05-18T02:55:18.743670Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

af6b991f7f845d4d777f3f064bacde9bdc42359573c879918d07353d7ba37f12

Aliases

arxiv: 1205.1231 · arxiv_version: 1205.1231v4 · doi: 10.48550/arxiv.1205.1231 · pith_short_12: V5VZSH37QROU · pith_short_16: V5VZSH37QROU2537 · pith_short_8: V5VZSH37

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/V5VZSH37QROU2537H4DEXLG6TP \
  | 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: af6b991f7f845d4d777f3f064bacde9bdc42359573c879918d07353d7ba37f12

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f38ee1a8ec9d394b92def44b6c8f700e92aed9d5c73580c1b249c77180063592",
    "cross_cats_sorted": [
      "math.AP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-05-06T16:12:01Z",
    "title_canon_sha256": "02636de46ee086c82adc0a920b359fa4bb3946cf9783abf4eaf4ec8bd657352f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.1231",
    "kind": "arxiv",
    "version": 4
  }
}