Pith Number

pith:3J2Y6SAW

pith:2013:3J2Y6SAWJHXPSNJYTEUGVCO6SM

not attested not anchored not stored refs pending

Integral isoperimetric transference and dimensionless Sobolev inequalities

Joaquim Martin, Mario Milman

arxiv:1309.1980 v1 · 2013-09-08 · 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{3J2Y6SAWJHXPSNJYTEUGVCO6SM}

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	2026-05-18T00:43:36.361452Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

da758f481649eef9353899286a89de9317954244cb38a9ba5fe103b72cca44ba

Aliases

arxiv: 1309.1980 · arxiv_version: 1309.1980v1 · doi: 10.48550/arxiv.1309.1980 · pith_short_12: 3J2Y6SAWJHXP · pith_short_16: 3J2Y6SAWJHXPSNJY · pith_short_8: 3J2Y6SAW

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/3J2Y6SAWJHXPSNJYTEUGVCO6SM \
  | 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: da758f481649eef9353899286a89de9317954244cb38a9ba5fe103b72cca44ba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e45860e04213b1ee4970d38fa86f36a5c9a177ccd718b3db0026c6d8df16ab06",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2013-09-08T17:06:31Z",
    "title_canon_sha256": "cb5aba6fc04a740311ff9c4aa95689ab9def0051dbeb4042a447aab2c1db6ab2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.1980",
    "kind": "arxiv",
    "version": 1
  }
}