Pith Number

pith:2GFQNRSG

pith:2013:2GFQNRSG3QKYXXGISULWOCZRZ7

not attested not anchored not stored refs pending

Faber-Krahn inequalities in sharp quantitative form

Bozhidar Velichkov, Guido De Philippis, Lorenzo Brasco

arxiv:1306.0392 v1 · 2013-06-03 · 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{2GFQNRSG3QKYXXGISULWOCZRZ7}

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	2026-05-18T01:28:15.211296Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d18b06c646dc158bdcc89517670b31cfe8df040f950ab9be3290439d515c38ab

Aliases

arxiv: 1306.0392 · arxiv_version: 1306.0392v1 · doi: 10.48550/arxiv.1306.0392 · pith_short_12: 2GFQNRSG3QKY · pith_short_16: 2GFQNRSG3QKYXXGI · pith_short_8: 2GFQNRSG

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/2GFQNRSG3QKYXXGISULWOCZRZ7 \
  | 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: d18b06c646dc158bdcc89517670b31cfe8df040f950ab9be3290439d515c38ab

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "97937f5fea462e6bd76e8e1810693e1faa088ceda6a0b02b2ed97da37b41aa06",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-06-03T13:09:45Z",
    "title_canon_sha256": "83eb79e8ddab00e0cfdabd41bd12db2ccb81b1113ee0cf1e2585c43ccb517d4e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.0392",
    "kind": "arxiv",
    "version": 1
  }
}