Pith Number

pith:G2J4LVTI

pith:2013:G2J4LVTIHD5KFB2DICTLO5WRNS

not attested not anchored not stored refs pending

Operators That Attain their Minima

Wladimir Neves, Xavier Carvajal

arxiv:1304.2684 v2 · 2013-04-09 · 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{G2J4LVTIHD5KFB2DICTLO5WRNS}

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	2026-05-18T03:25:43.171067Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3693c5d66838faa2874340a6b776d16c934ccc6ed16e9810dc112288a0da65ea

Aliases

arxiv: 1304.2684 · arxiv_version: 1304.2684v2 · doi: 10.48550/arxiv.1304.2684 · pith_short_12: G2J4LVTIHD5K · pith_short_16: G2J4LVTIHD5KFB2D · pith_short_8: G2J4LVTI

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/G2J4LVTIHD5KFB2DICTLO5WRNS \
  | 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: 3693c5d66838faa2874340a6b776d16c934ccc6ed16e9810dc112288a0da65ea

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "916b9a617940e43bc74be6d018b94aecc4f7e3b6a4f22e59d3638a6eccffe041",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2013-04-09T18:12:18Z",
    "title_canon_sha256": "52bde0ce027025c60cb4efcda4f2a60363ce004baabe06377f936a46e61675da"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.2684",
    "kind": "arxiv",
    "version": 2
  }
}