Pith Number

pith:GPWPVWR6

pith:2014:GPWPVWR6C3URLCSNUOHTJD3WKP

not attested not anchored not stored refs pending

Remainder Terms for Some Quantum Entropy Inequalities

Elliott H. Lieb, Eric A. Carlen

arxiv:1402.3840 v2 · 2014-02-16 · quant-ph · math-ph · math.MP · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GPWPVWR6C3URLCSNUOHTJD3WKP}

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	2026-05-18T02:39:48.400106Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

33ecfada3e16e9158a4da38f348f7653dc619ff3963212b163ccc8d09c748d5f

Aliases

arxiv: 1402.3840 · arxiv_version: 1402.3840v2 · doi: 10.48550/arxiv.1402.3840 · pith_short_12: GPWPVWR6C3UR · pith_short_16: GPWPVWR6C3URLCSN · pith_short_8: GPWPVWR6

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/GPWPVWR6C3URLCSNUOHTJD3WKP \
  | 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: 33ecfada3e16e9158a4da38f348f7653dc619ff3963212b163ccc8d09c748d5f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "79606255c6c043da3cfce618978d380c1e5cae01b5d4f0a290d257c095613b89",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2014-02-16T21:04:55Z",
    "title_canon_sha256": "cbfb91ced182e4d1b9d1316f0ce60411b317de6d1b065177b37aa567999407f3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1402.3840",
    "kind": "arxiv",
    "version": 2
  }
}