Pith Number

pith:VVBWUZB3

pith:2014:VVBWUZB3NSDM2AHNTVSKXEM2NG

not attested not anchored not stored refs pending

Some Operator and Trace Function Convexity Theorems

Elliott H. Lieb, Eric A. Carlen, Rupert L. Frank

arxiv:1409.0564 v5 · 2014-09-01 · math-ph · math.MP · quant-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VVBWUZB3NSDM2AHNTVSKXEM2NG}

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	2026-05-18T01:36:56.861870Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ad436a643b6c86cd00ed9d64ab919a698c39be4e0c650a0ab23f4be7616dbfd7

Aliases

arxiv: 1409.0564 · arxiv_version: 1409.0564v5 · doi: 10.48550/arxiv.1409.0564 · pith_short_12: VVBWUZB3NSDM · pith_short_16: VVBWUZB3NSDM2AHN · pith_short_8: VVBWUZB3

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/VVBWUZB3NSDM2AHNTVSKXEM2NG \
  | 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: ad436a643b6c86cd00ed9d64ab919a698c39be4e0c650a0ab23f4be7616dbfd7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cdd7ee8167a99e20f95acea3f9f7dd66ae02ea7ed35aa0e6ca15eb0583ad0426",
    "cross_cats_sorted": [
      "math.MP",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2014-09-01T21:00:11Z",
    "title_canon_sha256": "29e14ae8bc20f70d1ad30d5f1a8d8d47486ec76eabde1449c0116239bc09369b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1409.0564",
    "kind": "arxiv",
    "version": 5
  }
}