Pith Number

pith:VZCAH4VE

pith:2019:VZCAH4VEF7T572RADF67FBQ4CS

not attested not anchored not stored refs pending

Generality of Lieb's Concavity Theorem

De Huang

arxiv:1906.00002 v1 · 2019-05-30 · math.FA · 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{VZCAH4VEF7T572RADF67FBQ4CS}

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	2026-05-17T23:44:33.744811Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae4403f2a42fe7dfea20197df2861c1482543b488ec71f99dead5f0622103068

Aliases

arxiv: 1906.00002 · arxiv_version: 1906.00002v1 · doi: 10.48550/arxiv.1906.00002 · pith_short_12: VZCAH4VEF7T5 · pith_short_16: VZCAH4VEF7T572RA · pith_short_8: VZCAH4VE

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/VZCAH4VEF7T572RADF67FBQ4CS \
  | 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: ae4403f2a42fe7dfea20197df2861c1482543b488ec71f99dead5f0622103068

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "41f313ef71f126be8ecc5fb7c9826fbc4e1ce5e85cfb905f4e24e16d12d8ce80",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2019-05-30T21:37:01Z",
    "title_canon_sha256": "f6af9e640fac4f0a559f78c9b271162c0c7751f8d7c315e693a52fa68c125d61"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1906.00002",
    "kind": "arxiv",
    "version": 1
  }
}