Pith Number

pith:MSIXKXXL

pith:2011:MSIXKXXLP474SECZB3CXHSJTP4

not attested not anchored not stored refs pending

Convexity of quantum $\chi^2$-divergence

Frank Hansen

arxiv:1102.2989 v2 · 2011-02-15 · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MSIXKXXLP474SECZB3CXHSJTP4}

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	2026-05-18T03:44:24.695757Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6491755eeb7f3fc910590ec573c9337f1cdd29eb313d3407a16c5fecd9e9eb78

Aliases

arxiv: 1102.2989 · arxiv_version: 1102.2989v2 · doi: 10.48550/arxiv.1102.2989 · pith_short_12: MSIXKXXLP474 · pith_short_16: MSIXKXXLP474SECZ · pith_short_8: MSIXKXXL

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/MSIXKXXLP474SECZB3CXHSJTP4 \
  | 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: 6491755eeb7f3fc910590ec573c9337f1cdd29eb313d3407a16c5fecd9e9eb78

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7a10e90e5767e818e36dc0b3c02de01133170849461e6f24e3905d4242090435",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2011-02-15T08:21:10Z",
    "title_canon_sha256": "c724fad09a4b7dca247d783a8d8468244492ab766972ead1c18c5c861e37f24b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.2989",
    "kind": "arxiv",
    "version": 2
  }
}