Pith Number

pith:FCHJ2FMZ

pith:2018:FCHJ2FMZJPA276UBEB7YTLLCNV

not attested not anchored not stored refs pending

Strong Convexity of Sandwiched Entropies and Related Optimization Problems

Rajendra Bhatia, Tanvi Jain, Yongdo Lim

arxiv:1807.00978 v2 · 2018-07-03 · 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{FCHJ2FMZJPA276UBEB7YTLLCNV}

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	2026-05-18T00:03:16.013078Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

288e9d15994bc1affa81207f89ad626d6c3fe59b5bd22c8c7c3f8c2cbcad7b83

Aliases

arxiv: 1807.00978 · arxiv_version: 1807.00978v2 · doi: 10.48550/arxiv.1807.00978 · pith_short_12: FCHJ2FMZJPA2 · pith_short_16: FCHJ2FMZJPA276UB · pith_short_8: FCHJ2FMZ

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/FCHJ2FMZJPA276UBEB7YTLLCNV \
  | 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: 288e9d15994bc1affa81207f89ad626d6c3fe59b5bd22c8c7c3f8c2cbcad7b83

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e27ff247d29fa52548df3859f74528af819ff7bf8d5a92a8b32113a778edc92a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2018-07-03T05:12:19Z",
    "title_canon_sha256": "d21b8b145bf712d2589103fa9a26aeaaa49e55181e325f251753ecf8fd6452cd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1807.00978",
    "kind": "arxiv",
    "version": 2
  }
}