Pith Number

pith:DNSJH2L3

pith:2015:DNSJH2L32XRVIFNUYL6BTTG5IP

not attested not anchored not stored refs pending

On Variational Expressions for Quantum Relative Entropies

Marco Tomamichel, Mario Berta, Omar Fawzi

arxiv:1512.02615 v2 · 2015-12-08 · quant-ph · cs.IT · math-ph · math.IT · 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{DNSJH2L32XRVIFNUYL6BTTG5IP}

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	2026-05-18T00:31:05.635886Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1b6493e97bd5e35415b4c2fc19ccdd43eb1991aa7f8bb0fa96337e801eee79da

Aliases

arxiv: 1512.02615 · arxiv_version: 1512.02615v2 · doi: 10.48550/arxiv.1512.02615 · pith_short_12: DNSJH2L32XRV · pith_short_16: DNSJH2L32XRVIFNU · pith_short_8: DNSJH2L3

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/DNSJH2L32XRVIFNUYL6BTTG5IP \
  | 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: 1b6493e97bd5e35415b4c2fc19ccdd43eb1991aa7f8bb0fa96337e801eee79da

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f0cfe74afae426bf0ad938586ac5511bd436a513964c2c825925539ed4ef3bf1",
    "cross_cats_sorted": [
      "cs.IT",
      "math-ph",
      "math.IT",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2015-12-08T20:14:34Z",
    "title_canon_sha256": "45c0821570bfee671f64b16aa0018c600b4b3cac4eb53c578710f66a3489e591"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.02615",
    "kind": "arxiv",
    "version": 2
  }
}