Pith Number

pith:CODUZN37

pith:2003:CODUZN377WZCDDZ3S6EAAOSMDG

not attested not anchored not stored refs pending

Structure of states which satisfy strong subadditivity of quantum entropy with equality

Andreas Winter, Denes Petz, Patrick Hayden, Richard Jozsa

arxiv:quant-ph/0304007 v2 · 2003-04-01 · 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{CODUZN377WZCDDZ3S6EAAOSMDG}

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.

Cited by

4 papers in Pith

Conditional Independence of 1D Gibbs States with Applications to Efficient Learning

Random dilation superchannel

The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole

Entanglement inequalities, black holes and the architecture of typical states

Receipt and verification

First computed	2026-07-04T14:46:09.310814Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

13874cb77ffdb2218f3b9788003a4c199f6c338f79f85d0c39b684d94d483ffd

Aliases

arxiv: quant-ph/0304007 · arxiv_version: quant-ph/0304007v2 · doi: 10.48550/arxiv.quant-ph/0304007 · pith_short_12: CODUZN377WZC · pith_short_16: CODUZN377WZCDDZ3 · pith_short_8: CODUZN37

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/CODUZN377WZCDDZ3S6EAAOSMDG \
  | 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: 13874cb77ffdb2218f3b9788003a4c199f6c338f79f85d0c39b684d94d483ffd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bfce8c2f2cd0b94fbf037a614a3da499dfada3975bb9d84d4c42236096ea7542",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "quant-ph",
    "submitted_at": "2003-04-01T14:43:10Z",
    "title_canon_sha256": "688779d103ca96b36b2862fc79615b5b79b22bb24f50b959e2b51aec01caa2ae"
  },
  "schema_version": "1.0",
  "source": {
    "id": "quant-ph/0304007",
    "kind": "arxiv",
    "version": 2
  }
}