Pith Number

pith:COIDST27

pith:2000:COIDST27HMYC7HJBRWEPRQVEMS

not attested not anchored not stored refs pending

Relative entropy in quantum information theory

Benjamin Schumacher (Kenyon College), Michael D. Westmoreland (Denison University)

arxiv:quant-ph/0004045 v1 · 2000-04-10 · 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{COIDST27HMYC7HJBRWEPRQVEMS}

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

1 paper in Pith

Monotonicity of the Relative Entropy and the Two-sided Bogoliubov Inequality in von Neumann Algebras

Receipt and verification

First computed	2026-07-04T14:45:27.899333Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1390394f5f3b302f9d218d88f8c2a464928be7d250de302cc766c861240a391c

Aliases

arxiv: quant-ph/0004045 · arxiv_version: quant-ph/0004045v1 · doi: 10.48550/arxiv.quant-ph/0004045 · pith_short_12: COIDST27HMYC · pith_short_16: COIDST27HMYC7HJB · pith_short_8: COIDST27

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/COIDST27HMYC7HJBRWEPRQVEMS \
  | 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: 1390394f5f3b302f9d218d88f8c2a464928be7d250de302cc766c861240a391c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4018d9851dfb915d964e6efa7b168c31c9da09ce846b57fb55ac8ad0394ad6b4",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "quant-ph",
    "submitted_at": "2000-04-10T15:56:40Z",
    "title_canon_sha256": "c980ac5b1711b1d1237c3ec6f0257f621bcedb1e2c1e37a181863e66a2f504ea"
  },
  "schema_version": "1.0",
  "source": {
    "id": "quant-ph/0004045",
    "kind": "arxiv",
    "version": 1
  }
}