Pith Number

pith:VLVWM4WH

pith:2001:VLVWM4WHPUDPY6PQU5U6NNT4JD

not attested not anchored not stored refs pending

The asymptotic relative entropy of entanglement

B. De Moor, E. Jane, J. Eisert, K. Audenaert, M.B. Plenio, S. Virmani

arxiv:quant-ph/0103096 v2 · 2001-03-16 · 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{VLVWM4WHPUDPY6PQU5U6NNT4JD}

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	2026-07-04T14:48:02.770522Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aaeb6672c77d06fc79f0a769e6b67c48fd769ed728ea50398b57121fc671caa8

Aliases

arxiv: quant-ph/0103096 · arxiv_version: quant-ph/0103096v2 · doi: 10.48550/arxiv.quant-ph/0103096 · pith_short_12: VLVWM4WHPUDP · pith_short_16: VLVWM4WHPUDPY6PQ · pith_short_8: VLVWM4WH

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/VLVWM4WHPUDPY6PQU5U6NNT4JD \
  | 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: aaeb6672c77d06fc79f0a769e6b67c48fd769ed728ea50398b57121fc671caa8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6db37c71ebaacc12f462529a112f85cea3146847a80a771ef1406ca588d5e3f2",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "quant-ph",
    "submitted_at": "2001-03-16T19:10:53Z",
    "title_canon_sha256": "b9ebee160d36ee91ba4682fa6d14202724b2848facdaa9ed1b3cf08c4530d82b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "quant-ph/0103096",
    "kind": "arxiv",
    "version": 2
  }
}