Pith Number

pith:FA2ONE2Q

pith:2006:FA2ONE2Q6DZ22BQIC6WAKLHES3

not attested not anchored not stored refs pending

A Sharp Fannes-type Inequality for the von Neumann Entropy

Koenraad M.R. Audenaert

arxiv:quant-ph/0610146 v1 · 2006-10-18 · 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{FA2ONE2Q6DZ22BQIC6WAKLHES3}

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

SharedRep-RLHF: A Shared Representation Approach to RLHF with Diverse Preferences

Receipt and verification

First computed	2026-07-04T17:03:35.317059Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2834e69350f0f3ad060817ac052ce496f5ab6c43e19920918fcbc3919289216b

Aliases

arxiv: quant-ph/0610146 · arxiv_version: quant-ph/0610146v1 · doi: 10.48550/arxiv.quant-ph/0610146 · pith_short_12: FA2ONE2Q6DZ2 · pith_short_16: FA2ONE2Q6DZ22BQI · pith_short_8: FA2ONE2Q

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/FA2ONE2Q6DZ22BQIC6WAKLHES3 \
  | 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: 2834e69350f0f3ad060817ac052ce496f5ab6c43e19920918fcbc3919289216b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6e6bd1f843c1108f9546235d7e2818883f9d7bbd44f7ca7c7b571cc7bf43b0c0",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "quant-ph",
    "submitted_at": "2006-10-18T13:49:39Z",
    "title_canon_sha256": "1d06d7aa87253467ed6feb5d5c1c900e10078b49d1e7badfb162a4a65cd620a8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "quant-ph/0610146",
    "kind": "arxiv",
    "version": 1
  }
}