Pith Number

pith:Q63JCVZS

pith:2010:Q63JCVZS5UM67IH4KO52YYLKEN

not attested not anchored not stored refs pending

Non-Additivity of Minimum Output p-$\mathbf{R\acute{e}nyi}$ Entropy

Mingsheng Ying, Nengkun Yu

arxiv:1006.1733 v2 · 2010-06-09 · 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{Q63JCVZS5UM67IH4KO52YYLKEN}

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	2026-05-18T03:37:53.495780Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

87b6915732ed19efa0fc53bbac616a2349cd211d3b88f824ff2e0975ea9add75

Aliases

arxiv: 1006.1733 · arxiv_version: 1006.1733v2 · doi: 10.48550/arxiv.1006.1733 · pith_short_12: Q63JCVZS5UM6 · pith_short_16: Q63JCVZS5UM67IH4 · pith_short_8: Q63JCVZS

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/Q63JCVZS5UM67IH4KO52YYLKEN \
  | 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: 87b6915732ed19efa0fc53bbac616a2349cd211d3b88f824ff2e0975ea9add75

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ac68261a0d5b44d5555f0508c85617729515d6e4b473ca5e3855d94551b39b85",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2010-06-09T08:02:36Z",
    "title_canon_sha256": "25cff6519a0f046737581889859509b95a2b7c4df21b568ab145e95c65d27601"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1006.1733",
    "kind": "arxiv",
    "version": 2
  }
}