Pith Number

pith:AOF2VHWQ

pith:2026:AOF2VHWQCF7UNKH3D4YKPOFGQS

not attested not anchored not stored refs pending

Average entropy of Bogoliubov-Kubo-Mori random state ensemble

Lu wei, Sohail

arxiv:2606.17960 v1 · 2026-06-16 · math-ph · cs.IT · math.IT · math.MP · 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{AOF2VHWQCF7UNKH3D4YKPOFGQS}

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	2026-06-19T16:10:44.588081Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

038baa9ed0117f46a8fb1f30a7b8a6849de76bc6b51ba6d77b9de449d2c7d563

Aliases

arxiv: 2606.17960 · arxiv_version: 2606.17960v1 · doi: 10.48550/arxiv.2606.17960 · pith_short_12: AOF2VHWQCF7U · pith_short_16: AOF2VHWQCF7UNKH3 · pith_short_8: AOF2VHWQ

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/AOF2VHWQCF7UNKH3D4YKPOFGQS \
  | 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: 038baa9ed0117f46a8fb1f30a7b8a6849de76bc6b51ba6d77b9de449d2c7d563

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4e89a5aa3ed7494550f0b01eb50f7c50dcf24b98fe533c6be19080e13f17ed65",
    "cross_cats_sorted": [
      "cs.IT",
      "math.IT",
      "math.MP",
      "quant-ph"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-06-16T14:11:03Z",
    "title_canon_sha256": "6b9480fb3d532870c5b9f1c91786cac8a83bc3b72456ad49a29b99493c473efd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.17960",
    "kind": "arxiv",
    "version": 1
  }
}