Pith Number

pith:JEZD2SZK

pith:2011:JEZD2SZKYF73NV66LAEDNTOA3P

not attested not anchored not stored refs pending

Entropy, Stochastic Matrices, and Quantum Operations

Lin Zhang

arxiv:1110.6321 v2 · 2011-10-28 · 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{JEZD2SZKYF73NV66LAEDNTOA3P}

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	2026-05-18T02:59:45.350375Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

49323d4b2ac17fb6d7de580836cdc0dbdd10aae18387215c58547808efacad30

Aliases

arxiv: 1110.6321 · arxiv_version: 1110.6321v2 · doi: 10.48550/arxiv.1110.6321 · pith_short_12: JEZD2SZKYF73 · pith_short_16: JEZD2SZKYF73NV66 · pith_short_8: JEZD2SZK

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/JEZD2SZKYF73NV66LAEDNTOA3P \
  | 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: 49323d4b2ac17fb6d7de580836cdc0dbdd10aae18387215c58547808efacad30

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "18e31dd36659caa5a02549d9564b0ce11cbd59cf8e68bab9798076691c563567",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2011-10-28T12:50:57Z",
    "title_canon_sha256": "634fab6d0c8e00f07faafacec943ebf9fbeb46c76c42afa5ea9b810613962223"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.6321",
    "kind": "arxiv",
    "version": 2
  }
}