Pith Number

pith:7MHETY3N

pith:2026:7MHETY3NMTYT4UOYIHSNJMWB2W

not attested not anchored not stored refs pending

Exact characterizations for quantum conditional mutual information and some other entropies

Zhou Gang

arxiv:2603.14650 v2 · 2026-03-15 · quant-ph · math-ph · math.MP · math.OA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7MHETY3NMTYT4UOYIHSNJMWB2W}

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	2026-05-26T02:05:08.430126Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fb0e49e36d64f13e51d841e4d4b2c1d5a7adb99a44a5f376f0f9233faac36d4d

Aliases

arxiv: 2603.14650 · arxiv_version: 2603.14650v2 · doi: 10.48550/arxiv.2603.14650 · pith_short_12: 7MHETY3NMTYT · pith_short_16: 7MHETY3NMTYT4UOY · pith_short_8: 7MHETY3N

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/7MHETY3NMTYT4UOYIHSNJMWB2W \
  | 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: fb0e49e36d64f13e51d841e4d4b2c1d5a7adb99a44a5f376f0f9233faac36d4d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b4a7b998bedbd3d1aba7919d4906c6b349426accbe39c2a7ba53aa2f5503525d",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.OA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-03-15T23:08:57Z",
    "title_canon_sha256": "fa807e7dbe0e27062b9aca5cda62e1130bd78ee3bdf82bd2e2ba08c541ba02ef"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.14650",
    "kind": "arxiv",
    "version": 2
  }
}