Pith Number

pith:7TG4A2Y3

pith:2012:7TG4A2Y3N7OHQQPLGFZFCQ6YXT

not attested not anchored not stored refs pending

Majorization-preserving quantum channels

Lin Zhang

arxiv:1209.5233 v2 · 2012-09-24 · 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{7TG4A2Y3N7OHQQPLGFZFCQ6YXT}

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	2026-05-18T03:38:23.104983Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fccdc06b1b6fdc7841eb31725143d8bce4323923cf7d1182924361985b92c47b

Aliases

arxiv: 1209.5233 · arxiv_version: 1209.5233v2 · doi: 10.48550/arxiv.1209.5233 · pith_short_12: 7TG4A2Y3N7OH · pith_short_16: 7TG4A2Y3N7OHQQPL · pith_short_8: 7TG4A2Y3

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/7TG4A2Y3N7OHQQPLGFZFCQ6YXT \
  | 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: fccdc06b1b6fdc7841eb31725143d8bce4323923cf7d1182924361985b92c47b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eb62907ed964e4965db4c60ac78a90592365e8649f1581d087d8d0b9a6f46af4",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2012-09-24T11:41:34Z",
    "title_canon_sha256": "c728bfb04e55c0b68d64ceee1cde132295bc187587412bd3e4b41d71d4574a16"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.5233",
    "kind": "arxiv",
    "version": 2
  }
}