Pith Number

pith:ZI6VA2PM

pith:2016:ZI6VA2PMN6Z37LK52QBKY475GL

not attested not anchored not stored refs pending

Haagerup's inequality and additivity violation of the Minimum Output Entropy

Benoit Collins

arxiv:1603.00577 v1 · 2016-03-02 · math.OA · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZI6VA2PMN6Z37LK52QBKY475GL}

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	2026-05-17T23:52:44.722450Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ca3d5069ec6fb3bfad5dd402ac73fd32eb423a54e5f57213174af9283e20440a

Aliases

arxiv: 1603.00577 · arxiv_version: 1603.00577v1 · doi: 10.48550/arxiv.1603.00577 · pith_short_12: ZI6VA2PMN6Z3 · pith_short_16: ZI6VA2PMN6Z37LK5 · pith_short_8: ZI6VA2PM

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/ZI6VA2PMN6Z37LK52QBKY475GL \
  | 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: ca3d5069ec6fb3bfad5dd402ac73fd32eb423a54e5f57213174af9283e20440a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "602b4701e2c435a26df155635624d5a8e85cd946402149384b4f5e2c7785c7ea",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2016-03-02T04:53:30Z",
    "title_canon_sha256": "619f7ed6ae49626981496d5813677e764b6a1c2970b87b4382ed02a4202b02d9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.00577",
    "kind": "arxiv",
    "version": 1
  }
}