Pith Number

pith:W4CHA2LI

pith:2013:W4CHA2LI7TRWCMGBB5GSTUPGCZ

not attested not anchored not stored refs pending

Almost one bit violation for the additivity of the minimum output entropy

Benoit Collins, Ion Nechita, Serban T. Belinschi

arxiv:1305.1567 v3 · 2013-05-07 · math-ph · math.MP · math.OA · 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{W4CHA2LI7TRWCMGBB5GSTUPGCZ}

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	2026-05-18T01:06:23.274465Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b704706968fce36130c10f4d29d1e6164810dba36c92855f761842d2ffe3b347

Aliases

arxiv: 1305.1567 · arxiv_version: 1305.1567v3 · doi: 10.48550/arxiv.1305.1567 · pith_short_12: W4CHA2LI7TRW · pith_short_16: W4CHA2LI7TRWCMGB · pith_short_8: W4CHA2LI

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/W4CHA2LI7TRWCMGBB5GSTUPGCZ \
  | 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: b704706968fce36130c10f4d29d1e6164810dba36c92855f761842d2ffe3b347

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "36427bb6b8f512dc43ffbc6a8ef791b3c530e497f374b579e0a00587bd9a915e",
    "cross_cats_sorted": [
      "math.MP",
      "math.OA",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2013-05-07T16:09:29Z",
    "title_canon_sha256": "fa1615a0482921f4252da824715f22ecc4982d6afd08d240849b5f297962450f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1305.1567",
    "kind": "arxiv",
    "version": 3
  }
}