Pith Number

pith:VL5I2ACQ

pith:2011:VL5I2ACQAW6CVXW4OZDVHEBGVI

not attested not anchored not stored refs pending

The minimum entropy output of a quantum channel is locally additive

Gilad Gour, Shmuel Friedland

arxiv:1105.6122 v4 · 2011-05-30 · quant-ph · 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{VL5I2ACQAW6CVXW4OZDVHEBGVI}

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	2026-05-18T03:44:15.605059Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aafa8d005005bc2adedc7647539026aa31b37d8dfec4a5706aac2550a8488d30

Aliases

arxiv: 1105.6122 · arxiv_version: 1105.6122v4 · doi: 10.48550/arxiv.1105.6122 · pith_short_12: VL5I2ACQAW6C · pith_short_16: VL5I2ACQAW6CVXW4 · pith_short_8: VL5I2ACQ

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/VL5I2ACQAW6CVXW4OZDVHEBGVI \
  | 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: aafa8d005005bc2adedc7647539026aa31b37d8dfec4a5706aac2550a8488d30

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1366aecb9ac213822ba560eb4cb3172526c4ffbec830edd36200d1479d9c189d",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2011-05-30T21:50:29Z",
    "title_canon_sha256": "30a87387c13bbe5af13200b74077a73432d597dcf3ac4bc1490353df64da509e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.6122",
    "kind": "arxiv",
    "version": 4
  }
}