Pith Number

pith:J4SBD66H

pith:2009:J4SBD66HS6OMK4NYZITQJCGFY5

not attested not anchored not stored refs pending

Random quantum channels II: Entanglement of random subspaces, Renyi entropy estimates and additivity problems

Beno\^it Collins (ICJ), Ion Nechita (ICJ)

arxiv:0906.1877 v3 · 2009-06-10 · math.PR · 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{J4SBD66HS6OMK4NYZITQJCGFY5}

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	2026-05-18T02:27:29.802614Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4f2411fbc7979cc571b8ca270488c5c76ea6ac3be1dd4fb47bcbfad64c7fa1ad

Aliases

arxiv: 0906.1877 · arxiv_version: 0906.1877v3 · doi: 10.48550/arxiv.0906.1877 · pith_short_12: J4SBD66HS6OM · pith_short_16: J4SBD66HS6OMK4NY · pith_short_8: J4SBD66H

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/J4SBD66HS6OMK4NYZITQJCGFY5 \
  | 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: 4f2411fbc7979cc571b8ca270488c5c76ea6ac3be1dd4fb47bcbfad64c7fa1ad

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d0cc12107befb015f7127bf1f231bad2c58966308b133f7a8a7323c5ea9ec091",
    "cross_cats_sorted": [
      "math.OA",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2009-06-10T08:19:54Z",
    "title_canon_sha256": "e18ca4bb99e08beaa4883a81424a688b6ee92e17a14ffb99c27d7ae2265439ce"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0906.1877",
    "kind": "arxiv",
    "version": 3
  }
}