Pith Number

pith:O5PFBM4K

pith:2011:O5PFBM4KDVH6NPE5IJ32CMGGSW

not attested not anchored not stored refs pending

Conditions for equality between entanglement-assisted and unassisted classical capacities of a quantum channel

M. E. Shirokov

arxiv:1105.1040 v4 · 2011-05-05 · 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{O5PFBM4KDVH6NPE5IJ32CMGGSW}

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	2026-05-18T03:49:10.530295Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

775e50b38a1d4fe6bc9d4277a130c6958ad1717a3c50db173ba636ee85bc4abb

Aliases

arxiv: 1105.1040 · arxiv_version: 1105.1040v4 · doi: 10.48550/arxiv.1105.1040 · pith_short_12: O5PFBM4KDVH6 · pith_short_16: O5PFBM4KDVH6NPE5 · pith_short_8: O5PFBM4K

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/O5PFBM4KDVH6NPE5IJ32CMGGSW \
  | 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: 775e50b38a1d4fe6bc9d4277a130c6958ad1717a3c50db173ba636ee85bc4abb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bd7f09b80ddc4c380a30a7b711afe6d472962f28147b2adc458bfb7b943085d3",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2011-05-05T11:32:31Z",
    "title_canon_sha256": "4c46532d297b36ab1988a7ed6472c756adaee70268c47405b578fba0250d89f5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.1040",
    "kind": "arxiv",
    "version": 4
  }
}