Pith Number

pith:2A4RF2UT

pith:2010:2A4RF2UTFYG6KACZ77XTVKIM5G

not attested not anchored not stored refs pending

Operator-sum Representation for Bosonic Gaussian Channels

J. Solomon Ivan, Krishnakumar Sabapathy, R. Simon

arxiv:1012.4266 v1 · 2010-12-20 · 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{2A4RF2UTFYG6KACZ77XTVKIM5G}

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	2026-05-18T03:23:47.336155Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d03912ea932e0de50059ffef3aa90ce9a14b843619d96d3fda327551abe0af03

Aliases

arxiv: 1012.4266 · arxiv_version: 1012.4266v1 · doi: 10.48550/arxiv.1012.4266 · pith_short_12: 2A4RF2UTFYG6 · pith_short_16: 2A4RF2UTFYG6KACZ · pith_short_8: 2A4RF2UT

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/2A4RF2UTFYG6KACZ77XTVKIM5G \
  | 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: d03912ea932e0de50059ffef3aa90ce9a14b843619d96d3fda327551abe0af03

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0b3a63bf86059c76bbae1b0ae4671a0af3d8a7029797aa38351c5bb3750b8c33",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2010-12-20T09:24:59Z",
    "title_canon_sha256": "b471855b3e9660863d2dc6a8b25c02a84e7241b4ab91eefce39cacc6810b0157"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.4266",
    "kind": "arxiv",
    "version": 1
  }
}