Pith Number

pith:PUM5TQPU

pith:2009:PUM5TQPUMR7GTYLRI5BSPE2QQK

not attested not anchored not stored refs pending

Multiple-Input Multiple-Output Gaussian Broadcast Channels with Common and Confidential Messages

Hung D. Ly, Tie Liu, Yingbin Liang

arxiv:0907.2599 v1 · 2009-07-15 · cs.IT · math.IT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PUM5TQPUMR7GTYLRI5BSPE2QQK}

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	2026-05-18T00:58:48.022264Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7d19d9c1f4647e69e17147432793508281bae2156ff19c855fc06dc7eb9900bc

Aliases

arxiv: 0907.2599 · arxiv_version: 0907.2599v1 · doi: 10.48550/arxiv.0907.2599 · pith_short_12: PUM5TQPUMR7G · pith_short_16: PUM5TQPUMR7GTYLR · pith_short_8: PUM5TQPU

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/PUM5TQPUMR7GTYLRI5BSPE2QQK \
  | 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: 7d19d9c1f4647e69e17147432793508281bae2156ff19c855fc06dc7eb9900bc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c7b98dbd569d1a44f78706739189aa3f331acf5bc37dcbd24f0f8f7794200e2b",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2009-07-15T14:35:13Z",
    "title_canon_sha256": "a2cd4d8ed970c117075f4e19878d7c4fcc252076806965cd75a4e8e69e20a375"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0907.2599",
    "kind": "arxiv",
    "version": 1
  }
}