Pith Number

pith:HRYDFGZ4

pith:2008:HRYDFGZ4C5FNOWFLCX7WEZOXSG

not attested not anchored not stored refs pending

On Gaussian MIMO BC-MAC Duality With Multiple Transmit Covariance Constraints

H. Vincent Poor, Lan Zhang, Rui Zhang, Yan Xin, Ying-Chang Liang

arxiv:0809.4101 v1 · 2008-09-24 · 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{HRYDFGZ4C5FNOWFLCX7WEZOXSG}

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	2026-07-04T15:14:34.703763Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3c70329b3c174ad758ab15ff6265d7919fa90e1ad47e1b8bed15bba7875a8a4c

Aliases

arxiv: 0809.4101 · arxiv_version: 0809.4101v1 · doi: 10.48550/arxiv.0809.4101 · pith_short_12: HRYDFGZ4C5FN · pith_short_16: HRYDFGZ4C5FNOWFL · pith_short_8: HRYDFGZ4

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/HRYDFGZ4C5FNOWFLCX7WEZOXSG \
  | 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: 3c70329b3c174ad758ab15ff6265d7919fa90e1ad47e1b8bed15bba7875a8a4c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b16424f7ca61197dcd2fecc2c6a6189609dde4c85e21847c677103484d27d23e",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2008-09-24T06:32:11Z",
    "title_canon_sha256": "44f37a9d7f88d7f22c4ec67d778ec61e94918e4aeb56d6ea4b84f937ccd70fdb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0809.4101",
    "kind": "arxiv",
    "version": 1
  }
}