Pith Number

pith:FZXTWN2C

pith:2013:FZXTWN2CY72N7BXK3ZH6T3YQYI

not attested not anchored not stored refs pending

Weighted Sum Rate Optimization for Downlink Multiuser MIMO Systems with per Antenna Power Constraint: Downlink-Uplink Duality Approach

Luc Vandendorpe, Tadilo Endeshaw Bogale

arxiv:1311.6440 v1 · 2013-11-25 · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FZXTWN2CY72N7BXK3ZH6T3YQYI}

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	2026-05-18T03:06:14.126412Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2e6f3b3742c7f4df86eade4fe9ef10c23f60c1c9948800c8d45bffd3fb5885b9

Aliases

arxiv: 1311.6440 · arxiv_version: 1311.6440v1 · doi: 10.48550/arxiv.1311.6440 · pith_short_12: FZXTWN2CY72N · pith_short_16: FZXTWN2CY72N7BXK · pith_short_8: FZXTWN2C

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/FZXTWN2CY72N7BXK3ZH6T3YQYI \
  | 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: 2e6f3b3742c7f4df86eade4fe9ef10c23f60c1c9948800c8d45bffd3fb5885b9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0251de8d39e2f311b0f4776f9cf7cfeb4cbd2d3dd97dbb633956ea9c0755028c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2013-11-25T20:31:42Z",
    "title_canon_sha256": "4cd67b96288e5966d2434e845edc7a7a673d60aecd164bf4608e493652a4bbfb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.6440",
    "kind": "arxiv",
    "version": 1
  }
}