Pith Number

pith:IN4P2KM7

pith:2010:IN4P2KM7MCHN67WQ3PF6Z7XNJY

not attested not anchored not stored refs pending

MIMO B-MAC Interference Network Optimization under Rate Constraints by Polite Water-filling and Duality

An Liu, Haige Xiang, Wu Luo, Youjian (Eugene) Liu

arxiv:1007.0982 v1 · 2010-07-06 · 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{IN4P2KM7MCHN67WQ3PF6Z7XNJY}

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	2026-05-18T03:06:22.777498Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4378fd299f608edf7ed0dbcbecfeed4e12726cf69afc424205403f62ea7463f3

Aliases

arxiv: 1007.0982 · arxiv_version: 1007.0982v1 · doi: 10.48550/arxiv.1007.0982 · pith_short_12: IN4P2KM7MCHN · pith_short_16: IN4P2KM7MCHN67WQ · pith_short_8: IN4P2KM7

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/IN4P2KM7MCHN67WQ3PF6Z7XNJY \
  | 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: 4378fd299f608edf7ed0dbcbecfeed4e12726cf69afc424205403f62ea7463f3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "43124d8660ff9081994988443835a0fef1163f367ea80605c19f42e551301087",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2010-07-06T19:31:00Z",
    "title_canon_sha256": "423172344a14a29590c347a176c9d328233ea4c2d2fc00ef3b29a1f714959335"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1007.0982",
    "kind": "arxiv",
    "version": 1
  }
}