Pith Number

pith:7TQBOT3X

pith:2012:7TQBOT3XS45CDOXZQUYFRPG3UX

not attested not anchored not stored refs pending

Degrees of Freedom for MIMO Two-Way X Relay Channel

Jianhua Mo, Meixia Tao, Xiaodong Wang, Zhengzheng Xiang

arxiv:1208.4048 v2 · 2012-08-20 · 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{7TQBOT3XS45CDOXZQUYFRPG3UX}

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	2026-05-18T01:55:09.174730Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fce0174f77973a21baf9853058bcdba5caa0ff11f73284829022005989862747

Aliases

arxiv: 1208.4048 · arxiv_version: 1208.4048v2 · doi: 10.48550/arxiv.1208.4048 · pith_short_12: 7TQBOT3XS45C · pith_short_16: 7TQBOT3XS45CDOXZ · pith_short_8: 7TQBOT3X

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/7TQBOT3XS45CDOXZQUYFRPG3UX \
  | 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: fce0174f77973a21baf9853058bcdba5caa0ff11f73284829022005989862747

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ea56457fa7539a83f5d0c2925a210b1bb62a6a4a907f361d245eece13c6538c0",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2012-08-20T16:19:31Z",
    "title_canon_sha256": "eb50e40410d6e96e6ef94a845f4b7fcc313ef1b40a14a13c644dc4fe0a7023d1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.4048",
    "kind": "arxiv",
    "version": 2
  }
}