Pith Number

pith:S7WVYRDS

pith:2012:S7WVYRDSETJUJEVEZABA6TZRR3

not attested not anchored not stored refs pending

Degrees of Freedom of MIMO X Networks: Spatial Scale Invariance, One-Sided Decomposability and Linear Feasibility

Chunhua Geng, Hua Sun, Syed A. Jafar, Tiangao Gou

arxiv:1207.6137 v2 · 2012-07-25 · 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{S7WVYRDSETJUJEVEZABA6TZRR3}

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	2026-05-18T03:15:21.076802Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

97ed5c447224d34492a4c8020f4f318eec03639aa46b8919b806bc1341d81a19

Aliases

arxiv: 1207.6137 · arxiv_version: 1207.6137v2 · doi: 10.48550/arxiv.1207.6137 · pith_short_12: S7WVYRDSETJU · pith_short_16: S7WVYRDSETJUJEVE · pith_short_8: S7WVYRDS

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/S7WVYRDSETJUJEVEZABA6TZRR3 \
  | 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: 97ed5c447224d34492a4c8020f4f318eec03639aa46b8919b806bc1341d81a19

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0cfb3603f28803fe2d2f8f568d8a09465808ee32b52ed4045f7a6bf044a21a2c",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2012-07-25T21:46:21Z",
    "title_canon_sha256": "0e8b2e661a6386f24c82349959c883395140a90cf9c56e4e89fe26b837fa746f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.6137",
    "kind": "arxiv",
    "version": 2
  }
}