Pith Number

pith:LKW5SHVB

pith:2013:LKW5SHVBO4JTWZ4FEYME5IT7JP

not attested not anchored not stored refs pending

Subadditivity of Matrix phi-Entropy and Concentration of Random Matrices

Joel A. Tropp, Richard Y. Chen

arxiv:1308.2952 v1 · 2013-08-13 · cs.IT · math.IT · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LKW5SHVBO4JTWZ4FEYME5IT7JP}

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	2026-05-18T02:53:08.173625Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5aadd91ea177133b678526184ea27f4bd34d5c3c39229d9e3b0281b56850b818

Aliases

arxiv: 1308.2952 · arxiv_version: 1308.2952v1 · doi: 10.48550/arxiv.1308.2952 · pith_short_12: LKW5SHVBO4JT · pith_short_16: LKW5SHVBO4JTWZ4F · pith_short_8: LKW5SHVB

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/LKW5SHVBO4JTWZ4FEYME5IT7JP \
  | 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: 5aadd91ea177133b678526184ea27f4bd34d5c3c39229d9e3b0281b56850b818

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fac9a859394a8da5e40afa5aaedd98be02ab0b1507cff4fe399ec166a0cd5657",
    "cross_cats_sorted": [
      "math.IT",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2013-08-13T19:28:16Z",
    "title_canon_sha256": "ee23c5dffcdc5b5392af671094dab85335a65a56e0287623f006a1e8a0452dbe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.2952",
    "kind": "arxiv",
    "version": 1
  }
}