Pith Number

pith:B7IT57B4

pith:2015:B7IT57B4CLOAFQUADAVODNU7ON

not attested not anchored not stored refs pending

Second-Order Matrix Concentration Inequalities

Joel A. Tropp

arxiv:1504.05919 v2 · 2015-04-22 · math.PR · math.ST · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{B7IT57B4CLOAFQUADAVODNU7ON}

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	2026-05-18T01:09:55.362923Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0fd13efc3c12dc02c280182ae1b69f73571a04b74bc53b725fda64c58b45d4d4

Aliases

arxiv: 1504.05919 · arxiv_version: 1504.05919v2 · doi: 10.48550/arxiv.1504.05919 · pith_short_12: B7IT57B4CLOA · pith_short_16: B7IT57B4CLOAFQUA · pith_short_8: B7IT57B4

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/B7IT57B4CLOAFQUADAVODNU7ON \
  | 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: 0fd13efc3c12dc02c280182ae1b69f73571a04b74bc53b725fda64c58b45d4d4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f3b27105ef7c2ecafbc11eb942d28c0c1d5b5b80c9a17b5e0891cfaee228b5e5",
    "cross_cats_sorted": [
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-04-22T18:46:20Z",
    "title_canon_sha256": "be6fc0c9aa561624c220b4d49bdbf90af52c4674a1bf4e43746cccae20a56c9d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.05919",
    "kind": "arxiv",
    "version": 2
  }
}