Pith Number

pith:JRYX654W

pith:2015:JRYX654WKYFN6QPCC2RIXX4FTX

not attested not anchored not stored refs pending

An Introduction to Matrix Concentration Inequalities

Joel A. Tropp

arxiv:1501.01571 v1 · 2015-01-07 · math.PR · cs.DS · cs.IT · cs.NA · math.IT · stat.ML

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JRYX654WKYFN6QPCC2RIXX4FTX}

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.

Cited by

2 papers in Pith

Stability of digital and analog quantum simulations under noise

Select-then-differentiate: Solving Bilevel Optimization with Manifold Lower-level Solution Sets

Receipt and verification

First computed	2026-05-18T02:29:53.744853Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4c717f7796560adf41e216a28bdf859dc0983bb30c0f60058cc5a4a745df48a2

Aliases

arxiv: 1501.01571 · arxiv_version: 1501.01571v1 · doi: 10.48550/arxiv.1501.01571 · pith_short_12: JRYX654WKYFN · pith_short_16: JRYX654WKYFN6QPC · pith_short_8: JRYX654W

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/JRYX654WKYFN6QPCC2RIXX4FTX \
  | 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: 4c717f7796560adf41e216a28bdf859dc0983bb30c0f60058cc5a4a745df48a2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "68c6edab3028b78aa9cfb659f138a3ecd1e6096b399fea957c6cba212556bb4d",
    "cross_cats_sorted": [
      "cs.DS",
      "cs.IT",
      "cs.NA",
      "math.IT",
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-01-07T17:46:02Z",
    "title_canon_sha256": "88214327cf8b0cafeb017580ad05962c1da5fdecca8b19b9140d730578bdb27e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1501.01571",
    "kind": "arxiv",
    "version": 1
  }
}