Pith Number

pith:VKAOGB6T

pith:2011:VKAOGB6TQOVQM3J6BJ2HXLP2VB

not attested not anchored not stored refs pending

A comparison principle for functions of a uniformly random subspace

Joel A. Tropp

arxiv:1102.0534 v2 · 2011-02-02 · math.PR · math.MG · 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{VKAOGB6TQOVQM3J6BJ2HXLP2VB}

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	2026-05-18T02:53:15.865048Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aa80e307d383ab066d3e0a747badfaa84542d46cca02dea9a9c3ff2d8df3abf8

Aliases

arxiv: 1102.0534 · arxiv_version: 1102.0534v2 · doi: 10.48550/arxiv.1102.0534 · pith_short_12: VKAOGB6TQOVQ · pith_short_16: VKAOGB6TQOVQM3J6 · pith_short_8: VKAOGB6T

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/VKAOGB6TQOVQM3J6BJ2HXLP2VB \
  | 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: aa80e307d383ab066d3e0a747badfaa84542d46cca02dea9a9c3ff2d8df3abf8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4173c7f20e8940bafcf417bdfbe20c256a40e4f7fa375c9d0fbab60406056843",
    "cross_cats_sorted": [
      "math.MG",
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-02-02T19:22:48Z",
    "title_canon_sha256": "07db4af35078fac9fba14661219bbc0db3e0f8b7d0a5302474e09b733f7d5527"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.0534",
    "kind": "arxiv",
    "version": 2
  }
}