Pith Number

pith:BQY3V4XB

pith:2016:BQY3V4XBA432AGIAHOO4A6UIZY

not attested not anchored not stored refs pending

Order statistics of vectors with dependent coordinates, and the Karhunen-Lo\`eve basis

Alexander E. Litvak, Konstantin Tikhomirov

arxiv:1609.02126 v3 · 2016-09-07 · 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{BQY3V4XBA432AGIAHOO4A6UIZY}

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	2026-05-18T00:43:35.635185Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0c31baf2e10737a019003b9dc07a88ce385fcfc0c76d8ea841e07f252e2a0e10

Aliases

arxiv: 1609.02126 · arxiv_version: 1609.02126v3 · doi: 10.48550/arxiv.1609.02126 · pith_short_12: BQY3V4XBA432 · pith_short_16: BQY3V4XBA432AGIA · pith_short_8: BQY3V4XB

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/BQY3V4XBA432AGIAHOO4A6UIZY \
  | 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: 0c31baf2e10737a019003b9dc07a88ce385fcfc0c76d8ea841e07f252e2a0e10

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3ba5898dda40ee2c17914e38f4c75dbf446cd19684c8376e00670956e6e8ff96",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-09-07T19:27:18Z",
    "title_canon_sha256": "aadbf925cd7c521f051dd22c852ad7bc832b55c357d3acc1d3270dcac25e9a41"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.02126",
    "kind": "arxiv",
    "version": 3
  }
}