Pith Number

pith:GFW2E3EL

pith:2016:GFW2E3ELJ7C4DFYI7HFQQAFPF6

not attested not anchored not stored refs pending

Karhunen-Loeve expansions of Levy processes

Daniel Hackmann

arxiv:1603.00677 v1 · 2016-03-02 · 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{GFW2E3ELJ7C4DFYI7HFQQAFPF6}

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	2026-05-18T01:19:43.191098Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

316da26c8b4fc5c19708f9cb0800af2f8f43fcabd6e90de83804188b4de991c0

Aliases

arxiv: 1603.00677 · arxiv_version: 1603.00677v1 · doi: 10.48550/arxiv.1603.00677 · pith_short_12: GFW2E3ELJ7C4 · pith_short_16: GFW2E3ELJ7C4DFYI · pith_short_8: GFW2E3EL

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/GFW2E3ELJ7C4DFYI7HFQQAFPF6 \
  | 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: 316da26c8b4fc5c19708f9cb0800af2f8f43fcabd6e90de83804188b4de991c0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "96796dbfc724047d9bc61d6262b1c7401a183cf1ef1a7e45f9bb1f7323df7d5b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-03-02T12:18:28Z",
    "title_canon_sha256": "0ef2ad11d5502135c4db7228320332190cab1894b6e628d2fa4099e1646c61ae"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.00677",
    "kind": "arxiv",
    "version": 1
  }
}