Pith Number

pith:4FT4JVTS

pith:2016:4FT4JVTSMFA7PAQ4AAFHSQY2IG

not attested not anchored not stored refs pending

Complete Bernstein functions and subordinators with nested ranges. A note on a paper by P. Marchal

Chang-song Deng, Ren\'e L. Schilling

arxiv:1606.04610 v2 · 2016-06-15 · 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{4FT4JVTSMFA7PAQ4AAFHSQY2IG}

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	2026-05-18T00:57:27.407134Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e167c4d6726141f7821c000a79431a4186d6f798c156bcf6d17ffc15d54ec15a

Aliases

arxiv: 1606.04610 · arxiv_version: 1606.04610v2 · doi: 10.48550/arxiv.1606.04610 · pith_short_12: 4FT4JVTSMFA7 · pith_short_16: 4FT4JVTSMFA7PAQ4 · pith_short_8: 4FT4JVTS

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/4FT4JVTSMFA7PAQ4AAFHSQY2IG \
  | 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: e167c4d6726141f7821c000a79431a4186d6f798c156bcf6d17ffc15d54ec15a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1126b3d7efd1be98727fc1a134f36a84cc5ee67255219ccec5032ad9a701a795",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-06-15T01:30:35Z",
    "title_canon_sha256": "c2cde0430d218d21c8963e1c8a8324860d66905c97dbda176a22785f54c0df0f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.04610",
    "kind": "arxiv",
    "version": 2
  }
}