Pith Number

pith:4NDOIMRF

pith:2010:4NDOIMRFTWZIEBRRYOJKKTFD7A

not attested not anchored not stored refs pending

Characterizations of processes with stationary and independent increments under $G$-expectation

Yongsheng Song

arxiv:1009.0109 v2 · 2010-09-01 · 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{4NDOIMRFTWZIEBRRYOJKKTFD7A}

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	2026-05-18T04:13:55.288290Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e346e432259db2820631c392a54ca3f8082c2617f16bc765fa0db44efc0c3d25

Aliases

arxiv: 1009.0109 · arxiv_version: 1009.0109v2 · doi: 10.48550/arxiv.1009.0109 · pith_short_12: 4NDOIMRFTWZI · pith_short_16: 4NDOIMRFTWZIEBRR · pith_short_8: 4NDOIMRF

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/4NDOIMRFTWZIEBRRYOJKKTFD7A \
  | 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: e346e432259db2820631c392a54ca3f8082c2617f16bc765fa0db44efc0c3d25

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b8a096438d2a696ac04267a94b35471b114f6ef12e4b194035c37fe01ab9cfbd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-09-01T07:51:53Z",
    "title_canon_sha256": "e83a17640d0723b5c3f798965fbe170e941d15ec05f5186e55e4b2ab891f3d6e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.0109",
    "kind": "arxiv",
    "version": 2
  }
}