Pith Number

pith:PLSOLLED

pith:2013:PLSOLLEDOOFNSL6LG42EVXAWJ4

not attested not anchored not stored refs pending

The Martingale Property in the Context of Stochastic Differential Equations

Johannes Ruf

arxiv:1306.0218 v2 · 2013-06-02 · 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{PLSOLLEDOOFNSL6LG42EVXAWJ4}

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	2026-05-18T02:17:52.402440Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7ae4e5ac83738ad92fcb37344adc164f08661c820b0d59cd7f5e54d389a7a2ef

Aliases

arxiv: 1306.0218 · arxiv_version: 1306.0218v2 · doi: 10.48550/arxiv.1306.0218 · pith_short_12: PLSOLLEDOOFN · pith_short_16: PLSOLLEDOOFNSL6L · pith_short_8: PLSOLLED

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/PLSOLLEDOOFNSL6LG42EVXAWJ4 \
  | 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: 7ae4e5ac83738ad92fcb37344adc164f08661c820b0d59cd7f5e54d389a7a2ef

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9ef5fb1d2cef0426cbe090b8a7a14388722904db1069d0827b39e9f4cd9fff61",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-06-02T15:17:57Z",
    "title_canon_sha256": "5d6658dccb73d0d180bc2e22a71bcd7bf3c32ae82eb6a3e4e25de6b9deff15c9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.0218",
    "kind": "arxiv",
    "version": 2
  }
}