Pith Number

pith:OPTF4CEQ

pith:2010:OPTF4CEQIWKRZILPGKTECSUHPX

not attested not anchored not stored refs pending

Martingale property of generalized stochastic exponentials

Aleksandar Mijatovi\'c, Mikhail Urusov, Nika Novak

arxiv:1010.0969 v1 · 2010-10-05 · 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{OPTF4CEQIWKRZILPGKTECSUHPX}

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	2026-05-18T04:39:50.592401Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

73e65e089045951ca16f32a6414a877dc7b105bda4d7a87c84e8b5350dbf346e

Aliases

arxiv: 1010.0969 · arxiv_version: 1010.0969v1 · doi: 10.48550/arxiv.1010.0969 · pith_short_12: OPTF4CEQIWKR · pith_short_16: OPTF4CEQIWKRZILP · pith_short_8: OPTF4CEQ

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/OPTF4CEQIWKRZILPGKTECSUHPX \
  | 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: 73e65e089045951ca16f32a6414a877dc7b105bda4d7a87c84e8b5350dbf346e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d46f974b3971dc5c7191faef1f9f23f6440daa8ba0dc40da7f5a2cfc10d896b7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-10-05T18:31:23Z",
    "title_canon_sha256": "6cc6f11016d91a6d7661e612d2f1214b4d3d068d6244bdc3d9e65c572d42f120"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.0969",
    "kind": "arxiv",
    "version": 1
  }
}