Pith Number

pith:MXPKVJIV

pith:2012:MXPKVJIVQDY7GRGF4TUBEOH6G2

not attested not anchored not stored refs pending

New Optional Stopping Theorems and Maximal Inequalities on Stochastic Processes

Xinjia Chen

arxiv:1207.3733 v2 · 2012-07-16 · math.PR · math.ST · stat.TH

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MXPKVJIVQDY7GRGF4TUBEOH6G2}

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	2026-05-18T03:49:46.927561Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

65deaaa51580f1f344c5e4e81238fe369c008b07ad512522bf96c76acfe35638

Aliases

arxiv: 1207.3733 · arxiv_version: 1207.3733v2 · doi: 10.48550/arxiv.1207.3733 · pith_short_12: MXPKVJIVQDY7 · pith_short_16: MXPKVJIVQDY7GRGF · pith_short_8: MXPKVJIV

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/MXPKVJIVQDY7GRGF4TUBEOH6G2 \
  | 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: 65deaaa51580f1f344c5e4e81238fe369c008b07ad512522bf96c76acfe35638

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "17e4e009dacf2f06308839f28ca57119db9769165b4c4c58814da2883c04a3d0",
    "cross_cats_sorted": [
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-07-16T17:19:06Z",
    "title_canon_sha256": "1b874fe4614001641971179dc9d2eb0c3cac937ed9dcdec161302a674c5ac76c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.3733",
    "kind": "arxiv",
    "version": 2
  }
}