Pith Number

pith:HY443STJ

pith:2014:HY443STJPEASLS2DIWOFTY3YEF

not attested not anchored not stored refs pending

And$\hat{o}$-Douglas type characterization of generalized conditional expectations, optional projections and predictable projections

Liang Hong

arxiv:1402.1155 v2 · 2014-02-05 · 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{HY443STJPEASLS2DIWOFTY3YEF}

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	2026-05-18T02:55:47.944243Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3e39cdca69790125cb43459c59e3782167e0442886db68c095f54c6982128018

Aliases

arxiv: 1402.1155 · arxiv_version: 1402.1155v2 · doi: 10.48550/arxiv.1402.1155 · pith_short_12: HY443STJPEAS · pith_short_16: HY443STJPEASLS2D · pith_short_8: HY443STJ

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/HY443STJPEASLS2DIWOFTY3YEF \
  | 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: 3e39cdca69790125cb43459c59e3782167e0442886db68c095f54c6982128018

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0202297c4e175e5eb7b330435584ef01ea0a5ebd58c583fee9d8d8685cf6dedf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2014-02-05T20:29:44Z",
    "title_canon_sha256": "de527a44f4ccbca4ecb93a3413cf5d2a2d378884e24da648d5809946d1b54bd3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1402.1155",
    "kind": "arxiv",
    "version": 2
  }
}