Pith Number

pith:WLT4FLAO

pith:2015:WLT4FLAO3VZNGLPHCEZT6A6PON

not attested not anchored not stored refs pending

Integral representations of martingales for progressive enlargements of filtrations

Anna Aksamit, Marek Rutkowski, Monique Jeanblanc

arxiv:1512.03992 v2 · 2015-12-13 · 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{WLT4FLAO3VZNGLPHCEZT6A6PON}

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	2026-05-18T00:08:24.187046Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b2e7c2ac0edd72d32de711333f03cf736c81fe45f5f566169cc8719eaa7f3448

Aliases

arxiv: 1512.03992 · arxiv_version: 1512.03992v2 · doi: 10.48550/arxiv.1512.03992 · pith_short_12: WLT4FLAO3VZN · pith_short_16: WLT4FLAO3VZNGLPH · pith_short_8: WLT4FLAO

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/WLT4FLAO3VZNGLPHCEZT6A6PON \
  | 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: b2e7c2ac0edd72d32de711333f03cf736c81fe45f5f566169cc8719eaa7f3448

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "36c1692522155df3fce505e0f414d25b9b12fef3835aeeeb8d6e40f939eaebb2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-12-13T02:58:27Z",
    "title_canon_sha256": "34ad5a87abbf486874164910d61562050a846387a4f7db780bd18bf355288a72"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.03992",
    "kind": "arxiv",
    "version": 2
  }
}