Pith Number

pith:F5QXEEWM

pith:2026:F5QXEEWMEKFFQCX4S3BLIA7UPE

not attested not anchored not stored refs pending

Mean-Field Doubly Reflected Forward-Backward SDEs with Optional Barriers and $L^p$-Data

Erhan Bayraktar, Maurycy Rzymowski

arxiv:2608.04937 v1 · 2026-08-05 · 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{F5QXEEWMEKFFQCX4S3BLIA7UPE}

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	2026-08-06T01:47:44.082917Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2f617212cc228a580afc96c2b403f4790b80621cfde1d03bbcb8e133ab259b9f

Aliases

arxiv: 2608.04937 · arxiv_version: 2608.04937v1 · doi: 10.48550/arxiv.2608.04937 · pith_short_12: F5QXEEWMEKFF · pith_short_16: F5QXEEWMEKFFQCX4 · pith_short_8: F5QXEEWM

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/F5QXEEWMEKFFQCX4S3BLIA7UPE \
  | 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: 2f617212cc228a580afc96c2b403f4790b80621cfde1d03bbcb8e133ab259b9f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ef024f61652d0eb77e6c65b0a74ee56fc3a7e6736ca9019fc13860ea1b4b7be2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-08-05T15:05:34Z",
    "title_canon_sha256": "9431f03b7a7eb8d3b60c160aa4560ce998cf7b9d031985955a261c4ac89fe089"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.04937",
    "kind": "arxiv",
    "version": 1
  }
}