Pith Number

pith:DRJ6IJ25

pith:2026:DRJ6IJ25YBVH65T24I3DZSML4J

not attested not anchored not stored refs pending

On the boundaries, asymptotic law and Bernoulli-Doob representation of homogeneous bounded martingales

Damiano Brigo, Fr\'ed\'eric Vrins

arxiv:2607.12365 v1 · 2026-07-14 · 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{DRJ6IJ25YBVH65T24I3DZSML4J}

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	2026-07-15T01:21:30.943827Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1c53e4275dc06a7f767ae2363cc98be2762e9c3b5b24250d2ce81a4be63cce5f

Aliases

arxiv: 2607.12365 · arxiv_version: 2607.12365v1 · doi: 10.48550/arxiv.2607.12365 · pith_short_12: DRJ6IJ25YBVH · pith_short_16: DRJ6IJ25YBVH65T2 · pith_short_8: DRJ6IJ25

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/DRJ6IJ25YBVH65T24I3DZSML4J \
  | 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: 1c53e4275dc06a7f767ae2363cc98be2762e9c3b5b24250d2ce81a4be63cce5f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d8c1c5ed74f1a0b8b2462256e8dc491a8ad249945e59ca0e433f62c95a8a0ebe",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-07-14T05:41:01Z",
    "title_canon_sha256": "befe4b6f120a41756697547cdb88d863040b19c0207f7c71fc58827b2a18c75b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.12365",
    "kind": "arxiv",
    "version": 1
  }
}