Pith Number

pith:3D2PP7A7

pith:2026:3D2PP7A7T4CZQ2P3AEPFD2FHED

not attested not anchored not stored refs pending

Functional integration by parts formulae for stochastic Volterra processes

Alexandre Pannier

arxiv:2605.30068 v1 · 2026-05-28 · math.PR · q-fin.RM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3D2PP7A7T4CZQ2P3AEPFD2FHED}

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	2026-05-29T02:06:09.054910Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d8f4f7fc1f9f059869fb011e51e8a720c6c3c5499ef79cf38db06321ab4c8bab

Aliases

arxiv: 2605.30068 · arxiv_version: 2605.30068v1 · doi: 10.48550/arxiv.2605.30068 · pith_short_12: 3D2PP7A7T4CZ · pith_short_16: 3D2PP7A7T4CZQ2P3 · pith_short_8: 3D2PP7A7

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/3D2PP7A7T4CZQ2P3AEPFD2FHED \
  | 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: d8f4f7fc1f9f059869fb011e51e8a720c6c3c5499ef79cf38db06321ab4c8bab

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "058f1df672c18472a853d1ae327f6f484f7897365f99033669ebb07a149a110e",
    "cross_cats_sorted": [
      "q-fin.RM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-05-28T15:15:30Z",
    "title_canon_sha256": "e7ce8bb5c21068257bb75ae2aa0981f6bf040bac1b68b3f61ac2f6bb37ac7cfc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.30068",
    "kind": "arxiv",
    "version": 1
  }
}