Pith Number

pith:UMA34EXI

pith:2010:UMA34EXIQVA3QEP24UJQODWQWH

not attested not anchored not stored refs pending

Generalized covariation for Banach space valued processes, It\^o formula and applications

Cristina Di Girolami (LMM), Francesco Russo (ENSTA ParisTech, INRIA Rocquencourt)

arxiv:1012.2484 v3 · 2010-12-11 · 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{UMA34EXIQVA3QEP24UJQODWQWH}

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	2026-05-18T03:32:28.802777Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a301be12e88541b811fae513070ed0b1d3846df140b04e5735efacf40453f01a

Aliases

arxiv: 1012.2484 · arxiv_version: 1012.2484v3 · doi: 10.48550/arxiv.1012.2484 · pith_short_12: UMA34EXIQVA3 · pith_short_16: UMA34EXIQVA3QEP2 · pith_short_8: UMA34EXI

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/UMA34EXIQVA3QEP24UJQODWQWH \
  | 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: a301be12e88541b811fae513070ed0b1d3846df140b04e5735efacf40453f01a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f85315d10daa43562a3bc541c5aa723a6b12d1057387e11218d29d78c9a85789",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-12-11T19:44:08Z",
    "title_canon_sha256": "8ff4937fd7d74e0473f66fba010d9019b5304064846a75a2b807707587b4340d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.2484",
    "kind": "arxiv",
    "version": 3
  }
}