Pith Number

pith:M57OSUC4

pith:2005:M57OSUC4Z4FYYD7YCCKRHLOGW3

not attested not anchored not stored refs pending

Generalized Ito Formulae and Space-Time Lebesgue-Stieltjes Integrals of Local Times

A. Truman, H.Z. Zhao, K.D. Elworthy

arxiv:math/0505195 v2 · 2005-05-10 · 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{M57OSUC4Z4FYYD7YCCKRHLOGW3}

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	2026-05-18T01:35:33.364367Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

677ee9505ccf0b8c0ff8109513adc6b6d4517738c47e130c46bee847d46e3234

Aliases

arxiv: math/0505195 · arxiv_version: math/0505195v2 · doi: 10.48550/arxiv.math/0505195 · pith_short_12: M57OSUC4Z4FY · pith_short_16: M57OSUC4Z4FYYD7Y · pith_short_8: M57OSUC4

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/M57OSUC4Z4FYYD7YCCKRHLOGW3 \
  | 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: 677ee9505ccf0b8c0ff8109513adc6b6d4517738c47e130c46bee847d46e3234

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "51e8407e154261158c50083abce74a592139711acd253c516aa86e8348948a10",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2005-05-10T18:08:09Z",
    "title_canon_sha256": "92f9ae143ce37f497ed8d4333243b1f08febe55087738aa388fe6416170b50cc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0505195",
    "kind": "arxiv",
    "version": 2
  }
}