Pith Number

pith:XALKQ3JW

pith:2025:XALKQ3JWTAPITCH3HC7IQFZKVF

not attested not anchored not stored refs pending

The Fundamental Theorem of Calculus for Lebesgue-Stieltjes integrals involving non-monotonic derivators

F. Adri\'an F. Tojo, Lamiae Maia

arxiv:2509.05247 v3 · 2025-09-05 · math.CA

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XALKQ3JWTAPITCH3HC7IQFZKVF}

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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.

Cited by

1 paper in Pith

Constructive solutions of the heat equation with Stieltjes derivatives

Receipt and verification

First computed	2026-06-30T02:18:04.709657Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b816a86d36981e8988fb38be88172aa97d689995d62a777cbe9bacb91aff6bde

Aliases

arxiv: 2509.05247 · arxiv_version: 2509.05247v3 · doi: 10.48550/arxiv.2509.05247 · pith_short_12: XALKQ3JWTAPI · pith_short_16: XALKQ3JWTAPITCH3 · pith_short_8: XALKQ3JW

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/XALKQ3JWTAPITCH3HC7IQFZKVF \
  | 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: b816a86d36981e8988fb38be88172aa97d689995d62a777cbe9bacb91aff6bde

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "096fe163842e47c79b59adccbb2aed6c909909e9f6df3c97b421ab815873b4c4",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2025-09-05T16:59:52Z",
    "title_canon_sha256": "a6d2ae5bb3db77c733b7638461e05e28510ccad1377a5471428a9b2706b87a12"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.05247",
    "kind": "arxiv",
    "version": 3
  }
}