Pith Number

pith:QJINH7XS

pith:2026:QJINH7XSATPALG2GSTZS7VEB3F

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A philosophical history of infinitesimals

Karl Kuhlemann, Mikhail G. Katz, Taras Kudryk, Vladimir Kanovei

Leibnizian infinitesimals can be formalized rigorously in a choice-free conservative extension of ZF set theory.

arxiv:2605.13102 v1 · 2026-05-13 · math.HO

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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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.

Claims

C1strongest claim

We sketch a recent theory of infinitesimal analysis that formalizes Leibnizian definitions and heuristic principles while eschewing both the axiom of choice and ultrafilters, thus challenging received philosophical views on the nature of infinitesimals.

C2weakest assumption

That the newly introduced concept of ringinals provides a coherent arithmetic framework for infinitesimals that integrates with a conservative extension of ZF without introducing inconsistencies or relying on unstated assumptions about the continuum.

C3one line summary

Leibnizian infinitesimals can be formalized using ringinals in a conservative extension of ZF set theory without the axiom of choice or ultrafilters.

References

139 extracted · 139 resolved · 1 Pith anchors

[1] Gauss theorem and pointlike charges: When infinitesimals make the difference.The Physics Teacher61(2023), no 2023

[2] W.; Ferraro, Giovanni; Gray, Jeremy; Jesseph, Douglas; L¨ utzen, Jesper; Panza, Marco; Rabouin, David; Schubring, Gert 2022

[3] On the unviability of interpreting Leib- niz’s infinitesimals through non-standard analysis.Historia Math.66(2024), 26–42 2024

[4] On the failure of the correspondences al- leged between nonstandard analysis and Leibniz’s conception of infinitesimals (arxiv, in preparation) 2024

[5] The debate between Peletier and Clavius on superposi- tion.Historia Mathematica45(2018), no 2018

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T03:08:58.252031Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8250d3fef204de059b4694f32fd481d944e5514d161c0a6b061ff770d0d845d2

Aliases

arxiv: 2605.13102 · arxiv_version: 2605.13102v1 · doi: 10.48550/arxiv.2605.13102 · pith_short_12: QJINH7XSATPA · pith_short_16: QJINH7XSATPALG2G · pith_short_8: QJINH7XS

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/QJINH7XSATPALG2GSTZS7VEB3F \
  | 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: 8250d3fef204de059b4694f32fd481d944e5514d161c0a6b061ff770d0d845d2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4ef9e20faf0f1b10d19793c96a45f221d1de3db6e2696219a5fd8a30ea52bb1a",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.HO",
    "submitted_at": "2026-05-13T07:13:51Z",
    "title_canon_sha256": "bcd5d061738c34eac1d658dd6637b11b02b205d0177b5da693474e4398bbfdb8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13102",
    "kind": "arxiv",
    "version": 1
  }
}