https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/Head https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg http://www.nanopub.org/nschema#hasAssertion https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/assertion https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg http://www.nanopub.org/nschema#hasProvenance https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/provenance https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg http://www.nanopub.org/nschema#hasPublicationInfo https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/pubinfo https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://www.nanopub.org/nschema#Nanopublication https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/assertion https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/geolean-citation http://purl.org/dc/terms/description This statement was verified by Myles Axton (orcid:0000-0002-8042-4131) on 2026-07-18T15:17:00Z (16:17 UTC+1). https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/geolean-citation http://www.w3.org/1999/02/22-rdf-syntax-ns#type https://schema.org/Comment https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/geolean-citation http://www.w3.org/ns/prov#wasAttributedTo https://orcid.org/0000-0002-8042-4131 https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/geolean-citation https://schema.org/citation Bhavik Mehta, Zulip (leanprover-community.github.io archive), "tarski axiom geometry" topic, Oct 20 2021 at 12:39: "In the GeoLean branch of mathlib I also did a development of Tarskis axioms, covering about 70% of the Tarski work in the GeoCoq project." https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/geolean-citation https://schema.org/name GeoLean citation and human verification https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/geolean-citation https://schema.org/url https://leanprover-community.github.io/archive/stream/116395-maths/topic/tarski.20axiom.20geometry.html https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/motivation http://purl.org/dc/terms/description The motivation of this nanopublication is to advance the use of FAIA and ISCC to add provenance and human/agent-role attribution to the formalization of our shared mathematical culture. In particular, this nanopublication explores the negative space of what was not done. Many people over roughly 2500 years of mathematics deserve credit for the development of formal mathematical axioms and theorems. By formalizing part of this historical trajectory, this artifact is offered as a substrate for nanopublications that restore context and provenance to results typically stripped down to their elegant statement and proof — to the lamentation of teachers, students, engineers, statisticians, and curious readers. https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/motivation http://www.w3.org/1999/02/22-rdf-syntax-ns#type urn:sandbox:tarski-lean4-negative-space:vocab#Motivation https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/motivation https://schema.org/name Why this negative-space companion exists https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/non-origination http://purl.org/dc/terms/description Every axiom and every theorem in the bound artifact is prior art. The AI's contribution is confined to Lean 4 engineering and exposition; where proof details were re-derived in-session rather than recalled, what was re-derived is known mathematics. The complete inventory: https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/non-origination http://www.w3.org/1999/02/22-rdf-syntax-ns#type urn:sandbox:tarski-lean4-negative-space:vocab#NonOrigination https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/non-origination https://schema.org/name What the AI did not originate: the mathematics — all of it https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/non-origination urn:sandbox:tarski-lean4-negative-space:vocab#concerns https://w3id.org/np/RAXut_tYBIBaf53frjHN9ttCnUj4zq8JhXllSz7MyKpME/artifact https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/non-origination urn:sandbox:tarski-lean4-negative-space:vocab#items Axioms A1–A8 (cong_pseudo_refl, cong_inner_trans, cong_identity, segment_construction, five_segment, betw_identity, inner_pasch, lower_dim) — Tarski, 1926–27; A7 after Pasch, 1882 https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/non-origination urn:sandbox:tarski-lean4-negative-space:vocab#items Col, Out, SegLe and their permutation/trivia lemmas — SST ch. 4–6 vocabulary https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/non-origination urn:sandbox:tarski-lean4-negative-space:vocab#items Cong3 — SST Def. 4.1 (GeoCoq Cong_3) https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/non-origination urn:sandbox:tarski-lean4-negative-space:vocab#items Midpoint, midpoint_refl, midpoint_symm — SST ch. 7 vocabulary https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/non-origination urn:sandbox:tarski-lean4-negative-space:vocab#items betw_exchange2 — SST 3.6(2) (GeoCoq between_exchange2) https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/non-origination urn:sandbox:tarski-lean4-negative-space:vocab#items betw_exchange_left — SST 3.6(1) https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/non-origination urn:sandbox:tarski-lean4-negative-space:vocab#items betw_inner_trans — SST 3.5 https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/non-origination urn:sandbox:tarski-lean4-negative-space:vocab#items betw_left_trivial — SST 3.3 https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/non-origination urn:sandbox:tarski-lean4-negative-space:vocab#items betw_outer_trans — SST 3.7(1) https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/non-origination urn:sandbox:tarski-lean4-negative-space:vocab#items betw_outer_trans' — SST 3.7(2) https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/non-origination urn:sandbox:tarski-lean4-negative-space:vocab#items betw_symm — SST 3.2 https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/non-origination urn:sandbox:tarski-lean4-negative-space:vocab#items betw_transfer — SST 4.6 (GeoCoq l4_6) https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/non-origination urn:sandbox:tarski-lean4-negative-space:vocab#items betw_trivial — SST 3.1 https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/non-origination urn:sandbox:tarski-lean4-negative-space:vocab#items cong3_construction — SST 4.5 (GeoCoq l4_5) https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/non-origination urn:sandbox:tarski-lean4-negative-space:vocab#items cong_add — SST 2.11 (GeoCoq l2_11) https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/non-origination urn:sandbox:tarski-lean4-negative-space:vocab#items cong_comm — corollary of SST 2.4 + 2.5 https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/non-origination urn:sandbox:tarski-lean4-negative-space:vocab#items cong_left_comm — SST 2.4 https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/non-origination urn:sandbox:tarski-lean4-negative-space:vocab#items cong_refl — SST 2.1 https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/non-origination urn:sandbox:tarski-lean4-negative-space:vocab#items cong_reverse_identity — corollary of axiom A3 https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/non-origination urn:sandbox:tarski-lean4-negative-space:vocab#items cong_right_comm — SST 2.5 https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/non-origination urn:sandbox:tarski-lean4-negative-space:vocab#items cong_sub — SST 4.3 (GeoCoq l4_3) https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/non-origination urn:sandbox:tarski-lean4-negative-space:vocab#items cong_symm — SST 2.2 https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/non-origination urn:sandbox:tarski-lean4-negative-space:vocab#items cong_trans — SST 2.3 https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/non-origination urn:sandbox:tarski-lean4-negative-space:vocab#items cong_trivial — SST 2.8 https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/non-origination urn:sandbox:tarski-lean4-negative-space:vocab#items construction_uniqueness — SST 2.12 https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/non-origination urn:sandbox:tarski-lean4-negative-space:vocab#items inner_five_segment — SST 4.2 (GeoCoq l4_2) https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/non-origination urn:sandbox:tarski-lean4-negative-space:vocab#items reflect_betw — SST 7.15 (GeoCoq l7_15) https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/non-origination urn:sandbox:tarski-lean4-negative-space:vocab#items reflect_cong — SST 7.13 (GeoCoq l7_13) https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/non-origination urn:sandbox:tarski-lean4-negative-space:vocab#items symmetric_point_exists — SST 7.4 https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/non-origination urn:sandbox:tarski-lean4-negative-space:vocab#items symmetric_point_uniqueness — SST 7.5 https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/prior-art-geolean http://purl.org/dc/terms/description To the drafting AI's knowledge, Claude did not consult or port GeoLean in producing Tarski.lean. But GeoLean — Joseph Myers's Lean formalization of a large portion of GeoCoq's Tarski development, on a mathlib3 branch — predates this artifact and must be cited as a sibling ancestor alongside GeoCoq. The community view at the time (see sub:geolean-citation) was that axiomatic geometry belongs in standalone projects rather than in Mathlib itself. Tarski.lean is therefore not the first formalization of Tarski's axioms in Lean, but is, to the same knowledge, the first done as a self-contained, native-style Lean 4 development (GeoLean is Lean 3, Coq-styled). https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/prior-art-geolean http://purl.org/dc/terms/source https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/geolean-citation https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/prior-art-geolean http://www.w3.org/1999/02/22-rdf-syntax-ns#type urn:sandbox:tarski-lean4-negative-space:vocab#PriorArtDisclosure https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/prior-art-geolean https://schema.org/name Prior art the artifact does not originate: GeoLean https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/prior-art-geolean urn:sandbox:tarski-lean4-negative-space:vocab#concerns https://w3id.org/np/RAXut_tYBIBaf53frjHN9ttCnUj4zq8JhXllSz7MyKpME/artifact https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/unclaimed-credit http://purl.org/dc/terms/description As of this nanopublication's original drafting (2026-07-18T11:11:40Z), credit:validation — verification by compilation (`lean Tarski.lean`) — was claimed by no party: the artifact had never been compiled, and every correctness claim was a hand-verification claim. That gap has since closed. A follow-up session compiled the artifact successfully under two independent Lean 4 toolchains (leanprover/lean4-nightly:nightly-2023-05-16 and leanprover/lean4:v4.32.0), after finding and fixing the one error present (a use of Mathlib's `∃!` notation, unavailable in core Lean 4). credit:validation is now jointly claimed by Claude and Myles Axton, as recorded in the companion positive-space nanopublication (see sub:pubinfo dct:references). https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/unclaimed-credit http://www.w3.org/1999/02/22-rdf-syntax-ns#type urn:sandbox:tarski-lean4-negative-space:vocab#UnclaimedCredit https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/unclaimed-credit http://www.w3.org/ns/prov#hadRole https://credit.niso.org/contributor-roles/validation https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/unclaimed-credit https://schema.org/name Credit that was unclaimed when this inventory was first drafted — since resolved https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/provenance https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/activity http://purl.org/dc/terms/description Drafted in the same sandboxed session as the artifact it concerns, as a companion to the positive declaration, subsequently compiled, signed, and published as https://w3id.org/np/RAXut_tYBIBaf53frjHN9ttCnUj4zq8JhXllSz7MyKpME. The inventory was compiled by reading the artifact's theorem list against the SST concordance recorded there. Revised in a follow-up session to update the stale compilation-status claim, and to incorporate two further disclosures supplied by the human party: the motivation for this negative-space companion, and the GeoLean prior-art citation (with its Zulip source and human verification). https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/activity http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://www.w3.org/ns/prov#Activity https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/activity http://www.w3.org/ns/prov#startedAtTime 2026-07-18T11:11:40Z https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/activity http://www.w3.org/ns/prov#wasAssociatedWith https://w3id.org/np/RAXut_tYBIBaf53frjHN9ttCnUj4zq8JhXllSz7MyKpME/agent-claude https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/activity http://www.w3.org/ns/prov#wasAssociatedWith https://w3id.org/np/RAXut_tYBIBaf53frjHN9ttCnUj4zq8JhXllSz7MyKpME/agent-user https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/activity https://schema.org/name Negative-space inventory https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/assertion http://www.w3.org/ns/prov#wasGeneratedBy https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/activity https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg/pubinfo https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg http://purl.org/dc/terms/created 2026-07-18T15:28:18Z https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg http://purl.org/dc/terms/creator https://orcid.org/0000-0002-8042-4131 https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg http://purl.org/dc/terms/creator https://w3id.org/np/RAXut_tYBIBaf53frjHN9ttCnUj4zq8JhXllSz7MyKpME/agent-claude https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg http://purl.org/dc/terms/creator https://w3id.org/np/RAXut_tYBIBaf53frjHN9ttCnUj4zq8JhXllSz7MyKpME/agent-user https://w3id.org/np/RAbyUSg8hPy5xsGsGyFVyIoSk3XkETkUo3mg0aMxepyPg http://purl.org/dc/terms/description Negative-space companion to the Tarski.lean provenance declaration: what the artifact does not originate (the mathematics, all of it, and GeoLean as uncredited-until-now sibling prior art), and credit that was unclaimed as of first drafting. 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