[ { "@id": "https://w3id.org/np/RAXut_tYBIBaf53frjHN9ttCnUj4zq8JhXllSz7MyKpME/Head", "@graph": [ { "@id": "https://w3id.org/np/RAXut_tYBIBaf53frjHN9ttCnUj4zq8JhXllSz7MyKpME", "http://www.nanopub.org/nschema#hasAssertion": [ { "@id": "https://w3id.org/np/RAXut_tYBIBaf53frjHN9ttCnUj4zq8JhXllSz7MyKpME/assertion" } ], "http://www.nanopub.org/nschema#hasProvenance": [ { "@id": "https://w3id.org/np/RAXut_tYBIBaf53frjHN9ttCnUj4zq8JhXllSz7MyKpME/provenance" } ], "http://www.nanopub.org/nschema#hasPublicationInfo": [ { "@id": "https://w3id.org/np/RAXut_tYBIBaf53frjHN9ttCnUj4zq8JhXllSz7MyKpME/pubinfo" } ], "@type": [ "http://www.nanopub.org/nschema#Nanopublication" ] } ] }, { "@id": "https://w3id.org/np/RAXut_tYBIBaf53frjHN9ttCnUj4zq8JhXllSz7MyKpME/assertion", "@graph": [ { "@id": "https://w3id.org/np/RAXut_tYBIBaf53frjHN9ttCnUj4zq8JhXllSz7MyKpME/agent-claude", "http://purl.org/dc/terms/description": [ { "@value": "Drafted all Lean code and documentation; reconstructed and in places re-derived the proofs (see sub:faia). In a follow-up session, diagnosed and fixed the sole compile error and verified compilation under two toolchains (see sub:activity-verify). Not an author under prevailing scholarly norms; correctly credited by acknowledgment. All errors in the draft are attributable here, not to the mathematical tradition." } ], "@type": [ "http://www.w3.org/ns/prov#SoftwareAgent" ], "http://www.w3.org/ns/prov#hadRole": [ { "@id": "https://credit.niso.org/contributor-roles/software" }, { "@id": "https://credit.niso.org/contributor-roles/validation" }, { "@id": "https://credit.niso.org/contributor-roles/writing-original-draft" } ], "https://schema.org/name": [ { "@value": "Claude (Anthropic)" } ] }, { "@id": "https://w3id.org/np/RAXut_tYBIBaf53frjHN9ttCnUj4zq8JhXllSz7MyKpME/agent-euclid", "http://purl.org/dc/terms/description": [ { "@value": "The axiomatic ideal the artifact rebuilds; the original tower (Elements, Book I), including target propositions I.47–I.48 (Pythagoras and converse) and Definition I.10, echoed in the planned `Per` (SST ch. 8)." } ], "@type": [ "http://www.w3.org/ns/prov#Person" ], "http://www.w3.org/ns/prov#hadRole": [ { "@value": "Intellectual ancestor" } ], "https://schema.org/name": [ { "@value": "Euclid of Alexandria (fl. c. 300 BCE)" } ] }, { "@id": "https://w3id.org/np/RAXut_tYBIBaf53frjHN9ttCnUj4zq8JhXllSz7MyKpME/agent-geocoq", "http://purl.org/dc/terms/description": [ { "@value": "First machine-checked ascent of the SST development (Coq, from Narboux 2006 onward). The artifact reconstructs the GeoCoq architecture and navigated by its lemma map (l4_2 → inner_five_segment, l4_3 → cong_sub, l4_5 → cong3_construction, l4_6 → betw_transfer, l7_13 → reflect_cong, l7_15 → reflect_betw) but ports no GeoCoq code." } ], "@type": [ "http://www.w3.org/ns/prov#Organization" ], "http://www.w3.org/ns/prov#hadRole": [ { "@value": "Formal ancestor" } ], "https://schema.org/name": [ { "@value": "GeoCoq project (J. Narboux, M. Beeson, P. Boutry, G. Braun, C. Gries, P. Schreck, et al.)" } ], "https://schema.org/url": [ { "@id": "https://github.com/GeoCoq/GeoCoq" } ] }, { "@id": "https://w3id.org/np/RAXut_tYBIBaf53frjHN9ttCnUj4zq8JhXllSz7MyKpME/agent-gupta", "http://purl.org/dc/terms/description": [ { "@value": "PhD dissertation, UC Berkeley 1965, under Tarski: axiom independence and simplification (several axioms are as lean as A1–A8 because of him), and the perpendicular and midpoint constructions without any continuity axiom — SST 8.18 and 8.22, the declared next stage of this artifact, not yet contained in it." } ], "@type": [ "http://www.w3.org/ns/prov#Person" ], "http://www.w3.org/ns/prov#hadRole": [ { "@value": "Axiom simplifier; author of the continuity-free constructions ahead" } ], "https://schema.org/name": [ { "@value": "Haragauri Narayan Gupta (1925–2016)" } ] }, { "@id": "https://w3id.org/np/RAXut_tYBIBaf53frjHN9ttCnUj4zq8JhXllSz7MyKpME/agent-hilbert", "http://purl.org/dc/terms/description": [ { "@value": "Grundlagen der Geometrie (1899): the modern axiomatic program, and the segment arithmetic (Streckenrechnung, cf. SST ch. 14–15) that is the declared future route from this artifact to Pythagoras." } ], "@type": [ "http://www.w3.org/ns/prov#Person" ], "http://www.w3.org/ns/prov#hadRole": [ { "@value": "Program architect" } ], "https://schema.org/name": [ { "@value": "David Hilbert (1862–1943)" } ] }, { "@id": "https://w3id.org/np/RAXut_tYBIBaf53frjHN9ttCnUj4zq8JhXllSz7MyKpME/agent-pasch", "http://purl.org/dc/terms/description": [ { "@value": "Discovered that order is an assumption, not a triviality (Vorlesungen über neuere Geometrie, 1882). Namesake of axiom A7 (`inner_pasch`), on which the whole of Stage 2 rests: SST 3.1 (betw_trivial, indirectly), 3.2 (betw_symm), 3.5 (betw_inner_trans)." } ], "@type": [ "http://www.w3.org/ns/prov#Person" ], "http://www.w3.org/ns/prov#hadRole": [ { "@value": "Axiom source" } ], "https://schema.org/name": [ { "@value": "Moritz Pasch (1843–1930)" } ] }, { "@id": "https://w3id.org/np/RAXut_tYBIBaf53frjHN9ttCnUj4zq8JhXllSz7MyKpME/agent-schwabhaeuser", "http://purl.org/dc/terms/description": [ { "@value": "Completed and published the treatise: Schwabhäuser, Szmielew, Tarski, 'Metamathematische Methoden in der Geometrie', Springer 1983. Every 'SST n.m' tag in the artifact cites all three authors through his numbering." } ], "@type": [ "http://www.w3.org/ns/prov#Person" ], "http://www.w3.org/ns/prov#hadRole": [ { "@value": "Systematizer and publisher" } ], "https://schema.org/name": [ { "@value": "Wolfram Schwabhäuser (1931–1985)" } ] }, { "@id": "https://w3id.org/np/RAXut_tYBIBaf53frjHN9ttCnUj4zq8JhXllSz7MyKpME/agent-szmielew", "http://purl.org/dc/terms/description": [ { "@value": "Part I of SST grew from her lectures; the artifact follows her development lemma-for-lemma: SST 2.1–2.5, 2.8, 2.11, 2.12 (congruence calculus, segment addition, construction uniqueness); 3.1–3.3, 3.5, 3.6(1), 3.6(2), 3.7(1), 3.7(2) (betweenness calculus); 4.2, 4.3, 4.5, 4.6 (congruence–betweenness bridge); 7.4, 7.5, 7.13, 7.15 (point reflection and its isometry). She died before publication; her share of the credit is frequently understated." } ], "@type": [ "http://www.w3.org/ns/prov#Person" ], "http://www.w3.org/ns/prov#hadRole": [ { "@value": "Development author (followed lemma-for-lemma)" } ], "https://schema.org/name": [ { "@value": "Wanda Szmielew (1918–1976)" } ] }, { "@id": "https://w3id.org/np/RAXut_tYBIBaf53frjHN9ttCnUj4zq8JhXllSz7MyKpME/agent-tarski", "http://purl.org/dc/terms/description": [ { "@value": "The axiom system formalized as the `Tarski` typeclass, axioms A1–A8 (cong_pseudo_refl, cong_inner_trans, cong_identity, segment_construction, five_segment, betw_identity, inner_pasch, lower_dim), developed 1926–27; completeness and decidability of elementary geometry, guaranteeing the synthetic development agrees with EuclideanSpace ℝ (Fin n) on all first-order sentences. Survey citation: Tarski & Givant, 'Tarski's System of Geometry', Bulletin of Symbolic Logic 5(2), 1999." } ], "@type": [ "http://www.w3.org/ns/prov#Person" ], "http://www.w3.org/ns/prov#hadRole": [ { "@value": "Axiom-system author; metatheorist" } ], "https://schema.org/name": [ { "@value": "Alfred Tarski (1901–1983)" } ] }, { "@id": "https://w3id.org/np/RAXut_tYBIBaf53frjHN9ttCnUj4zq8JhXllSz7MyKpME/agent-user", "http://purl.org/dc/terms/description": [ { "@value": "Set the organizing question and metaphor (being 'trapped' in EuclideanSpace ℝ (Fin n) with only straightedge and compass), chose each descent (perpendiculars → compiling file → SST ch. 4 block → SST 7.13), and supplied the persistence that drove the artifact to zero `sorry`s. Directed the follow-up session that found a working Lean toolchain, compiled the artifact, and requested the fix for the sole compile error. Holds the director's and verifier's credit." } ], "@type": [ "http://www.w3.org/ns/prov#Person" ], "http://www.w3.org/ns/prov#hadRole": [ { "@id": "https://credit.niso.org/contributor-roles/conceptualization" }, { "@id": "https://credit.niso.org/contributor-roles/supervision" }, { "@id": "https://credit.niso.org/contributor-roles/validation" } ], "https://schema.org/identifier": [ { "@id": "https://orcid.org/0000-0002-8042-4131" } ], "https://schema.org/name": [ { "@value": "Myles Axton" } ], "https://schema.org/sameAs": [ { "@id": "https://orcid.org/0000-0002-8042-4131" } ] }, { "@id": "https://w3id.org/np/RAXut_tYBIBaf53frjHN9ttCnUj4zq8JhXllSz7MyKpME/artifact", "http://purl.org/dc/terms/contributor": [ { "@id": "https://w3id.org/np/RAXut_tYBIBaf53frjHN9ttCnUj4zq8JhXllSz7MyKpME/agent-claude" }, { "@id": "https://w3id.org/np/RAXut_tYBIBaf53frjHN9ttCnUj4zq8JhXllSz7MyKpME/agent-euclid" }, { "@id": "https://w3id.org/np/RAXut_tYBIBaf53frjHN9ttCnUj4zq8JhXllSz7MyKpME/agent-geocoq" }, { "@id": "https://w3id.org/np/RAXut_tYBIBaf53frjHN9ttCnUj4zq8JhXllSz7MyKpME/agent-gupta" }, { "@id": "https://w3id.org/np/RAXut_tYBIBaf53frjHN9ttCnUj4zq8JhXllSz7MyKpME/agent-hilbert" }, { "@id": "https://w3id.org/np/RAXut_tYBIBaf53frjHN9ttCnUj4zq8JhXllSz7MyKpME/agent-pasch" }, { "@id": "https://w3id.org/np/RAXut_tYBIBaf53frjHN9ttCnUj4zq8JhXllSz7MyKpME/agent-schwabhaeuser" }, { "@id": "https://w3id.org/np/RAXut_tYBIBaf53frjHN9ttCnUj4zq8JhXllSz7MyKpME/agent-szmielew" }, { "@id": "https://w3id.org/np/RAXut_tYBIBaf53frjHN9ttCnUj4zq8JhXllSz7MyKpME/agent-tarski" }, { "@id": "https://w3id.org/np/RAXut_tYBIBaf53frjHN9ttCnUj4zq8JhXllSz7MyKpME/agent-user" } ], "http://purl.org/dc/terms/relation": [ { "@id": "https://w3id.org/np/RAXut_tYBIBaf53frjHN9ttCnUj4zq8JhXllSz7MyKpME/dedication" } ], "http://purl.org/dc/terms/tableOfContents": [ { "@id": "https://w3id.org/np/RAXut_tYBIBaf53frjHN9ttCnUj4zq8JhXllSz7MyKpME/sst-map" } ], "http://purl.org/faia/terms/declaration": [ { "@id": "https://w3id.org/np/RAXut_tYBIBaf53frjHN9ttCnUj4zq8JhXllSz7MyKpME/faia" } ], "http://purl.org/iscc/terms/iscc": [ { "@value": "ISCC:PENDING — see sub:isccNote" } ], "@type": [ "http://www.w3.org/ns/prov#Entity", "https://schema.org/SoftwareSourceCode" ], "https://schema.org/codeRepository": [ { "@id": "https://github.com/johnmaxton/lean4-starter/blob/90018aec70b2bb8950c1045cac443731825d79ef/Tarski.lean" } ], "https://schema.org/contentSize": [ { "@value": "28435 bytes (648 lines)" } ], "https://schema.org/description": [ { "@value": "A synthetic development of Tarski's Euclidean geometry following Schwabhäuser–Szmielew–Tarski (SST) chapters 2–7: eleven axioms over two primitives (betweenness, segment congruence), developed through SST 7.13/7.15 (point reflection is an isometry). Zero `sorry`s. Compiles cleanly (`lean Tarski.lean` and `lake build`, exit 0) under both leanprover/lean4-nightly:nightly-2023-05-16 and leanprover/lean4:v4.32.0, confirming the dependency-free (core-Lean-4-only) claim across toolchain versions." } ], "https://schema.org/name": [ { "@value": "Tarski.lean" } ], "https://schema.org/programmingLanguage": [ { "@value": "Lean 4 (core language only; no Mathlib dependency)" } ], "https://schema.org/sha256": [ { "@value": "1372181e2284465648cf15fdd9b7a761ceef9288224feccfd71fb63a5417bfd1" } ] }, { "@id": "https://w3id.org/np/RAXut_tYBIBaf53frjHN9ttCnUj4zq8JhXllSz7MyKpME/dedication", "http://purl.org/dc/terms/description": [ { "@value": "Myles Axton thanks his father, Richard Axton (1941–2021), for his introduction to Euclidean geometry and the inspiration to do more with less (straight edge and compass only)." } ], "@type": [ "https://schema.org/Comment" ], "https://schema.org/about": [ { "@id": "https://w3id.org/np/RAXut_tYBIBaf53frjHN9ttCnUj4zq8JhXllSz7MyKpME/person-richard-axton" } ], "https://schema.org/name": [ { "@value": "Dedication" } ] }, { "@id": "https://w3id.org/np/RAXut_tYBIBaf53frjHN9ttCnUj4zq8JhXllSz7MyKpME/sst-map", "@type": [ "https://schema.org/Dataset" ], "https://schema.org/description": [ { "@value": "Lean name = SST number [= GeoCoq name where applicable]: cong_refl = 2.1; cong_symm = 2.2; cong_trans = 2.3; cong_left_comm = 2.4; cong_right_comm = 2.5; cong_trivial = 2.8; cong_add = 2.11 [l2_11]; construction_uniqueness = 2.12; betw_trivial = 3.1; betw_symm = 3.2; betw_left_trivial = 3.3; betw_inner_trans = 3.5; betw_exchange_left = 3.6(1); betw_exchange2 = 3.6(2) [between_exchange2]; betw_outer_trans = 3.7(1); betw_outer_trans' = 3.7(2); Cong3 = Def. 4.1 [Cong_3]; inner_five_segment = 4.2 [l4_2]; cong_sub = 4.3 [l4_3]; cong3_construction = 4.5 [l4_5]; betw_transfer = 4.6 [l4_6]; symmetric_point_exists = 7.4; symmetric_point_uniqueness = 7.5; reflect_cong = 7.13 [l7_13]; reflect_betw = 7.15 [l7_15]. Axioms A1–A8 = Tarski. Declared future work: Per = Euclid Def. I.10 / SST ch. 8; perpendiculars and midpoints = 8.18, 8.22 (Gupta); target theorem = Pythagoras, Euclid I.47–I.48, via segment arithmetic, SST ch. 14–15 (Hilbert)." } ], "https://schema.org/name": [ { "@value": "Theorem-to-source concordance" } ] }, { "@id": "https://w3id.org/np/RAXut_tYBIBaf53frjHN9ttCnUj4zq8JhXllSz7MyKpME/faia", "http://purl.org/faia/terms/aiContribution": [ { "@value": "Reconstruction of the SST/GeoCoq proof architecture from model memory; independent re-derivation where memory was insufficient (the SST 4.5 scaffold bookkeeping; SST 3.7(2) via mirror application of 3.7(1); the five-segment slot assignments in SST 7.13); translation into dependency-free core Lean 4; expository docstrings. In the follow-up session: diagnosed and fixed one compile error (the `example` at the end of Stage 5 used Mathlib's `∃!` unique-existence notation, unavailable in core Lean 4; rewritten as its explicit unfolding), then verified compilation." } ], "http://purl.org/faia/terms/aiSystem": [ { "@value": "Claude (Anthropic), Claude Fable 5, chat interface, sandboxed (no network, no Lean toolchain), for the original drafting session; Claude (Anthropic), Claude Sonnet 5, Claude Code CLI, with network and a working Lean 4 toolchain, for the subsequent compilation and fix session." } ], "http://purl.org/faia/terms/humanOversight": [ { "@value": "Every construction and proof step was chosen or approved turn-by-turn in dialogue; the human set direction, scope, and the requirement of resolving all `sorry`s. The human also directed the follow-up build/fix/compile session and reviewed its result before this declaration was finalized." } ], "http://purl.org/faia/terms/knownLimitations": [ { "@value": "The artifact now compiles cleanly under two independent Lean 4 toolchains (see schema:description); this discharges the compilation-verification limitation noted in the original sandbox draft. Remaining limitations: the mathematical content has not been cross-checked against an independent formalization (e.g. GeoCoq itself) beyond the lemma-map correspondence in sub:sst-map, and no ISCC or trusted timestamp has yet been minted (see sub:isccNote, sub:timestampNote)." } ], "http://purl.org/faia/terms/mode": [ { "@value": "AI-drafted, human-directed" } ], "http://purl.org/faia/terms/originalityStatement": [ { "@value": "No new mathematics. Every theorem in the artifact is prior art carrying an SST number (see sub:sst-map). The creative contributions of the AI-human collaboration are formalization engineering and exposition only." } ], "@type": [ "http://purl.org/faia/terms/AIUsageDeclaration" ] }, { "@id": "https://w3id.org/np/RAXut_tYBIBaf53frjHN9ttCnUj4zq8JhXllSz7MyKpME/person-richard-axton", "http://purl.org/dc/terms/description": [ { "@value": "Introduced Myles Axton to Euclidean geometry. The artifact's governing constraint — do more with less, straight edge and compass only — is his inspiration, and it is the same austerity that runs from Euclid's instruments through Tarski's two primitives to Gupta's removal of the continuity axiom." } ], "@type": [ "http://www.w3.org/ns/prov#Person" ], "http://www.w3.org/ns/prov#hadRole": [ { "@value": "Dedicatee; first teacher" } ], "https://schema.org/name": [ { "@value": "Richard Axton (1941–2021)" } ] }, { "@id": "https://w3id.org/np/RAXut_tYBIBaf53frjHN9ttCnUj4zq8JhXllSz7MyKpME/isccNote", "http://purl.org/dc/terms/description": [ { "@value": "ISO 24138 ISCC generation (Meta-, Content-, Data-, Instance-Code units) requires the iscc-core reference implementation, unavailable when this declaration was drafted. The declaration is therefore provisionally bound by the SHA-256 digest recorded in sub:artifact, computed over the compiled, current version of Tarski.lean. Upon finalization: (1) run `iscc-core` over the frozen file to mint the ISCC and replace the PENDING value; (2) obtain an RFC 3161 trusted timestamp or ledger anchor for this document; (3) sign the nanopublication with the declarant's key (this step is completed as of publication of this nanopub)." } ], "@type": [ "https://schema.org/Comment" ], "https://schema.org/name": [ { "@value": "ISCC binding status" } ] }, { "@id": "https://w3id.org/np/RAXut_tYBIBaf53frjHN9ttCnUj4zq8JhXllSz7MyKpME/timestampNote", "http://purl.org/dc/terms/description": [ { "@value": "All timestamps herein are the system clock of the drafting/verification sessions (self-asserted), not trusted timestamps. They are honest but not tamper-evident." } ], "@type": [ "https://schema.org/Comment" ], "https://schema.org/name": [ { "@value": "Timestamp status" } ] } ] }, { "@id": "https://w3id.org/np/RAXut_tYBIBaf53frjHN9ttCnUj4zq8JhXllSz7MyKpME/provenance", "@graph": [ { "@id": "https://w3id.org/np/RAXut_tYBIBaf53frjHN9ttCnUj4zq8JhXllSz7MyKpME/activity", "http://purl.org/dc/terms/description": [ { "@value": "A single sandboxed chat session beginning from the Pythagorean theorem in Mathlib's inner product spaces (norm_add_sq_eq_norm_sq_add_norm_sq_of_inner_eq_zero) and EuclideanSpace ℝ (Fin n), pivoting to the synthetic question, and building the Lean 4 artifact over successive turns. 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