{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:5DKL2SPACCRTCXTRWNOT2FHI2X","short_pith_number":"pith:5DKL2SPA","schema_version":"1.0","canonical_sha256":"e8d4bd49e010a3315e71b35d3d14e8d5c1ab9b410b4e23aa940ec514cffe1e3b","source":{"kind":"arxiv","id":"2209.12929","version":3},"attestation_state":"computed","paper":{"title":"Noncommutative Differential Geometry on Infinitesimal Spaces","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.NA","math-ph","math.MP"],"primary_cat":"math.NA","authors_text":"Damien Tageddine, Jean-Christophe Nave","submitted_at":"2022-09-26T18:02:50Z","abstract_excerpt":"In this paper, we use the language of noncommutative differential geometry to formalise discrete differential calculus. We begin with a brief review of inverse limit of posets as an approximation of topological spaces. We then show how to associate a $C^*$-algebra over a poset, giving it a piecewise-linear structure. Furthermore, we explain how dually the algebra of continuous function $C(M)$ over a manifold $M$ can be approximated by a direct limit of $C^*$-algebras over posets. Finally, in the spirit of noncommutative differential geometry, we define a finite dimensional spectral triple on e"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2209.12929","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NA","submitted_at":"2022-09-26T18:02:50Z","cross_cats_sorted":["cs.NA","math-ph","math.MP"],"title_canon_sha256":"176300b071bf0186d6a908d92ba827700766f7b928f3e0482e0e5b7f9ede64a5","abstract_canon_sha256":"5d159fcf6c4ad737b799e8a1ab9914bb96b1050ac39d40051c76fee1c87f6e79"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:03:09.677599Z","signature_b64":"R0AgxKFpJgERqlK7WABbJPpKWZrgEBZOitvXS4aI0ORoZ7Uvx3MPu+3keMXJe2HMLcVsUjwfi1LWDzIL4+3NAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e8d4bd49e010a3315e71b35d3d14e8d5c1ab9b410b4e23aa940ec514cffe1e3b","last_reissued_at":"2026-07-05T06:03:09.677091Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:03:09.677091Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Noncommutative Differential Geometry on Infinitesimal Spaces","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.NA","math-ph","math.MP"],"primary_cat":"math.NA","authors_text":"Damien Tageddine, Jean-Christophe Nave","submitted_at":"2022-09-26T18:02:50Z","abstract_excerpt":"In this paper, we use the language of noncommutative differential geometry to formalise discrete differential calculus. We begin with a brief review of inverse limit of posets as an approximation of topological spaces. We then show how to associate a $C^*$-algebra over a poset, giving it a piecewise-linear structure. Furthermore, we explain how dually the algebra of continuous function $C(M)$ over a manifold $M$ can be approximated by a direct limit of $C^*$-algebras over posets. Finally, in the spirit of noncommutative differential geometry, we define a finite dimensional spectral triple on e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.12929","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2209.12929/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2209.12929","created_at":"2026-07-05T06:03:09.677151+00:00"},{"alias_kind":"arxiv_version","alias_value":"2209.12929v3","created_at":"2026-07-05T06:03:09.677151+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.12929","created_at":"2026-07-05T06:03:09.677151+00:00"},{"alias_kind":"pith_short_12","alias_value":"5DKL2SPACCRT","created_at":"2026-07-05T06:03:09.677151+00:00"},{"alias_kind":"pith_short_16","alias_value":"5DKL2SPACCRTCXTR","created_at":"2026-07-05T06:03:09.677151+00:00"},{"alias_kind":"pith_short_8","alias_value":"5DKL2SPA","created_at":"2026-07-05T06:03:09.677151+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5DKL2SPACCRTCXTRWNOT2FHI2X","json":"https://pith.science/pith/5DKL2SPACCRTCXTRWNOT2FHI2X.json","graph_json":"https://pith.science/api/pith-number/5DKL2SPACCRTCXTRWNOT2FHI2X/graph.json","events_json":"https://pith.science/api/pith-number/5DKL2SPACCRTCXTRWNOT2FHI2X/events.json","paper":"https://pith.science/paper/5DKL2SPA"},"agent_actions":{"view_html":"https://pith.science/pith/5DKL2SPACCRTCXTRWNOT2FHI2X","download_json":"https://pith.science/pith/5DKL2SPACCRTCXTRWNOT2FHI2X.json","view_paper":"https://pith.science/paper/5DKL2SPA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2209.12929&json=true","fetch_graph":"https://pith.science/api/pith-number/5DKL2SPACCRTCXTRWNOT2FHI2X/graph.json","fetch_events":"https://pith.science/api/pith-number/5DKL2SPACCRTCXTRWNOT2FHI2X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5DKL2SPACCRTCXTRWNOT2FHI2X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5DKL2SPACCRTCXTRWNOT2FHI2X/action/storage_attestation","attest_author":"https://pith.science/pith/5DKL2SPACCRTCXTRWNOT2FHI2X/action/author_attestation","sign_citation":"https://pith.science/pith/5DKL2SPACCRTCXTRWNOT2FHI2X/action/citation_signature","submit_replication":"https://pith.science/pith/5DKL2SPACCRTCXTRWNOT2FHI2X/action/replication_record"}},"created_at":"2026-07-05T06:03:09.677151+00:00","updated_at":"2026-07-05T06:03:09.677151+00:00"}