{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:CPKWX2MT72FJREYNENKKD52WK6","short_pith_number":"pith:CPKWX2MT","schema_version":"1.0","canonical_sha256":"13d56be993fe8a98930d2354a1f756579f07f9e23980ea39757e5f41ff6c33ec","source":{"kind":"arxiv","id":"1610.09871","version":1},"attestation_state":"computed","paper":{"title":"Primary spectrum of $\\mathcal{C}^\\infty(M)$ and jets theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jes\\'us Mu\\~noz-D\\'iaz, Ricardo J. Alonso-Blanco","submitted_at":"2016-10-31T11:23:13Z","abstract_excerpt":"We consider, for each smooth manifold $M$, the set $\\mathbb{M}$ comprised by all the primary ideals of $\\mathcal{C}^\\infty(M)$ which are closed and whose radical is maximal. The classical Lie theory of jets (jets of submanifolds) must be extended to $\\mathbb{M}$ in order to have nice functorial properties. We will begin with the purely algebraic notions, referred always to the ring $\\mathcal{C}^\\infty(M)$. Subsequently it will be introduced the differentiable structures on each jets space of a given type. The theory of contact systems, which generalizes the classical one, has a part purely alg"},"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":"1610.09871","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-10-31T11:23:13Z","cross_cats_sorted":[],"title_canon_sha256":"4101cfb3511486c8c81fecb7db9b54a4eb59891f876d934f0ce5f5f84c8a0e82","abstract_canon_sha256":"1261655bd8004d04294370bc62795fdf680fd307662bd5d011e22a390ad572b7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:47.023499Z","signature_b64":"3i0/kTyWdSg03eCmoW5BbMFOtGMIdmzwqGgJzIw++WVxqShihMUyraiYXxRaHdGcgZIwcl5CAF9nCPthyNruAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"13d56be993fe8a98930d2354a1f756579f07f9e23980ea39757e5f41ff6c33ec","last_reissued_at":"2026-05-18T01:00:47.023103Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:47.023103Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Primary spectrum of $\\mathcal{C}^\\infty(M)$ and jets theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jes\\'us Mu\\~noz-D\\'iaz, Ricardo J. Alonso-Blanco","submitted_at":"2016-10-31T11:23:13Z","abstract_excerpt":"We consider, for each smooth manifold $M$, the set $\\mathbb{M}$ comprised by all the primary ideals of $\\mathcal{C}^\\infty(M)$ which are closed and whose radical is maximal. The classical Lie theory of jets (jets of submanifolds) must be extended to $\\mathbb{M}$ in order to have nice functorial properties. We will begin with the purely algebraic notions, referred always to the ring $\\mathcal{C}^\\infty(M)$. Subsequently it will be introduced the differentiable structures on each jets space of a given type. The theory of contact systems, which generalizes the classical one, has a part purely alg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09871","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1610.09871","created_at":"2026-05-18T01:00:47.023158+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.09871v1","created_at":"2026-05-18T01:00:47.023158+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.09871","created_at":"2026-05-18T01:00:47.023158+00:00"},{"alias_kind":"pith_short_12","alias_value":"CPKWX2MT72FJ","created_at":"2026-05-18T12:30:09.641336+00:00"},{"alias_kind":"pith_short_16","alias_value":"CPKWX2MT72FJREYN","created_at":"2026-05-18T12:30:09.641336+00:00"},{"alias_kind":"pith_short_8","alias_value":"CPKWX2MT","created_at":"2026-05-18T12:30:09.641336+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/CPKWX2MT72FJREYNENKKD52WK6","json":"https://pith.science/pith/CPKWX2MT72FJREYNENKKD52WK6.json","graph_json":"https://pith.science/api/pith-number/CPKWX2MT72FJREYNENKKD52WK6/graph.json","events_json":"https://pith.science/api/pith-number/CPKWX2MT72FJREYNENKKD52WK6/events.json","paper":"https://pith.science/paper/CPKWX2MT"},"agent_actions":{"view_html":"https://pith.science/pith/CPKWX2MT72FJREYNENKKD52WK6","download_json":"https://pith.science/pith/CPKWX2MT72FJREYNENKKD52WK6.json","view_paper":"https://pith.science/paper/CPKWX2MT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.09871&json=true","fetch_graph":"https://pith.science/api/pith-number/CPKWX2MT72FJREYNENKKD52WK6/graph.json","fetch_events":"https://pith.science/api/pith-number/CPKWX2MT72FJREYNENKKD52WK6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CPKWX2MT72FJREYNENKKD52WK6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CPKWX2MT72FJREYNENKKD52WK6/action/storage_attestation","attest_author":"https://pith.science/pith/CPKWX2MT72FJREYNENKKD52WK6/action/author_attestation","sign_citation":"https://pith.science/pith/CPKWX2MT72FJREYNENKKD52WK6/action/citation_signature","submit_replication":"https://pith.science/pith/CPKWX2MT72FJREYNENKKD52WK6/action/replication_record"}},"created_at":"2026-05-18T01:00:47.023158+00:00","updated_at":"2026-05-18T01:00:47.023158+00:00"}