{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:KIGICTFKCSTEQTRWHEBOCMCKZ3","short_pith_number":"pith:KIGICTFK","schema_version":"1.0","canonical_sha256":"520c814caa14a6484e363902e1304aced9e71d19961ea43971852a8418cf1c14","source":{"kind":"arxiv","id":"1008.4617","version":1},"attestation_state":"computed","paper":{"title":"Dynamical Systems on Spectral Metric Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Jean V. Bellissard, Kamran Reihani, Matilde Marcolli","submitted_at":"2010-08-26T22:59:54Z","abstract_excerpt":"Let (A,H,D) be a spectral triple, namely: A is a C*-algebra, H is a Hilbert space on which A acts and D is a selfadjoint operator with compact resolvent such that the set of elements of A having a bounded commutator with D is dense. A spectral metric space, the noncommutative analog of a complete metric space, is a spectral triple (A,H,D) with additional properties which guaranty that the Connes metric induces the weak*-topology on the state space of A. A *-automorphism respecting the metric defined a dynamical system. This article gives various answers to the question: is there a canonical sp"},"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":"1008.4617","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-08-26T22:59:54Z","cross_cats_sorted":[],"title_canon_sha256":"a1086b52e893bcc4e009fe6166450ff66a61d026d86a173cd403c2bf8aaa69ee","abstract_canon_sha256":"5c6c9bf3b7b28e10fe29333f3241e25efb435d550f6a2d30f578fb08433ebf6e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:44.602852Z","signature_b64":"KgOuVKmydDmgbDodLIWdnvIpfhUTEfGObH/U7GM1rCRkv/7SgF7iJZ2kaLJ3NbdaqlZvNtyavku3dx6v0OBaAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"520c814caa14a6484e363902e1304aced9e71d19961ea43971852a8418cf1c14","last_reissued_at":"2026-05-18T04:41:44.602261Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:44.602261Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dynamical Systems on Spectral Metric Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Jean V. Bellissard, Kamran Reihani, Matilde Marcolli","submitted_at":"2010-08-26T22:59:54Z","abstract_excerpt":"Let (A,H,D) be a spectral triple, namely: A is a C*-algebra, H is a Hilbert space on which A acts and D is a selfadjoint operator with compact resolvent such that the set of elements of A having a bounded commutator with D is dense. A spectral metric space, the noncommutative analog of a complete metric space, is a spectral triple (A,H,D) with additional properties which guaranty that the Connes metric induces the weak*-topology on the state space of A. A *-automorphism respecting the metric defined a dynamical system. This article gives various answers to the question: is there a canonical sp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.4617","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":"1008.4617","created_at":"2026-05-18T04:41:44.602351+00:00"},{"alias_kind":"arxiv_version","alias_value":"1008.4617v1","created_at":"2026-05-18T04:41:44.602351+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.4617","created_at":"2026-05-18T04:41:44.602351+00:00"},{"alias_kind":"pith_short_12","alias_value":"KIGICTFKCSTE","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_16","alias_value":"KIGICTFKCSTEQTRW","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_8","alias_value":"KIGICTFK","created_at":"2026-05-18T12:26:09.077623+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/KIGICTFKCSTEQTRWHEBOCMCKZ3","json":"https://pith.science/pith/KIGICTFKCSTEQTRWHEBOCMCKZ3.json","graph_json":"https://pith.science/api/pith-number/KIGICTFKCSTEQTRWHEBOCMCKZ3/graph.json","events_json":"https://pith.science/api/pith-number/KIGICTFKCSTEQTRWHEBOCMCKZ3/events.json","paper":"https://pith.science/paper/KIGICTFK"},"agent_actions":{"view_html":"https://pith.science/pith/KIGICTFKCSTEQTRWHEBOCMCKZ3","download_json":"https://pith.science/pith/KIGICTFKCSTEQTRWHEBOCMCKZ3.json","view_paper":"https://pith.science/paper/KIGICTFK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1008.4617&json=true","fetch_graph":"https://pith.science/api/pith-number/KIGICTFKCSTEQTRWHEBOCMCKZ3/graph.json","fetch_events":"https://pith.science/api/pith-number/KIGICTFKCSTEQTRWHEBOCMCKZ3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KIGICTFKCSTEQTRWHEBOCMCKZ3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KIGICTFKCSTEQTRWHEBOCMCKZ3/action/storage_attestation","attest_author":"https://pith.science/pith/KIGICTFKCSTEQTRWHEBOCMCKZ3/action/author_attestation","sign_citation":"https://pith.science/pith/KIGICTFKCSTEQTRWHEBOCMCKZ3/action/citation_signature","submit_replication":"https://pith.science/pith/KIGICTFKCSTEQTRWHEBOCMCKZ3/action/replication_record"}},"created_at":"2026-05-18T04:41:44.602351+00:00","updated_at":"2026-05-18T04:41:44.602351+00:00"}