{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:FIHUCOL7QK3T2TOAY6UMZFTLFA","short_pith_number":"pith:FIHUCOL7","schema_version":"1.0","canonical_sha256":"2a0f41397f82b73d4dc0c7a8cc966b283dedaf737f3b5467410f9c16369783dd","source":{"kind":"arxiv","id":"2006.13771","version":1},"attestation_state":"computed","paper":{"title":"Weil positivity and Trace formula, the archimedean place","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA","math.QA"],"primary_cat":"math.NT","authors_text":"Alain Connes, Caterina Consani","submitted_at":"2020-06-24T14:35:52Z","abstract_excerpt":"We provide a potential conceptual reason for the positivity of the Weil functional using the Hilbert space framework of the semi-local trace formula of the paper \"Trace formula in noncommutative geometry and the zeros of the Riemann zeta function\". (Selecta Math. 5 (1999), no. 1, 29--106). We explore in great details the simplest case of the single archimedean place. The root of the positivity is the trace of the scaling action compressed onto the orthogonal complement of the range of the cutoff projections associated to the cutoff in phase space, for cutoff parameter equal to 1. We express th"},"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":"2006.13771","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-06-24T14:35:52Z","cross_cats_sorted":["math.OA","math.QA"],"title_canon_sha256":"a3e8722049bda5624d252f30ea42884aeedcb389a3f69a7800110f55a50f4670","abstract_canon_sha256":"9c20d02477f9253381662e60787ea18dc7541af77c827564e6fe58ed261d581c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:13:19.866109Z","signature_b64":"HJuKsUf5H8ECUibxIYgYWf1dqP/SpNJ+qkvsZb4XGTM/c07GqVOF/QahHPWk1PaJ/3LaMlmO4kpjuD/Efq9dBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2a0f41397f82b73d4dc0c7a8cc966b283dedaf737f3b5467410f9c16369783dd","last_reissued_at":"2026-07-05T01:13:19.865646Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:13:19.865646Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Weil positivity and Trace formula, the archimedean place","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA","math.QA"],"primary_cat":"math.NT","authors_text":"Alain Connes, Caterina Consani","submitted_at":"2020-06-24T14:35:52Z","abstract_excerpt":"We provide a potential conceptual reason for the positivity of the Weil functional using the Hilbert space framework of the semi-local trace formula of the paper \"Trace formula in noncommutative geometry and the zeros of the Riemann zeta function\". (Selecta Math. 5 (1999), no. 1, 29--106). We explore in great details the simplest case of the single archimedean place. The root of the positivity is the trace of the scaling action compressed onto the orthogonal complement of the range of the cutoff projections associated to the cutoff in phase space, for cutoff parameter equal to 1. We express th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.13771","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2006.13771/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":"2006.13771","created_at":"2026-07-05T01:13:19.865704+00:00"},{"alias_kind":"arxiv_version","alias_value":"2006.13771v1","created_at":"2026-07-05T01:13:19.865704+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.13771","created_at":"2026-07-05T01:13:19.865704+00:00"},{"alias_kind":"pith_short_12","alias_value":"FIHUCOL7QK3T","created_at":"2026-07-05T01:13:19.865704+00:00"},{"alias_kind":"pith_short_16","alias_value":"FIHUCOL7QK3T2TOA","created_at":"2026-07-05T01:13:19.865704+00:00"},{"alias_kind":"pith_short_8","alias_value":"FIHUCOL7","created_at":"2026-07-05T01:13:19.865704+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.20224","citing_title":"High-Precision Approximation of Riemann Zeros via the Truncated Weil Form","ref_index":5,"is_internal_anchor":false},{"citing_arxiv_id":"2605.20224","citing_title":"High-Precision Approximation of Riemann Zeros via the Truncated Weil Form","ref_index":5,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FIHUCOL7QK3T2TOAY6UMZFTLFA","json":"https://pith.science/pith/FIHUCOL7QK3T2TOAY6UMZFTLFA.json","graph_json":"https://pith.science/api/pith-number/FIHUCOL7QK3T2TOAY6UMZFTLFA/graph.json","events_json":"https://pith.science/api/pith-number/FIHUCOL7QK3T2TOAY6UMZFTLFA/events.json","paper":"https://pith.science/paper/FIHUCOL7"},"agent_actions":{"view_html":"https://pith.science/pith/FIHUCOL7QK3T2TOAY6UMZFTLFA","download_json":"https://pith.science/pith/FIHUCOL7QK3T2TOAY6UMZFTLFA.json","view_paper":"https://pith.science/paper/FIHUCOL7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2006.13771&json=true","fetch_graph":"https://pith.science/api/pith-number/FIHUCOL7QK3T2TOAY6UMZFTLFA/graph.json","fetch_events":"https://pith.science/api/pith-number/FIHUCOL7QK3T2TOAY6UMZFTLFA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FIHUCOL7QK3T2TOAY6UMZFTLFA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FIHUCOL7QK3T2TOAY6UMZFTLFA/action/storage_attestation","attest_author":"https://pith.science/pith/FIHUCOL7QK3T2TOAY6UMZFTLFA/action/author_attestation","sign_citation":"https://pith.science/pith/FIHUCOL7QK3T2TOAY6UMZFTLFA/action/citation_signature","submit_replication":"https://pith.science/pith/FIHUCOL7QK3T2TOAY6UMZFTLFA/action/replication_record"}},"created_at":"2026-07-05T01:13:19.865704+00:00","updated_at":"2026-07-05T01:13:19.865704+00:00"}