{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:OR7VIS6VNG5UPJ2XWIC73EL4YJ","short_pith_number":"pith:OR7VIS6V","schema_version":"1.0","canonical_sha256":"747f544bd569bb47a757b205fd917cc2783374820386ebd2bdd3f08a8bab72d0","source":{"kind":"arxiv","id":"1908.10733","version":1},"attestation_state":"computed","paper":{"title":"The relative Mishchenko--Fomenko higher index and almost flat bundles II: Almost flat index pairing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.KT","authors_text":"Yosuke Kubota","submitted_at":"2019-08-28T14:04:31Z","abstract_excerpt":"This is the second part of a series of papers which bridges the Chang--Weinberger--Yu relative higher index and geometry of almost flat hermitian vector bundles on manifolds with boundary. In this paper we apply the description of the relative higher index given in Part I to provide the relative version of the Hanke--Schick theorem, which relates the relative higher index with index pairing of a K-homology cycle with almost flat relative vector bundles. We also deal with the quantitative version and the dual problem of this theorem."},"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":"1908.10733","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2019-08-28T14:04:31Z","cross_cats_sorted":[],"title_canon_sha256":"aaabb7f8dbca78e999303418493832c865f0cd675aaf74086e0bf1d5911a4a35","abstract_canon_sha256":"dc51f76aab3b32bd8ce34744fdfa97fd03632aa4cb141d51e23002cf0f5eb140"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:00:20.750280Z","signature_b64":"lUvu4TLQt+9OFdBZaR1fvTr7qtcxf5x1EUBQpi93VyNtTrkASGYRSirlAEZiUwBR7HeLdMEOMJgSYy4cGdusCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"747f544bd569bb47a757b205fd917cc2783374820386ebd2bdd3f08a8bab72d0","last_reissued_at":"2026-07-05T00:00:20.749809Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:00:20.749809Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The relative Mishchenko--Fomenko higher index and almost flat bundles II: Almost flat index pairing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.KT","authors_text":"Yosuke Kubota","submitted_at":"2019-08-28T14:04:31Z","abstract_excerpt":"This is the second part of a series of papers which bridges the Chang--Weinberger--Yu relative higher index and geometry of almost flat hermitian vector bundles on manifolds with boundary. In this paper we apply the description of the relative higher index given in Part I to provide the relative version of the Hanke--Schick theorem, which relates the relative higher index with index pairing of a K-homology cycle with almost flat relative vector bundles. We also deal with the quantitative version and the dual problem of this theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.10733","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/1908.10733/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":"1908.10733","created_at":"2026-07-05T00:00:20.749866+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.10733v1","created_at":"2026-07-05T00:00:20.749866+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.10733","created_at":"2026-07-05T00:00:20.749866+00:00"},{"alias_kind":"pith_short_12","alias_value":"OR7VIS6VNG5U","created_at":"2026-07-05T00:00:20.749866+00:00"},{"alias_kind":"pith_short_16","alias_value":"OR7VIS6VNG5UPJ2X","created_at":"2026-07-05T00:00:20.749866+00:00"},{"alias_kind":"pith_short_8","alias_value":"OR7VIS6V","created_at":"2026-07-05T00:00:20.749866+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/OR7VIS6VNG5UPJ2XWIC73EL4YJ","json":"https://pith.science/pith/OR7VIS6VNG5UPJ2XWIC73EL4YJ.json","graph_json":"https://pith.science/api/pith-number/OR7VIS6VNG5UPJ2XWIC73EL4YJ/graph.json","events_json":"https://pith.science/api/pith-number/OR7VIS6VNG5UPJ2XWIC73EL4YJ/events.json","paper":"https://pith.science/paper/OR7VIS6V"},"agent_actions":{"view_html":"https://pith.science/pith/OR7VIS6VNG5UPJ2XWIC73EL4YJ","download_json":"https://pith.science/pith/OR7VIS6VNG5UPJ2XWIC73EL4YJ.json","view_paper":"https://pith.science/paper/OR7VIS6V","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.10733&json=true","fetch_graph":"https://pith.science/api/pith-number/OR7VIS6VNG5UPJ2XWIC73EL4YJ/graph.json","fetch_events":"https://pith.science/api/pith-number/OR7VIS6VNG5UPJ2XWIC73EL4YJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OR7VIS6VNG5UPJ2XWIC73EL4YJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OR7VIS6VNG5UPJ2XWIC73EL4YJ/action/storage_attestation","attest_author":"https://pith.science/pith/OR7VIS6VNG5UPJ2XWIC73EL4YJ/action/author_attestation","sign_citation":"https://pith.science/pith/OR7VIS6VNG5UPJ2XWIC73EL4YJ/action/citation_signature","submit_replication":"https://pith.science/pith/OR7VIS6VNG5UPJ2XWIC73EL4YJ/action/replication_record"}},"created_at":"2026-07-05T00:00:20.749866+00:00","updated_at":"2026-07-05T00:00:20.749866+00:00"}