{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:OR7VIS6VNG5UPJ2XWIC73EL4YJ","short_pith_number":"pith:OR7VIS6V","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"},"canonical_sha256":"747f544bd569bb47a757b205fd917cc2783374820386ebd2bdd3f08a8bab72d0","source":{"kind":"arxiv","id":"1908.10733","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.10733","created_at":"2026-07-05T00:00:20Z"},{"alias_kind":"arxiv_version","alias_value":"1908.10733v1","created_at":"2026-07-05T00:00:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.10733","created_at":"2026-07-05T00:00:20Z"},{"alias_kind":"pith_short_12","alias_value":"OR7VIS6VNG5U","created_at":"2026-07-05T00:00:20Z"},{"alias_kind":"pith_short_16","alias_value":"OR7VIS6VNG5UPJ2X","created_at":"2026-07-05T00:00:20Z"},{"alias_kind":"pith_short_8","alias_value":"OR7VIS6V","created_at":"2026-07-05T00:00:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:OR7VIS6VNG5UPJ2XWIC73EL4YJ","target":"record","payload":{"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"},"canonical_sha256":"747f544bd569bb47a757b205fd917cc2783374820386ebd2bdd3f08a8bab72d0","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"},"source_kind":"arxiv","source_id":"1908.10733","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:00:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZRIUDXgs8dS+F8ZcAwv0nDp8u+vGuHvT3bl7E7dr+N757McVCQ0jhDYa/Mw+uYvz9zBtYLSLipxv/LzhEqugBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T22:02:47.541031Z"},"content_sha256":"0ed1dd729cc8c31fcb9f430b727b308c38be71d4ca8058a1fa0fb3058ccf7707","schema_version":"1.0","event_id":"sha256:0ed1dd729cc8c31fcb9f430b727b308c38be71d4ca8058a1fa0fb3058ccf7707"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:OR7VIS6VNG5UPJ2XWIC73EL4YJ","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:00:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ATVL3q8LGeXcjkcSUqHubEwfZd0QGz4LFonT5pVtJjOXiaNJAseJoXsZrUQRPqgETTYwM6Qbf2ngIBnVWvx0BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T22:02:47.541935Z"},"content_sha256":"551b4e5d9f475d47fb900c0685a13da22168e41fa2afc97863d30c21e8174964","schema_version":"1.0","event_id":"sha256:551b4e5d9f475d47fb900c0685a13da22168e41fa2afc97863d30c21e8174964"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OR7VIS6VNG5UPJ2XWIC73EL4YJ/bundle.json","state_url":"https://pith.science/pith/OR7VIS6VNG5UPJ2XWIC73EL4YJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OR7VIS6VNG5UPJ2XWIC73EL4YJ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-16T22:02:47Z","links":{"resolver":"https://pith.science/pith/OR7VIS6VNG5UPJ2XWIC73EL4YJ","bundle":"https://pith.science/pith/OR7VIS6VNG5UPJ2XWIC73EL4YJ/bundle.json","state":"https://pith.science/pith/OR7VIS6VNG5UPJ2XWIC73EL4YJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OR7VIS6VNG5UPJ2XWIC73EL4YJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:OR7VIS6VNG5UPJ2XWIC73EL4YJ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"dc51f76aab3b32bd8ce34744fdfa97fd03632aa4cb141d51e23002cf0f5eb140","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2019-08-28T14:04:31Z","title_canon_sha256":"aaabb7f8dbca78e999303418493832c865f0cd675aaf74086e0bf1d5911a4a35"},"schema_version":"1.0","source":{"id":"1908.10733","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.10733","created_at":"2026-07-05T00:00:20Z"},{"alias_kind":"arxiv_version","alias_value":"1908.10733v1","created_at":"2026-07-05T00:00:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.10733","created_at":"2026-07-05T00:00:20Z"},{"alias_kind":"pith_short_12","alias_value":"OR7VIS6VNG5U","created_at":"2026-07-05T00:00:20Z"},{"alias_kind":"pith_short_16","alias_value":"OR7VIS6VNG5UPJ2X","created_at":"2026-07-05T00:00:20Z"},{"alias_kind":"pith_short_8","alias_value":"OR7VIS6V","created_at":"2026-07-05T00:00:20Z"}],"graph_snapshots":[{"event_id":"sha256:551b4e5d9f475d47fb900c0685a13da22168e41fa2afc97863d30c21e8174964","target":"graph","created_at":"2026-07-05T00:00:20Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.10733/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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.","authors_text":"Yosuke Kubota","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2019-08-28T14:04:31Z","title":"The relative Mishchenko--Fomenko higher index and almost flat bundles II: Almost flat index pairing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.10733","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:0ed1dd729cc8c31fcb9f430b727b308c38be71d4ca8058a1fa0fb3058ccf7707","target":"record","created_at":"2026-07-05T00:00:20Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"dc51f76aab3b32bd8ce34744fdfa97fd03632aa4cb141d51e23002cf0f5eb140","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2019-08-28T14:04:31Z","title_canon_sha256":"aaabb7f8dbca78e999303418493832c865f0cd675aaf74086e0bf1d5911a4a35"},"schema_version":"1.0","source":{"id":"1908.10733","kind":"arxiv","version":1}},"canonical_sha256":"747f544bd569bb47a757b205fd917cc2783374820386ebd2bdd3f08a8bab72d0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"747f544bd569bb47a757b205fd917cc2783374820386ebd2bdd3f08a8bab72d0","first_computed_at":"2026-07-05T00:00:20.749809Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:00:20.749809Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lUvu4TLQt+9OFdBZaR1fvTr7qtcxf5x1EUBQpi93VyNtTrkASGYRSirlAEZiUwBR7HeLdMEOMJgSYy4cGdusCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T00:00:20.750280Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.10733","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0ed1dd729cc8c31fcb9f430b727b308c38be71d4ca8058a1fa0fb3058ccf7707","sha256:551b4e5d9f475d47fb900c0685a13da22168e41fa2afc97863d30c21e8174964"],"state_sha256":"53dbe77202f986fe518b020061ed5c7a9cf1835be6adb1dcdf37a55327436c73"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l9bQ0Q8jUI203htnJ+NvFCaaDwM8k4Qs+yERwG0iXeSpMweLXzyLCVU57e8eZ/81gvNsEibzzJhanCCxHcE4Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T22:02:47.548625Z","bundle_sha256":"9b32af3a799d2f5db76c4b6b674221303d3277dfc81d2d11e80fb4ccb6f004a7"}}