{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2004:CJXUKNSMFAILTKRRW7K4JLTLF5","short_pith_number":"pith:CJXUKNSM","schema_version":"1.0","canonical_sha256":"126f45364c2810b9aa31b7d5c4ae6b2f6b2ec508455d336b387cedf12842e73f","source":{"kind":"arxiv","id":"math/0407401","version":1},"attestation_state":"computed","paper":{"title":"Cut-and-Paste on Foliated Bundles","license":"","headline":"","cross_cats":["math.KT"],"primary_cat":"math.DG","authors_text":"Eric Leichtnam, Paolo Piazza","submitted_at":"2004-07-23T12:50:25Z","abstract_excerpt":"We discuss the behaviour of the signature index class of closed foliated bundles under the operation of cutting and pasting. Along the way we establish several index theoretic results: we define Atiyah-Patodi-Singer (APS) index classes for Dirac-type operators on foliated bundles with boundary; we prove a relative index theorem for the difference of two APS-index classes associated to different boundary conditions; we prove a gluing formula on closed foliated bundles that are the union of two foliated bundles with boundary; we establish a variational formula for APS-index classes of a 1-parame"},"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":"math/0407401","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2004-07-23T12:50:25Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"1b76178e4725ad288d53f47c31e1e1ba8f7c3dc0fceea7c8758333a102bc4265","abstract_canon_sha256":"55ac40903682574027106bd653627bb1ae5ce06e00610b38c036db5715e798cf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:26.167082Z","signature_b64":"4yRmjNTzXqI1ZmtssRSdk6LyLaq+WMdFDqiKf6+j5HlsmctCj2Aog/ZRO/3++G/0T+em6atEiPrFVVNIFKxuBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"126f45364c2810b9aa31b7d5c4ae6b2f6b2ec508455d336b387cedf12842e73f","last_reissued_at":"2026-05-18T01:05:26.166478Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:26.166478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cut-and-Paste on Foliated Bundles","license":"","headline":"","cross_cats":["math.KT"],"primary_cat":"math.DG","authors_text":"Eric Leichtnam, Paolo Piazza","submitted_at":"2004-07-23T12:50:25Z","abstract_excerpt":"We discuss the behaviour of the signature index class of closed foliated bundles under the operation of cutting and pasting. Along the way we establish several index theoretic results: we define Atiyah-Patodi-Singer (APS) index classes for Dirac-type operators on foliated bundles with boundary; we prove a relative index theorem for the difference of two APS-index classes associated to different boundary conditions; we prove a gluing formula on closed foliated bundles that are the union of two foliated bundles with boundary; we establish a variational formula for APS-index classes of a 1-parame"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0407401","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":"math/0407401","created_at":"2026-05-18T01:05:26.166559+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0407401v1","created_at":"2026-05-18T01:05:26.166559+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0407401","created_at":"2026-05-18T01:05:26.166559+00:00"},{"alias_kind":"pith_short_12","alias_value":"CJXUKNSMFAIL","created_at":"2026-05-18T12:25:52.051335+00:00"},{"alias_kind":"pith_short_16","alias_value":"CJXUKNSMFAILTKRR","created_at":"2026-05-18T12:25:52.051335+00:00"},{"alias_kind":"pith_short_8","alias_value":"CJXUKNSM","created_at":"2026-05-18T12:25:52.051335+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/CJXUKNSMFAILTKRRW7K4JLTLF5","json":"https://pith.science/pith/CJXUKNSMFAILTKRRW7K4JLTLF5.json","graph_json":"https://pith.science/api/pith-number/CJXUKNSMFAILTKRRW7K4JLTLF5/graph.json","events_json":"https://pith.science/api/pith-number/CJXUKNSMFAILTKRRW7K4JLTLF5/events.json","paper":"https://pith.science/paper/CJXUKNSM"},"agent_actions":{"view_html":"https://pith.science/pith/CJXUKNSMFAILTKRRW7K4JLTLF5","download_json":"https://pith.science/pith/CJXUKNSMFAILTKRRW7K4JLTLF5.json","view_paper":"https://pith.science/paper/CJXUKNSM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0407401&json=true","fetch_graph":"https://pith.science/api/pith-number/CJXUKNSMFAILTKRRW7K4JLTLF5/graph.json","fetch_events":"https://pith.science/api/pith-number/CJXUKNSMFAILTKRRW7K4JLTLF5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CJXUKNSMFAILTKRRW7K4JLTLF5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CJXUKNSMFAILTKRRW7K4JLTLF5/action/storage_attestation","attest_author":"https://pith.science/pith/CJXUKNSMFAILTKRRW7K4JLTLF5/action/author_attestation","sign_citation":"https://pith.science/pith/CJXUKNSMFAILTKRRW7K4JLTLF5/action/citation_signature","submit_replication":"https://pith.science/pith/CJXUKNSMFAILTKRRW7K4JLTLF5/action/replication_record"}},"created_at":"2026-05-18T01:05:26.166559+00:00","updated_at":"2026-05-18T01:05:26.166559+00:00"}