{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:KEKPVWDU7PEWAAPJR7U77U2DGD","short_pith_number":"pith:KEKPVWDU","schema_version":"1.0","canonical_sha256":"5114fad874fbc96001e98fe9ffd34330fd06dd170e0fe5c5a72a26af01a303a9","source":{"kind":"arxiv","id":"1708.08336","version":3},"attestation_state":"computed","paper":{"title":"APS index theorem for even-dimensional manifolds with non-compact boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Maxim Braverman, Pengshuai Shi","submitted_at":"2017-08-24T19:26:21Z","abstract_excerpt":"We study the index of the APS boundary value problem for a strongly Callias-type operator $D$ on a complete even dimensional Riemannian manifold $M$ (the odd dimensional case was considered in our previous paper arXiv:1706.06737). We use this index to define the relative $\\eta$-invariant $\\eta(A_1,A_0)$ of two strongly Callias-type operators, which are equal outside of a compact set. Even though in our situation the $\\eta$-invariants of $A_1$ and $A_0$ are not defined, the relative $\\eta$-invariant behaves as if it were the difference $\\eta(A_1)-\\eta(A_0)$. We also define the spectral flow of "},"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":"1708.08336","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-08-24T19:26:21Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"d9ad99ebe8eeb5733a1d4fdff2b525912c6d0cda0f86e702f8a46d60e6813472","abstract_canon_sha256":"f3a0316bf031aa3da3af2d390a2c924e07c30ed42357696436a79396ed1a110a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:43.958127Z","signature_b64":"4dp5bpYcysEJNYYQ8vFXH2VZCSYsuRaHMiBdl72zaa0JkTb9kTgY94VFAwNvNYum5h/dlLIIVBTq577JAqhXDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5114fad874fbc96001e98fe9ffd34330fd06dd170e0fe5c5a72a26af01a303a9","last_reissued_at":"2026-05-17T23:59:43.957699Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:43.957699Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"APS index theorem for even-dimensional manifolds with non-compact boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Maxim Braverman, Pengshuai Shi","submitted_at":"2017-08-24T19:26:21Z","abstract_excerpt":"We study the index of the APS boundary value problem for a strongly Callias-type operator $D$ on a complete even dimensional Riemannian manifold $M$ (the odd dimensional case was considered in our previous paper arXiv:1706.06737). We use this index to define the relative $\\eta$-invariant $\\eta(A_1,A_0)$ of two strongly Callias-type operators, which are equal outside of a compact set. Even though in our situation the $\\eta$-invariants of $A_1$ and $A_0$ are not defined, the relative $\\eta$-invariant behaves as if it were the difference $\\eta(A_1)-\\eta(A_0)$. We also define the spectral flow of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.08336","kind":"arxiv","version":3},"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":"1708.08336","created_at":"2026-05-17T23:59:43.957770+00:00"},{"alias_kind":"arxiv_version","alias_value":"1708.08336v3","created_at":"2026-05-17T23:59:43.957770+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.08336","created_at":"2026-05-17T23:59:43.957770+00:00"},{"alias_kind":"pith_short_12","alias_value":"KEKPVWDU7PEW","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_16","alias_value":"KEKPVWDU7PEWAAPJ","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_8","alias_value":"KEKPVWDU","created_at":"2026-05-18T12:31:24.725408+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/KEKPVWDU7PEWAAPJR7U77U2DGD","json":"https://pith.science/pith/KEKPVWDU7PEWAAPJR7U77U2DGD.json","graph_json":"https://pith.science/api/pith-number/KEKPVWDU7PEWAAPJR7U77U2DGD/graph.json","events_json":"https://pith.science/api/pith-number/KEKPVWDU7PEWAAPJR7U77U2DGD/events.json","paper":"https://pith.science/paper/KEKPVWDU"},"agent_actions":{"view_html":"https://pith.science/pith/KEKPVWDU7PEWAAPJR7U77U2DGD","download_json":"https://pith.science/pith/KEKPVWDU7PEWAAPJR7U77U2DGD.json","view_paper":"https://pith.science/paper/KEKPVWDU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1708.08336&json=true","fetch_graph":"https://pith.science/api/pith-number/KEKPVWDU7PEWAAPJR7U77U2DGD/graph.json","fetch_events":"https://pith.science/api/pith-number/KEKPVWDU7PEWAAPJR7U77U2DGD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KEKPVWDU7PEWAAPJR7U77U2DGD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KEKPVWDU7PEWAAPJR7U77U2DGD/action/storage_attestation","attest_author":"https://pith.science/pith/KEKPVWDU7PEWAAPJR7U77U2DGD/action/author_attestation","sign_citation":"https://pith.science/pith/KEKPVWDU7PEWAAPJR7U77U2DGD/action/citation_signature","submit_replication":"https://pith.science/pith/KEKPVWDU7PEWAAPJR7U77U2DGD/action/replication_record"}},"created_at":"2026-05-17T23:59:43.957770+00:00","updated_at":"2026-05-17T23:59:43.957770+00:00"}