{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:B26V6OOMZQKS4A6C5KRQRROLES","short_pith_number":"pith:B26V6OOM","schema_version":"1.0","canonical_sha256":"0ebd5f39cccc152e03c2eaa308c5cb24934dfa9daa20467b1d94368b9080b362","source":{"kind":"arxiv","id":"1112.5515","version":1},"attestation_state":"computed","paper":{"title":"On the Index Formula for an Isometric Diffeomorphism","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.FA","math.KT"],"primary_cat":"math.AP","authors_text":"A. Savin, B. Sternin, E. Schrohe","submitted_at":"2011-12-23T05:29:27Z","abstract_excerpt":"We give an elementary solution of the index problem for elliptic operators associated with the shift operator along the trajectories of an isometric diffeomorphism of a closed smooth manifold. This solution is based on a reduction (which preserves the index) of the operator to an elliptic pseudodifferential operator on a manifold of a higher dimension and an application of an Atiyah--Singer type formula. The final index formula is given in terms of the symbol of the operator on the original manifold."},"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":"1112.5515","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-12-23T05:29:27Z","cross_cats_sorted":["math.DS","math.FA","math.KT"],"title_canon_sha256":"6eee47faee6dc9a9430ee2b222a8f5d02d408ca46fb8a4d015d7cc88ef7ad944","abstract_canon_sha256":"4d3839cd18fdc8f5d07cafd290cb191d59161a8f4a8aad2a047caffffc7eada2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:05:46.595995Z","signature_b64":"0WGlhlDIxplIfSNWjJEPAEsDSf3EaBqGyIK7kfwzXfvaJ3ERY+sylEhlqUR9ZN5qVELhGWqbbMwapFBI4i1uBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ebd5f39cccc152e03c2eaa308c5cb24934dfa9daa20467b1d94368b9080b362","last_reissued_at":"2026-05-18T04:05:46.595424Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:05:46.595424Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Index Formula for an Isometric Diffeomorphism","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.FA","math.KT"],"primary_cat":"math.AP","authors_text":"A. Savin, B. Sternin, E. Schrohe","submitted_at":"2011-12-23T05:29:27Z","abstract_excerpt":"We give an elementary solution of the index problem for elliptic operators associated with the shift operator along the trajectories of an isometric diffeomorphism of a closed smooth manifold. This solution is based on a reduction (which preserves the index) of the operator to an elliptic pseudodifferential operator on a manifold of a higher dimension and an application of an Atiyah--Singer type formula. The final index formula is given in terms of the symbol of the operator on the original manifold."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.5515","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":"1112.5515","created_at":"2026-05-18T04:05:46.595536+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.5515v1","created_at":"2026-05-18T04:05:46.595536+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.5515","created_at":"2026-05-18T04:05:46.595536+00:00"},{"alias_kind":"pith_short_12","alias_value":"B26V6OOMZQKS","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_16","alias_value":"B26V6OOMZQKS4A6C","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_8","alias_value":"B26V6OOM","created_at":"2026-05-18T12:26:24.575870+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/B26V6OOMZQKS4A6C5KRQRROLES","json":"https://pith.science/pith/B26V6OOMZQKS4A6C5KRQRROLES.json","graph_json":"https://pith.science/api/pith-number/B26V6OOMZQKS4A6C5KRQRROLES/graph.json","events_json":"https://pith.science/api/pith-number/B26V6OOMZQKS4A6C5KRQRROLES/events.json","paper":"https://pith.science/paper/B26V6OOM"},"agent_actions":{"view_html":"https://pith.science/pith/B26V6OOMZQKS4A6C5KRQRROLES","download_json":"https://pith.science/pith/B26V6OOMZQKS4A6C5KRQRROLES.json","view_paper":"https://pith.science/paper/B26V6OOM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.5515&json=true","fetch_graph":"https://pith.science/api/pith-number/B26V6OOMZQKS4A6C5KRQRROLES/graph.json","fetch_events":"https://pith.science/api/pith-number/B26V6OOMZQKS4A6C5KRQRROLES/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/B26V6OOMZQKS4A6C5KRQRROLES/action/timestamp_anchor","attest_storage":"https://pith.science/pith/B26V6OOMZQKS4A6C5KRQRROLES/action/storage_attestation","attest_author":"https://pith.science/pith/B26V6OOMZQKS4A6C5KRQRROLES/action/author_attestation","sign_citation":"https://pith.science/pith/B26V6OOMZQKS4A6C5KRQRROLES/action/citation_signature","submit_replication":"https://pith.science/pith/B26V6OOMZQKS4A6C5KRQRROLES/action/replication_record"}},"created_at":"2026-05-18T04:05:46.595536+00:00","updated_at":"2026-05-18T04:05:46.595536+00:00"}