{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:LEVGCEINHKCRF3FSHT44M5P4TP","short_pith_number":"pith:LEVGCEIN","schema_version":"1.0","canonical_sha256":"592a61110d3a8512ecb23cf9c675fc9bc62b2d12c1c1f7c454498c5392bafc18","source":{"kind":"arxiv","id":"0907.5283","version":2},"attestation_state":"computed","paper":{"title":"Orientation reversal of manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Daniel M\\\"ullner","submitted_at":"2009-07-30T15:51:43Z","abstract_excerpt":"We call a closed, connected, orientable manifold in one of the categories TOP, PL or DIFF chiral if it does not admit an orientation-reversing automorphism and amphicheiral otherwise. Moreover, we call a manifold strongly chiral if it does not admit a self-map of degree -1. We prove that there are strongly chiral, smooth manifolds in every oriented bordism class in every dimension greater than two. We also produce simply-connected, strongly chiral manifolds in every dimension greater than six. For every positive integer k, we exhibit lens spaces with an orientation-reversing self-diffeomorphis"},"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":"0907.5283","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-07-30T15:51:43Z","cross_cats_sorted":[],"title_canon_sha256":"8380e437ac12ffcdf5500c7c70828dead994f0e68736bba930f455a1f7a0259c","abstract_canon_sha256":"e4b5b3f568e96597b27fee30fc767463fe70a7e806cc738ae46e87044bb29c00"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:33:04.357407Z","signature_b64":"IOZcim1KwmmDOmlIbIzZ4uuZcjULuDSQ1RJSkdU1QG94ja9WhGUn+tqDrTyItWJHGdOnEundAEtmpwaJx0LGDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"592a61110d3a8512ecb23cf9c675fc9bc62b2d12c1c1f7c454498c5392bafc18","last_reissued_at":"2026-05-18T04:33:04.356597Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:33:04.356597Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Orientation reversal of manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Daniel M\\\"ullner","submitted_at":"2009-07-30T15:51:43Z","abstract_excerpt":"We call a closed, connected, orientable manifold in one of the categories TOP, PL or DIFF chiral if it does not admit an orientation-reversing automorphism and amphicheiral otherwise. Moreover, we call a manifold strongly chiral if it does not admit a self-map of degree -1. We prove that there are strongly chiral, smooth manifolds in every oriented bordism class in every dimension greater than two. We also produce simply-connected, strongly chiral manifolds in every dimension greater than six. For every positive integer k, we exhibit lens spaces with an orientation-reversing self-diffeomorphis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.5283","kind":"arxiv","version":2},"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":"0907.5283","created_at":"2026-05-18T04:33:04.356724+00:00"},{"alias_kind":"arxiv_version","alias_value":"0907.5283v2","created_at":"2026-05-18T04:33:04.356724+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.5283","created_at":"2026-05-18T04:33:04.356724+00:00"},{"alias_kind":"pith_short_12","alias_value":"LEVGCEINHKCR","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_16","alias_value":"LEVGCEINHKCRF3FS","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_8","alias_value":"LEVGCEIN","created_at":"2026-05-18T12:26:00.592388+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/LEVGCEINHKCRF3FSHT44M5P4TP","json":"https://pith.science/pith/LEVGCEINHKCRF3FSHT44M5P4TP.json","graph_json":"https://pith.science/api/pith-number/LEVGCEINHKCRF3FSHT44M5P4TP/graph.json","events_json":"https://pith.science/api/pith-number/LEVGCEINHKCRF3FSHT44M5P4TP/events.json","paper":"https://pith.science/paper/LEVGCEIN"},"agent_actions":{"view_html":"https://pith.science/pith/LEVGCEINHKCRF3FSHT44M5P4TP","download_json":"https://pith.science/pith/LEVGCEINHKCRF3FSHT44M5P4TP.json","view_paper":"https://pith.science/paper/LEVGCEIN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0907.5283&json=true","fetch_graph":"https://pith.science/api/pith-number/LEVGCEINHKCRF3FSHT44M5P4TP/graph.json","fetch_events":"https://pith.science/api/pith-number/LEVGCEINHKCRF3FSHT44M5P4TP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LEVGCEINHKCRF3FSHT44M5P4TP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LEVGCEINHKCRF3FSHT44M5P4TP/action/storage_attestation","attest_author":"https://pith.science/pith/LEVGCEINHKCRF3FSHT44M5P4TP/action/author_attestation","sign_citation":"https://pith.science/pith/LEVGCEINHKCRF3FSHT44M5P4TP/action/citation_signature","submit_replication":"https://pith.science/pith/LEVGCEINHKCRF3FSHT44M5P4TP/action/replication_record"}},"created_at":"2026-05-18T04:33:04.356724+00:00","updated_at":"2026-05-18T04:33:04.356724+00:00"}