{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:KS4MBUBBCW4L7ST4V7OOXTWOOH","short_pith_number":"pith:KS4MBUBB","schema_version":"1.0","canonical_sha256":"54b8c0d02115b8bfca7cafdcebcece71ef057b821930ffd5130a2fdb33b535c7","source":{"kind":"arxiv","id":"2606.02186","version":1},"attestation_state":"computed","paper":{"title":"Higher-Rank Orthogonal Twists, APS Boundary Conditions, and $O(2)$-Equivariant Spectral Flow on a Warped Cylinder","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th","math.DG","math.MP"],"primary_cat":"math-ph","authors_text":"Sanchita Sharma, Taro Kimura","submitted_at":"2026-06-01T12:42:42Z","abstract_excerpt":"We study $O(2)$-equivariant spectral flow for Dirac operators on a finite warped cylinder equipped with fixed admissible regularized APS boundary conditions. The twisting bundle is a real higher-rank orthogonal bundle, and reflection symmetry is implemented by a fiber involution. After complexifying the twisting bundle and diagonalizing the orthogonal twist, the Dirac equation decomposes into a scalar Fourier-mode radial equation, with moving rotating blocks and stationary neutral blocks. After regrouping conjugate and reflection-paired blocks, the crossing contributions define real $RO(O(2))$"},"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":"2606.02186","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-06-01T12:42:42Z","cross_cats_sorted":["hep-th","math.DG","math.MP"],"title_canon_sha256":"0de700c8078dbe93c6ae3a9c75d095de9543b5d347a419545921f293dee7fe92","abstract_canon_sha256":"58aaadc309f3e78cf9281fe1fef3053a8a2ef44c7d2118e1951684e457408f87"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T03:04:52.649550Z","signature_b64":"v5s7gafOvXJls1dYcA3QRYZd1J/wf0dhRKchovfAEZiSGHqpB2T9xApJ6S1i/EY3TDgaIxUHt3vMseqOouOyDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"54b8c0d02115b8bfca7cafdcebcece71ef057b821930ffd5130a2fdb33b535c7","last_reissued_at":"2026-06-02T03:04:52.649057Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T03:04:52.649057Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Higher-Rank Orthogonal Twists, APS Boundary Conditions, and $O(2)$-Equivariant Spectral Flow on a Warped Cylinder","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th","math.DG","math.MP"],"primary_cat":"math-ph","authors_text":"Sanchita Sharma, Taro Kimura","submitted_at":"2026-06-01T12:42:42Z","abstract_excerpt":"We study $O(2)$-equivariant spectral flow for Dirac operators on a finite warped cylinder equipped with fixed admissible regularized APS boundary conditions. The twisting bundle is a real higher-rank orthogonal bundle, and reflection symmetry is implemented by a fiber involution. After complexifying the twisting bundle and diagonalizing the orthogonal twist, the Dirac equation decomposes into a scalar Fourier-mode radial equation, with moving rotating blocks and stationary neutral blocks. After regrouping conjugate and reflection-paired blocks, the crossing contributions define real $RO(O(2))$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.02186","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/2606.02186/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2606.02186","created_at":"2026-06-02T03:04:52.649114+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.02186v1","created_at":"2026-06-02T03:04:52.649114+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.02186","created_at":"2026-06-02T03:04:52.649114+00:00"},{"alias_kind":"pith_short_12","alias_value":"KS4MBUBBCW4L","created_at":"2026-06-02T03:04:52.649114+00:00"},{"alias_kind":"pith_short_16","alias_value":"KS4MBUBBCW4L7ST4","created_at":"2026-06-02T03:04:52.649114+00:00"},{"alias_kind":"pith_short_8","alias_value":"KS4MBUBB","created_at":"2026-06-02T03:04:52.649114+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/KS4MBUBBCW4L7ST4V7OOXTWOOH","json":"https://pith.science/pith/KS4MBUBBCW4L7ST4V7OOXTWOOH.json","graph_json":"https://pith.science/api/pith-number/KS4MBUBBCW4L7ST4V7OOXTWOOH/graph.json","events_json":"https://pith.science/api/pith-number/KS4MBUBBCW4L7ST4V7OOXTWOOH/events.json","paper":"https://pith.science/paper/KS4MBUBB"},"agent_actions":{"view_html":"https://pith.science/pith/KS4MBUBBCW4L7ST4V7OOXTWOOH","download_json":"https://pith.science/pith/KS4MBUBBCW4L7ST4V7OOXTWOOH.json","view_paper":"https://pith.science/paper/KS4MBUBB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.02186&json=true","fetch_graph":"https://pith.science/api/pith-number/KS4MBUBBCW4L7ST4V7OOXTWOOH/graph.json","fetch_events":"https://pith.science/api/pith-number/KS4MBUBBCW4L7ST4V7OOXTWOOH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KS4MBUBBCW4L7ST4V7OOXTWOOH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KS4MBUBBCW4L7ST4V7OOXTWOOH/action/storage_attestation","attest_author":"https://pith.science/pith/KS4MBUBBCW4L7ST4V7OOXTWOOH/action/author_attestation","sign_citation":"https://pith.science/pith/KS4MBUBBCW4L7ST4V7OOXTWOOH/action/citation_signature","submit_replication":"https://pith.science/pith/KS4MBUBBCW4L7ST4V7OOXTWOOH/action/replication_record"}},"created_at":"2026-06-02T03:04:52.649114+00:00","updated_at":"2026-06-02T03:04:52.649114+00:00"}