{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:QQ5MJ3U3JUWCLA2ACI5L7AZVFV","short_pith_number":"pith:QQ5MJ3U3","schema_version":"1.0","canonical_sha256":"843ac4ee9b4d2c258340123abf83352d57223da443265cd7a98bf55611db9bd1","source":{"kind":"arxiv","id":"1012.3215","version":1},"attestation_state":"computed","paper":{"title":"Levinson's theorem and higher degree traces for Aharonov-Bohm operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"J. Kellendonk, K. Pankrashkin, S. Richard","submitted_at":"2010-12-15T02:49:31Z","abstract_excerpt":"We study Levinson type theorems for the family of Aharonov-Bohm models from different perspectives. The first one is purely analytical involving the explicit calculation of the wave-operators and allowing to determine precisely the various contributions to the left hand side of Levinson's theorem, namely those due to the scattering operator, the terms at 0-energy and at infinite energy. The second one is based on non-commutative topology revealing the topological nature of Levinson's theorem. We then include the parameters of the family into the topological description obtaining a new type 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":"1012.3215","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-12-15T02:49:31Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"dc5f7832e9c964770975b64a95d11cbdc0f36ef7e82c58e05a9ba75b398d500c","abstract_canon_sha256":"f576509b7f182c16fa04d8f19905a6f47454514236fd5f00a54cd8a5bb11cef4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:04:24.658012Z","signature_b64":"6fqHaaYPgSd2Dlpay65ey7ndYkoF5d/DuJnbPYwlIV/ss9AyzkqLLHv3GfL/f+avX1gI5qSEmeuFyrs++TXYCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"843ac4ee9b4d2c258340123abf83352d57223da443265cd7a98bf55611db9bd1","last_reissued_at":"2026-05-18T02:04:24.657515Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:04:24.657515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Levinson's theorem and higher degree traces for Aharonov-Bohm operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"J. Kellendonk, K. Pankrashkin, S. Richard","submitted_at":"2010-12-15T02:49:31Z","abstract_excerpt":"We study Levinson type theorems for the family of Aharonov-Bohm models from different perspectives. The first one is purely analytical involving the explicit calculation of the wave-operators and allowing to determine precisely the various contributions to the left hand side of Levinson's theorem, namely those due to the scattering operator, the terms at 0-energy and at infinite energy. The second one is based on non-commutative topology revealing the topological nature of Levinson's theorem. We then include the parameters of the family into the topological description obtaining a new type of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.3215","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":"1012.3215","created_at":"2026-05-18T02:04:24.657591+00:00"},{"alias_kind":"arxiv_version","alias_value":"1012.3215v1","created_at":"2026-05-18T02:04:24.657591+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.3215","created_at":"2026-05-18T02:04:24.657591+00:00"},{"alias_kind":"pith_short_12","alias_value":"QQ5MJ3U3JUWC","created_at":"2026-05-18T12:26:12.377268+00:00"},{"alias_kind":"pith_short_16","alias_value":"QQ5MJ3U3JUWCLA2A","created_at":"2026-05-18T12:26:12.377268+00:00"},{"alias_kind":"pith_short_8","alias_value":"QQ5MJ3U3","created_at":"2026-05-18T12:26:12.377268+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/QQ5MJ3U3JUWCLA2ACI5L7AZVFV","json":"https://pith.science/pith/QQ5MJ3U3JUWCLA2ACI5L7AZVFV.json","graph_json":"https://pith.science/api/pith-number/QQ5MJ3U3JUWCLA2ACI5L7AZVFV/graph.json","events_json":"https://pith.science/api/pith-number/QQ5MJ3U3JUWCLA2ACI5L7AZVFV/events.json","paper":"https://pith.science/paper/QQ5MJ3U3"},"agent_actions":{"view_html":"https://pith.science/pith/QQ5MJ3U3JUWCLA2ACI5L7AZVFV","download_json":"https://pith.science/pith/QQ5MJ3U3JUWCLA2ACI5L7AZVFV.json","view_paper":"https://pith.science/paper/QQ5MJ3U3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1012.3215&json=true","fetch_graph":"https://pith.science/api/pith-number/QQ5MJ3U3JUWCLA2ACI5L7AZVFV/graph.json","fetch_events":"https://pith.science/api/pith-number/QQ5MJ3U3JUWCLA2ACI5L7AZVFV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QQ5MJ3U3JUWCLA2ACI5L7AZVFV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QQ5MJ3U3JUWCLA2ACI5L7AZVFV/action/storage_attestation","attest_author":"https://pith.science/pith/QQ5MJ3U3JUWCLA2ACI5L7AZVFV/action/author_attestation","sign_citation":"https://pith.science/pith/QQ5MJ3U3JUWCLA2ACI5L7AZVFV/action/citation_signature","submit_replication":"https://pith.science/pith/QQ5MJ3U3JUWCLA2ACI5L7AZVFV/action/replication_record"}},"created_at":"2026-05-18T02:04:24.657591+00:00","updated_at":"2026-05-18T02:04:24.657591+00:00"}