{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:HCFFW3HWSOLTLBBO5KCDHETXBN","short_pith_number":"pith:HCFFW3HW","schema_version":"1.0","canonical_sha256":"388a5b6cf6939735842eea843392770b41f44a36cf541c1000b24b119ffbf2c2","source":{"kind":"arxiv","id":"1810.10603","version":2},"attestation_state":"computed","paper":{"title":"The bulk-edge correspondence for continuous dislocated systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alexis Drouot","submitted_at":"2018-10-24T20:17:53Z","abstract_excerpt":"We study topological aspects of defect modes for a family of operators $\\{\\mathscr{P}(t)\\}_{t \\in [0,2\\pi]}$ on $L^2(\\mathbb{R})$. $\\mathscr{P}(t)$ is a periodic Schr\\\"odinger operator $P_0$ perturbed by a dislocated potential. This potential is periodic on the left and on the right, but acquires a phase defect $t$ from $-\\infty$ relative to $+\\infty$. When $t=\\pi$ and the dislocation is small and adiabatic, Fefferman, Lee-Thorp and Weinstein showed in previous work that Dirac points of $P_0$ (degeneracies in the band spectrum of $P_0$) bifurcate to defect modes of $\\mathscr{P}(\\pi)$.\n  We sho"},"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":"1810.10603","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-24T20:17:53Z","cross_cats_sorted":[],"title_canon_sha256":"2c6ba8bd8103bcef44beb851e7a381e102cf5f83e1b666ad419782a1b554f319","abstract_canon_sha256":"03d5901541e29cfe0c5c1ee316e70a4e62a5277a00c128b0665f3ed4bb3b811f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:19.353174Z","signature_b64":"+CUHwBRkYEw7ZrdCXjbKZv3rUn4m+VIutLY39L5PP1WgIQGgBOL0L7ryVN22s9RvaGLvj4wKidPgOfb5+bZ4BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"388a5b6cf6939735842eea843392770b41f44a36cf541c1000b24b119ffbf2c2","last_reissued_at":"2026-05-17T23:55:19.352683Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:19.352683Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The bulk-edge correspondence for continuous dislocated systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alexis Drouot","submitted_at":"2018-10-24T20:17:53Z","abstract_excerpt":"We study topological aspects of defect modes for a family of operators $\\{\\mathscr{P}(t)\\}_{t \\in [0,2\\pi]}$ on $L^2(\\mathbb{R})$. $\\mathscr{P}(t)$ is a periodic Schr\\\"odinger operator $P_0$ perturbed by a dislocated potential. This potential is periodic on the left and on the right, but acquires a phase defect $t$ from $-\\infty$ relative to $+\\infty$. When $t=\\pi$ and the dislocation is small and adiabatic, Fefferman, Lee-Thorp and Weinstein showed in previous work that Dirac points of $P_0$ (degeneracies in the band spectrum of $P_0$) bifurcate to defect modes of $\\mathscr{P}(\\pi)$.\n  We sho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.10603","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":"1810.10603","created_at":"2026-05-17T23:55:19.352760+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.10603v2","created_at":"2026-05-17T23:55:19.352760+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.10603","created_at":"2026-05-17T23:55:19.352760+00:00"},{"alias_kind":"pith_short_12","alias_value":"HCFFW3HWSOLT","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_16","alias_value":"HCFFW3HWSOLTLBBO","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_8","alias_value":"HCFFW3HW","created_at":"2026-05-18T12:32:28.185984+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.01377","citing_title":"Edge states in ordinary differential equations for dislocations","ref_index":7,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HCFFW3HWSOLTLBBO5KCDHETXBN","json":"https://pith.science/pith/HCFFW3HWSOLTLBBO5KCDHETXBN.json","graph_json":"https://pith.science/api/pith-number/HCFFW3HWSOLTLBBO5KCDHETXBN/graph.json","events_json":"https://pith.science/api/pith-number/HCFFW3HWSOLTLBBO5KCDHETXBN/events.json","paper":"https://pith.science/paper/HCFFW3HW"},"agent_actions":{"view_html":"https://pith.science/pith/HCFFW3HWSOLTLBBO5KCDHETXBN","download_json":"https://pith.science/pith/HCFFW3HWSOLTLBBO5KCDHETXBN.json","view_paper":"https://pith.science/paper/HCFFW3HW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.10603&json=true","fetch_graph":"https://pith.science/api/pith-number/HCFFW3HWSOLTLBBO5KCDHETXBN/graph.json","fetch_events":"https://pith.science/api/pith-number/HCFFW3HWSOLTLBBO5KCDHETXBN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HCFFW3HWSOLTLBBO5KCDHETXBN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HCFFW3HWSOLTLBBO5KCDHETXBN/action/storage_attestation","attest_author":"https://pith.science/pith/HCFFW3HWSOLTLBBO5KCDHETXBN/action/author_attestation","sign_citation":"https://pith.science/pith/HCFFW3HWSOLTLBBO5KCDHETXBN/action/citation_signature","submit_replication":"https://pith.science/pith/HCFFW3HWSOLTLBBO5KCDHETXBN/action/replication_record"}},"created_at":"2026-05-17T23:55:19.352760+00:00","updated_at":"2026-05-17T23:55:19.352760+00:00"}