{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:EWF223OUNBMSJNDFEEZQ5LTX3Y","short_pith_number":"pith:EWF223OU","schema_version":"1.0","canonical_sha256":"258bad6dd4685924b46521330eae77de183a298870778b4b0cb3ad073c0405de","source":{"kind":"arxiv","id":"2412.14255","version":2},"attestation_state":"computed","paper":{"title":"Zero energy modes with Gaussian, exponential, or polynomial decay: Exact solutions in hermitian and nonhermitian regimes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mes-hall","cond-mat.supr-con","math-ph","math.MP","quant-ph"],"primary_cat":"hep-th","authors_text":"Angela Nigro, Pasquale Marra","submitted_at":"2024-12-18T19:00:04Z","abstract_excerpt":"Topological zero modes in topological insulators or superconductors are exponentially localized at the phase transition between a topologically trivial and nontrivial phase. These modes are solutions of a Jackiw-Rebbi equation modified with an additional term which is quadratic in the momentum. Moreover, localized fermionic modes can also be induced by harmonic potentials in superfluids and superconductors or in atomic nuclei. Here, by using inverse methods, we consider in the same framework exponentially-localized zero modes, as well as Gaussian modes induced by harmonic potentials (with supe"},"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":"2412.14255","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2024-12-18T19:00:04Z","cross_cats_sorted":["cond-mat.mes-hall","cond-mat.supr-con","math-ph","math.MP","quant-ph"],"title_canon_sha256":"7c637e728d1a52d8a4c463b885cd8cd2ed6bf386700f8c51c0e0fd91bf6adb03","abstract_canon_sha256":"302c9fe231eccbbf0e41ffa19a4fc9da99418dcfd67cd39b95f40c24e393db8d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:57:30.604519Z","signature_b64":"ObCvQm+yaGlK3UiR4VUP/WvjTZ5ZBTO69Dq6v6aYiKeeGdhrVXmw5JmyU1xsjZDkEKYa1CPeG3nTBr5AaUC5CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"258bad6dd4685924b46521330eae77de183a298870778b4b0cb3ad073c0405de","last_reissued_at":"2026-07-05T10:57:30.603953Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:57:30.603953Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Zero energy modes with Gaussian, exponential, or polynomial decay: Exact solutions in hermitian and nonhermitian regimes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mes-hall","cond-mat.supr-con","math-ph","math.MP","quant-ph"],"primary_cat":"hep-th","authors_text":"Angela Nigro, Pasquale Marra","submitted_at":"2024-12-18T19:00:04Z","abstract_excerpt":"Topological zero modes in topological insulators or superconductors are exponentially localized at the phase transition between a topologically trivial and nontrivial phase. These modes are solutions of a Jackiw-Rebbi equation modified with an additional term which is quadratic in the momentum. Moreover, localized fermionic modes can also be induced by harmonic potentials in superfluids and superconductors or in atomic nuclei. Here, by using inverse methods, we consider in the same framework exponentially-localized zero modes, as well as Gaussian modes induced by harmonic potentials (with supe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.14255","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.14255/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":"2412.14255","created_at":"2026-07-05T10:57:30.604020+00:00"},{"alias_kind":"arxiv_version","alias_value":"2412.14255v2","created_at":"2026-07-05T10:57:30.604020+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.14255","created_at":"2026-07-05T10:57:30.604020+00:00"},{"alias_kind":"pith_short_12","alias_value":"EWF223OUNBMS","created_at":"2026-07-05T10:57:30.604020+00:00"},{"alias_kind":"pith_short_16","alias_value":"EWF223OUNBMSJNDF","created_at":"2026-07-05T10:57:30.604020+00:00"},{"alias_kind":"pith_short_8","alias_value":"EWF223OU","created_at":"2026-07-05T10:57:30.604020+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/EWF223OUNBMSJNDFEEZQ5LTX3Y","json":"https://pith.science/pith/EWF223OUNBMSJNDFEEZQ5LTX3Y.json","graph_json":"https://pith.science/api/pith-number/EWF223OUNBMSJNDFEEZQ5LTX3Y/graph.json","events_json":"https://pith.science/api/pith-number/EWF223OUNBMSJNDFEEZQ5LTX3Y/events.json","paper":"https://pith.science/paper/EWF223OU"},"agent_actions":{"view_html":"https://pith.science/pith/EWF223OUNBMSJNDFEEZQ5LTX3Y","download_json":"https://pith.science/pith/EWF223OUNBMSJNDFEEZQ5LTX3Y.json","view_paper":"https://pith.science/paper/EWF223OU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2412.14255&json=true","fetch_graph":"https://pith.science/api/pith-number/EWF223OUNBMSJNDFEEZQ5LTX3Y/graph.json","fetch_events":"https://pith.science/api/pith-number/EWF223OUNBMSJNDFEEZQ5LTX3Y/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EWF223OUNBMSJNDFEEZQ5LTX3Y/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EWF223OUNBMSJNDFEEZQ5LTX3Y/action/storage_attestation","attest_author":"https://pith.science/pith/EWF223OUNBMSJNDFEEZQ5LTX3Y/action/author_attestation","sign_citation":"https://pith.science/pith/EWF223OUNBMSJNDFEEZQ5LTX3Y/action/citation_signature","submit_replication":"https://pith.science/pith/EWF223OUNBMSJNDFEEZQ5LTX3Y/action/replication_record"}},"created_at":"2026-07-05T10:57:30.604020+00:00","updated_at":"2026-07-05T10:57:30.604020+00:00"}