{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:NS7EKL543GJI3QZVFQSDFTJ2E7","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"8effdc8147ef59cf3fb432a24284b5088755476198fc0a6c55f0f3dc4d96a5b9","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-11-30T15:08:01Z","title_canon_sha256":"696f377c61cde13a399c4aefbbbc164529f1e0f8d38d6e5e44b905038cd1c191"},"schema_version":"1.0","source":{"id":"1211.7281","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.7281","created_at":"2026-05-18T01:22:25Z"},{"alias_kind":"arxiv_version","alias_value":"1211.7281v2","created_at":"2026-05-18T01:22:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.7281","created_at":"2026-05-18T01:22:25Z"},{"alias_kind":"pith_short_12","alias_value":"NS7EKL543GJI","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NS7EKL543GJI3QZV","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NS7EKL54","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:8de64520877bea7789a56dfb9b701a60478e590955caee8250c3e3351d431002","target":"graph","created_at":"2026-05-18T01:22:25Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper we consider the time dependent one-dimensional Schr\\\"odinger equation with multiple Dirac delta potentials {of different strengths}. We prove that the classical dispersion property holds under some restrictions on the strengths and on the lengths of the finite intervals. The result is obtained in a more general setting of a Laplace operator on a tree with $\\delta$-coupling conditions at the vertices. The proof relies on a careful analysis of the properties of the resolvent of the associated Hamiltonian. With respect to the analysis done in \\cite{MR2858075} for Kirchhoff condition","authors_text":"L. I. Ignat, V. Banica","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-11-30T15:08:01Z","title":"Dispersion for the Schr\\\"odinger equation on the line with multiple Dirac delta potentials and on delta trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.7281","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:485b91f6bbe6ad86f14e19f9b2c612e34983d300d0148ea82b984145073288c4","target":"record","created_at":"2026-05-18T01:22:25Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"8effdc8147ef59cf3fb432a24284b5088755476198fc0a6c55f0f3dc4d96a5b9","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-11-30T15:08:01Z","title_canon_sha256":"696f377c61cde13a399c4aefbbbc164529f1e0f8d38d6e5e44b905038cd1c191"},"schema_version":"1.0","source":{"id":"1211.7281","kind":"arxiv","version":2}},"canonical_sha256":"6cbe452fbcd9928dc3352c2432cd3a27ebdc9726cdcb47955d13a34c9e889a15","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6cbe452fbcd9928dc3352c2432cd3a27ebdc9726cdcb47955d13a34c9e889a15","first_computed_at":"2026-05-18T01:22:25.931209Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:25.931209Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AdsaZDgaTozTcAaCL4tkP9BXXGpPHubIOCZyXCIcnPFaoRxCdoWUyVimQFAz+yGmPrOdEFzVEKxSqINSw84xAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:25.931912Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.7281","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:485b91f6bbe6ad86f14e19f9b2c612e34983d300d0148ea82b984145073288c4","sha256:8de64520877bea7789a56dfb9b701a60478e590955caee8250c3e3351d431002"],"state_sha256":"d261bfe7ac233045d3869694e38d6ed58288c257c85a5d4a0698276c31bef16e"}