{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:JBTSKZXV4SE2K5VEEC7YNG3NTH","short_pith_number":"pith:JBTSKZXV","canonical_record":{"source":{"id":"0707.2491","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"nlin.PS","submitted_at":"2007-07-17T12:26:23Z","cross_cats_sorted":["nlin.SI"],"title_canon_sha256":"97f620716d7c333127adf2fb30d02a7e3faf0708a1caeb1009a0dabe353eda8d","abstract_canon_sha256":"682bb187805fe7e4c98b752dfcd3e519acee314d3b7a0080fc4d3e8d9862a9e1"},"schema_version":"1.0"},"canonical_sha256":"48672566f5e489a576a420bf869b6d99cf1cc30767e4a9bc1ae71b2b69290001","source":{"kind":"arxiv","id":"0707.2491","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0707.2491","created_at":"2026-05-18T02:16:29Z"},{"alias_kind":"arxiv_version","alias_value":"0707.2491v2","created_at":"2026-05-18T02:16:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0707.2491","created_at":"2026-05-18T02:16:29Z"},{"alias_kind":"pith_short_12","alias_value":"JBTSKZXV4SE2","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"JBTSKZXV4SE2K5VE","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"JBTSKZXV","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:JBTSKZXV4SE2K5VEEC7YNG3NTH","target":"record","payload":{"canonical_record":{"source":{"id":"0707.2491","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"nlin.PS","submitted_at":"2007-07-17T12:26:23Z","cross_cats_sorted":["nlin.SI"],"title_canon_sha256":"97f620716d7c333127adf2fb30d02a7e3faf0708a1caeb1009a0dabe353eda8d","abstract_canon_sha256":"682bb187805fe7e4c98b752dfcd3e519acee314d3b7a0080fc4d3e8d9862a9e1"},"schema_version":"1.0"},"canonical_sha256":"48672566f5e489a576a420bf869b6d99cf1cc30767e4a9bc1ae71b2b69290001","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:16:29.343046Z","signature_b64":"RXpcdptDguQHT1Q1eWwHsgIA62ZN0zP+elZaR6gHCJGPGQORfJWZKOOGCLUaURWchm6Je5kpWGHBlocuMS4KDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"48672566f5e489a576a420bf869b6d99cf1cc30767e4a9bc1ae71b2b69290001","last_reissued_at":"2026-05-18T02:16:29.342332Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:16:29.342332Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0707.2491","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:16:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"12rQGSLmUvVR6wEjWq7Ll9k+6+weh/MBFHaS+JfIFaaj6rKUIbPHB5cPRttJiFvAmLaWtVFhcKrw1tY/cFQnCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T14:25:49.841346Z"},"content_sha256":"89f0f3db6fb44acf2589f5bd376b65f088dfe2711dd4d14f538a47e5037f671e","schema_version":"1.0","event_id":"sha256:89f0f3db6fb44acf2589f5bd376b65f088dfe2711dd4d14f538a47e5037f671e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:JBTSKZXV4SE2K5VEEC7YNG3NTH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Instability of bound states of a nonlinear Schr\\\"odinger equation with a Dirac potential","license":"","headline":"","cross_cats":["nlin.SI"],"primary_cat":"nlin.PS","authors_text":"Baruch Ksherim, Gadi Fibich, Reika Fukuizumi, Stefan Le-Coz, Yonatan Sivan","submitted_at":"2007-07-17T12:26:23Z","abstract_excerpt":"We study analytically and numerically the stability of the standing waves for a nonlinear Schr\\\"odinger equation with a point defect and a power type nonlinearity. A main difficulty is to compute the number of negative eigenvalues of the linearized operator around the standing waves, and it is overcome by a perturbation method and continuation arguments. Among others, in the case of a repulsive defect, we show that the standing wave solution is stable in $\\hurad$ and unstable in $\\hu$ under subcritical nonlinearity. Further we investigate the nature of instability: under critical or supercriti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.2491","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:16:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6QckmmM4ukgDvnVlkgdQekFgHC+mhNPBeY6G8NDYhDu2sY7hytTK2kHmWcMiKKnVFwG5a/9Xgr6TtEoKFMpLCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T14:25:49.841698Z"},"content_sha256":"62a58628c2e9a76740057bf63d44bb8e5970127c42783dda562e49735f795af9","schema_version":"1.0","event_id":"sha256:62a58628c2e9a76740057bf63d44bb8e5970127c42783dda562e49735f795af9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JBTSKZXV4SE2K5VEEC7YNG3NTH/bundle.json","state_url":"https://pith.science/pith/JBTSKZXV4SE2K5VEEC7YNG3NTH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JBTSKZXV4SE2K5VEEC7YNG3NTH/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-01T14:25:49Z","links":{"resolver":"https://pith.science/pith/JBTSKZXV4SE2K5VEEC7YNG3NTH","bundle":"https://pith.science/pith/JBTSKZXV4SE2K5VEEC7YNG3NTH/bundle.json","state":"https://pith.science/pith/JBTSKZXV4SE2K5VEEC7YNG3NTH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JBTSKZXV4SE2K5VEEC7YNG3NTH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:JBTSKZXV4SE2K5VEEC7YNG3NTH","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":"682bb187805fe7e4c98b752dfcd3e519acee314d3b7a0080fc4d3e8d9862a9e1","cross_cats_sorted":["nlin.SI"],"license":"","primary_cat":"nlin.PS","submitted_at":"2007-07-17T12:26:23Z","title_canon_sha256":"97f620716d7c333127adf2fb30d02a7e3faf0708a1caeb1009a0dabe353eda8d"},"schema_version":"1.0","source":{"id":"0707.2491","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0707.2491","created_at":"2026-05-18T02:16:29Z"},{"alias_kind":"arxiv_version","alias_value":"0707.2491v2","created_at":"2026-05-18T02:16:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0707.2491","created_at":"2026-05-18T02:16:29Z"},{"alias_kind":"pith_short_12","alias_value":"JBTSKZXV4SE2","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"JBTSKZXV4SE2K5VE","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"JBTSKZXV","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:62a58628c2e9a76740057bf63d44bb8e5970127c42783dda562e49735f795af9","target":"graph","created_at":"2026-05-18T02:16:29Z","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":"We study analytically and numerically the stability of the standing waves for a nonlinear Schr\\\"odinger equation with a point defect and a power type nonlinearity. A main difficulty is to compute the number of negative eigenvalues of the linearized operator around the standing waves, and it is overcome by a perturbation method and continuation arguments. Among others, in the case of a repulsive defect, we show that the standing wave solution is stable in $\\hurad$ and unstable in $\\hu$ under subcritical nonlinearity. Further we investigate the nature of instability: under critical or supercriti","authors_text":"Baruch Ksherim, Gadi Fibich, Reika Fukuizumi, Stefan Le-Coz, Yonatan Sivan","cross_cats":["nlin.SI"],"headline":"","license":"","primary_cat":"nlin.PS","submitted_at":"2007-07-17T12:26:23Z","title":"Instability of bound states of a nonlinear Schr\\\"odinger equation with a Dirac potential"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.2491","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":"sha256:89f0f3db6fb44acf2589f5bd376b65f088dfe2711dd4d14f538a47e5037f671e","target":"record","created_at":"2026-05-18T02:16:29Z","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":"682bb187805fe7e4c98b752dfcd3e519acee314d3b7a0080fc4d3e8d9862a9e1","cross_cats_sorted":["nlin.SI"],"license":"","primary_cat":"nlin.PS","submitted_at":"2007-07-17T12:26:23Z","title_canon_sha256":"97f620716d7c333127adf2fb30d02a7e3faf0708a1caeb1009a0dabe353eda8d"},"schema_version":"1.0","source":{"id":"0707.2491","kind":"arxiv","version":2}},"canonical_sha256":"48672566f5e489a576a420bf869b6d99cf1cc30767e4a9bc1ae71b2b69290001","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"48672566f5e489a576a420bf869b6d99cf1cc30767e4a9bc1ae71b2b69290001","first_computed_at":"2026-05-18T02:16:29.342332Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:16:29.342332Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RXpcdptDguQHT1Q1eWwHsgIA62ZN0zP+elZaR6gHCJGPGQORfJWZKOOGCLUaURWchm6Je5kpWGHBlocuMS4KDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:16:29.343046Z","signed_message":"canonical_sha256_bytes"},"source_id":"0707.2491","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:89f0f3db6fb44acf2589f5bd376b65f088dfe2711dd4d14f538a47e5037f671e","sha256:62a58628c2e9a76740057bf63d44bb8e5970127c42783dda562e49735f795af9"],"state_sha256":"7ce8445fe7423c76be4944d354a8c82403174ea5f28aedd5fe2b2c1c7322c418"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x2zCdnJtNVqpPXh7qUmhk5adpabT3//0HJQ3hgrLem84Nr44eHEpM+6ctjvhMD0igiESIHy3dsm7/S6vuHoDDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T14:25:49.843601Z","bundle_sha256":"b72fd4a929835a3c0681dbb34656af89bc104833fbffa71c809c1a3509f21b78"}}