{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:BKNNIUJ4WOVWUZCE4SHNWMCTJ2","short_pith_number":"pith:BKNNIUJ4","canonical_record":{"source":{"id":"0807.1878","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-07-11T16:05:39Z","cross_cats_sorted":["math.AP","math.MP"],"title_canon_sha256":"b7f2ef2f5119ccbe602717b8a08f1d282431b4b052acd3da8358f8a0858c48fc","abstract_canon_sha256":"097d6051ecc55d2dc0b48a8af5c0f00ce40a1cf8a0ca245cd5c8c4aedf44c59d"},"schema_version":"1.0"},"canonical_sha256":"0a9ad4513cb3ab6a6444e48edb30534ebf31eebf3b065e7e633ec1304f3c7bb7","source":{"kind":"arxiv","id":"0807.1878","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0807.1878","created_at":"2026-05-18T04:33:27Z"},{"alias_kind":"arxiv_version","alias_value":"0807.1878v2","created_at":"2026-05-18T04:33:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0807.1878","created_at":"2026-05-18T04:33:27Z"},{"alias_kind":"pith_short_12","alias_value":"BKNNIUJ4WOVW","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"BKNNIUJ4WOVWUZCE","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"BKNNIUJ4","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:BKNNIUJ4WOVWUZCE4SHNWMCTJ2","target":"record","payload":{"canonical_record":{"source":{"id":"0807.1878","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-07-11T16:05:39Z","cross_cats_sorted":["math.AP","math.MP"],"title_canon_sha256":"b7f2ef2f5119ccbe602717b8a08f1d282431b4b052acd3da8358f8a0858c48fc","abstract_canon_sha256":"097d6051ecc55d2dc0b48a8af5c0f00ce40a1cf8a0ca245cd5c8c4aedf44c59d"},"schema_version":"1.0"},"canonical_sha256":"0a9ad4513cb3ab6a6444e48edb30534ebf31eebf3b065e7e633ec1304f3c7bb7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:33:27.428037Z","signature_b64":"6OX6TBq1S0quCbSVYeWDxK0p9Cr37XWJfD9OeNKPDCASHteBtuixdyAqNc9ezbwhOhvoz6ZT8A7XUOMUjf6dBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0a9ad4513cb3ab6a6444e48edb30534ebf31eebf3b065e7e633ec1304f3c7bb7","last_reissued_at":"2026-05-18T04:33:27.427565Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:33:27.427565Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0807.1878","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":"2026-05-18T04:33:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VQhGPLDmBBpAkEehxB4ouLGFziENzSul4zKlCtMGCPxcGPx49afoFoe/65zfz3L1JKuPwGOB+beKn6MmtiKGAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T19:08:20.531074Z"},"content_sha256":"cc0bdfac05f070bd02fcb2dd4b7f314e9773c8830794cd7b0c8429a62e08671b","schema_version":"1.0","event_id":"sha256:cc0bdfac05f070bd02fcb2dd4b7f314e9773c8830794cd7b0c8429a62e08671b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:BKNNIUJ4WOVWUZCE4SHNWMCTJ2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On asymptotic stability of solitons for nonlinear Sch\\\"odinger equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"A.I. Komech, D. Stuart, E.A. Kopylova","submitted_at":"2008-07-11T16:05:39Z","abstract_excerpt":"The long-time asymptotics is analyzed for finite energy solutions of the 1D Schr\\\"odinger equation coupled to a nonlinear oscillator; mathematically the system under study is a nonlinear Schr\\\"odinger equation, whose nonlinear term includes a Dirac delta. The coupled system is invariant with respect to the phase rotation group U(1). This article, which extends the results of a previous one, provides a proof of asymptotic stability of solitary wave solutions in the case that the linearization contains a single discrete oscillatory mode satisfying a non-degeneracy assumption of the type known as"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.1878","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":"2026-05-18T04:33:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SqtbFm48rG9wnPEj/Nnm+yYSXj8eazIdLTP8jp3gNZr2lzrdpuhI/IG5FLbuXZu7PYnmGTQtrA0VCoJeRN1UBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T19:08:20.531439Z"},"content_sha256":"c50aa2832ab6b96e88517bb16d291f9a19156a3c5cf311b95b845b08aff82f9e","schema_version":"1.0","event_id":"sha256:c50aa2832ab6b96e88517bb16d291f9a19156a3c5cf311b95b845b08aff82f9e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BKNNIUJ4WOVWUZCE4SHNWMCTJ2/bundle.json","state_url":"https://pith.science/pith/BKNNIUJ4WOVWUZCE4SHNWMCTJ2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BKNNIUJ4WOVWUZCE4SHNWMCTJ2/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":"2026-06-26T19:08:20Z","links":{"resolver":"https://pith.science/pith/BKNNIUJ4WOVWUZCE4SHNWMCTJ2","bundle":"https://pith.science/pith/BKNNIUJ4WOVWUZCE4SHNWMCTJ2/bundle.json","state":"https://pith.science/pith/BKNNIUJ4WOVWUZCE4SHNWMCTJ2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BKNNIUJ4WOVWUZCE4SHNWMCTJ2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:BKNNIUJ4WOVWUZCE4SHNWMCTJ2","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":"097d6051ecc55d2dc0b48a8af5c0f00ce40a1cf8a0ca245cd5c8c4aedf44c59d","cross_cats_sorted":["math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-07-11T16:05:39Z","title_canon_sha256":"b7f2ef2f5119ccbe602717b8a08f1d282431b4b052acd3da8358f8a0858c48fc"},"schema_version":"1.0","source":{"id":"0807.1878","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0807.1878","created_at":"2026-05-18T04:33:27Z"},{"alias_kind":"arxiv_version","alias_value":"0807.1878v2","created_at":"2026-05-18T04:33:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0807.1878","created_at":"2026-05-18T04:33:27Z"},{"alias_kind":"pith_short_12","alias_value":"BKNNIUJ4WOVW","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"BKNNIUJ4WOVWUZCE","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"BKNNIUJ4","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:c50aa2832ab6b96e88517bb16d291f9a19156a3c5cf311b95b845b08aff82f9e","target":"graph","created_at":"2026-05-18T04:33:27Z","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":"The long-time asymptotics is analyzed for finite energy solutions of the 1D Schr\\\"odinger equation coupled to a nonlinear oscillator; mathematically the system under study is a nonlinear Schr\\\"odinger equation, whose nonlinear term includes a Dirac delta. The coupled system is invariant with respect to the phase rotation group U(1). This article, which extends the results of a previous one, provides a proof of asymptotic stability of solitary wave solutions in the case that the linearization contains a single discrete oscillatory mode satisfying a non-degeneracy assumption of the type known as","authors_text":"A.I. Komech, D. Stuart, E.A. Kopylova","cross_cats":["math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-07-11T16:05:39Z","title":"On asymptotic stability of solitons for nonlinear Sch\\\"odinger equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.1878","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:cc0bdfac05f070bd02fcb2dd4b7f314e9773c8830794cd7b0c8429a62e08671b","target":"record","created_at":"2026-05-18T04:33:27Z","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":"097d6051ecc55d2dc0b48a8af5c0f00ce40a1cf8a0ca245cd5c8c4aedf44c59d","cross_cats_sorted":["math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-07-11T16:05:39Z","title_canon_sha256":"b7f2ef2f5119ccbe602717b8a08f1d282431b4b052acd3da8358f8a0858c48fc"},"schema_version":"1.0","source":{"id":"0807.1878","kind":"arxiv","version":2}},"canonical_sha256":"0a9ad4513cb3ab6a6444e48edb30534ebf31eebf3b065e7e633ec1304f3c7bb7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0a9ad4513cb3ab6a6444e48edb30534ebf31eebf3b065e7e633ec1304f3c7bb7","first_computed_at":"2026-05-18T04:33:27.427565Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:33:27.427565Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6OX6TBq1S0quCbSVYeWDxK0p9Cr37XWJfD9OeNKPDCASHteBtuixdyAqNc9ezbwhOhvoz6ZT8A7XUOMUjf6dBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:33:27.428037Z","signed_message":"canonical_sha256_bytes"},"source_id":"0807.1878","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cc0bdfac05f070bd02fcb2dd4b7f314e9773c8830794cd7b0c8429a62e08671b","sha256:c50aa2832ab6b96e88517bb16d291f9a19156a3c5cf311b95b845b08aff82f9e"],"state_sha256":"bdcb38064374d26fa5e62c5238d5d05b144cf8bd53142ed8381cc64c99265cb0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PBx/MVyk6nq1A2yLGn4mgFMvJVVFsSxctiXLpKjyFm+ytQBDZpGAi5rOMtZvH35n9kpFGMiTJJlKmwUz7FfbCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T19:08:20.533406Z","bundle_sha256":"c3fe56c476a71af2d4dc111cff65a87868f6130e9aa433eeb3c99d6dc29e83ad"}}