{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:NGKI3MMUQS4XRK5A3SWWMASOBO","short_pith_number":"pith:NGKI3MMU","canonical_record":{"source":{"id":"0904.4040","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-04-26T17:30:42Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"6391f3e27d427d659efaab542c5129a1ca0377cd99f09145bc8c399b0d81bf93","abstract_canon_sha256":"2b87087aef32d9f420b269ded57a93ccaa1ef72a4f9bb8e490ce3bb4b200a2f6"},"schema_version":"1.0"},"canonical_sha256":"69948db19484b978aba0dcad66024e0baf8a208105b515e194182b3a135d6a3d","source":{"kind":"arxiv","id":"0904.4040","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0904.4040","created_at":"2026-05-18T02:13:57Z"},{"alias_kind":"arxiv_version","alias_value":"0904.4040v1","created_at":"2026-05-18T02:13:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.4040","created_at":"2026-05-18T02:13:57Z"},{"alias_kind":"pith_short_12","alias_value":"NGKI3MMUQS4X","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"NGKI3MMUQS4XRK5A","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"NGKI3MMU","created_at":"2026-05-18T12:26:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:NGKI3MMUQS4XRK5A3SWWMASOBO","target":"record","payload":{"canonical_record":{"source":{"id":"0904.4040","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-04-26T17:30:42Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"6391f3e27d427d659efaab542c5129a1ca0377cd99f09145bc8c399b0d81bf93","abstract_canon_sha256":"2b87087aef32d9f420b269ded57a93ccaa1ef72a4f9bb8e490ce3bb4b200a2f6"},"schema_version":"1.0"},"canonical_sha256":"69948db19484b978aba0dcad66024e0baf8a208105b515e194182b3a135d6a3d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:13:57.281742Z","signature_b64":"watSMlGqBZWehm+sSxYNkkBW9bmniSjHNbLN5rPsUL/2cXejP36pPoPfFk28ddD93tEsOCzVDNndujBHDu91BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"69948db19484b978aba0dcad66024e0baf8a208105b515e194182b3a135d6a3d","last_reissued_at":"2026-05-18T02:13:57.281074Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:13:57.281074Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0904.4040","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:13:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hnL64cHp6D7oHfSvz5ESptkQcyaDBcHDqKRdGqSmkTiPzTl+VdcGbn2nC3gPw5qGimQkpQfteOGpTYAiR7prDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T23:03:54.840372Z"},"content_sha256":"e9b6c823b2ca8de3e6b83cb4686e598428060b8912f60e262e8e3b6c0c8a857e","schema_version":"1.0","event_id":"sha256:e9b6c823b2ca8de3e6b83cb4686e598428060b8912f60e262e8e3b6c0c8a857e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:NGKI3MMUQS4XRK5A3SWWMASOBO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gamow Vectors in a Periodically Perturbed Quantum System","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Min Huang","submitted_at":"2009-04-26T17:30:42Z","abstract_excerpt":"We analyze the behavior of the wave function $\\psi(x,t)$ for one dimensional time-dependent Hamiltonian $H=-\\partial_x^2\\pm2\\delta(x)(1+2r\\cos\\omega t)$ where $\\psi(x,0)$ is compactly supported. We show that $\\psi(x,t)$ has a Borel summable expansion containing finitely many terms of the form $\\sum_{n=-\\infty}^{\\infty} e^{i^{3/2}\\sqrt{-\\lambda_{k}+n\\omegai}|x|} A_{k,n} e^{-\\lambda_{k}t+n\\omega it}$, where $\\lambda_k$ represents the associated resonance. This expression defines Gamow vectors and resonances in a rigorous and physically relevant way for all frequencies and amplitudes in a time-de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.4040","kind":"arxiv","version":1},"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":"2026-05-18T02:13:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"boH8+ckQkw0iYRD34jvTEv+EQm2gPwyLcpeaFAR3RbHzjrPau8L7B4SsydPXwDrksarvoCdlmx094u6zvGIGDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T23:03:54.841045Z"},"content_sha256":"0f0c99407c6a671fa2486eda082d0c6b398152883a28340d425db5349e3a1527","schema_version":"1.0","event_id":"sha256:0f0c99407c6a671fa2486eda082d0c6b398152883a28340d425db5349e3a1527"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NGKI3MMUQS4XRK5A3SWWMASOBO/bundle.json","state_url":"https://pith.science/pith/NGKI3MMUQS4XRK5A3SWWMASOBO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NGKI3MMUQS4XRK5A3SWWMASOBO/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":"2026-05-23T23:03:54Z","links":{"resolver":"https://pith.science/pith/NGKI3MMUQS4XRK5A3SWWMASOBO","bundle":"https://pith.science/pith/NGKI3MMUQS4XRK5A3SWWMASOBO/bundle.json","state":"https://pith.science/pith/NGKI3MMUQS4XRK5A3SWWMASOBO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NGKI3MMUQS4XRK5A3SWWMASOBO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:NGKI3MMUQS4XRK5A3SWWMASOBO","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":"2b87087aef32d9f420b269ded57a93ccaa1ef72a4f9bb8e490ce3bb4b200a2f6","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-04-26T17:30:42Z","title_canon_sha256":"6391f3e27d427d659efaab542c5129a1ca0377cd99f09145bc8c399b0d81bf93"},"schema_version":"1.0","source":{"id":"0904.4040","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0904.4040","created_at":"2026-05-18T02:13:57Z"},{"alias_kind":"arxiv_version","alias_value":"0904.4040v1","created_at":"2026-05-18T02:13:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.4040","created_at":"2026-05-18T02:13:57Z"},{"alias_kind":"pith_short_12","alias_value":"NGKI3MMUQS4X","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"NGKI3MMUQS4XRK5A","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"NGKI3MMU","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:0f0c99407c6a671fa2486eda082d0c6b398152883a28340d425db5349e3a1527","target":"graph","created_at":"2026-05-18T02:13:57Z","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 analyze the behavior of the wave function $\\psi(x,t)$ for one dimensional time-dependent Hamiltonian $H=-\\partial_x^2\\pm2\\delta(x)(1+2r\\cos\\omega t)$ where $\\psi(x,0)$ is compactly supported. We show that $\\psi(x,t)$ has a Borel summable expansion containing finitely many terms of the form $\\sum_{n=-\\infty}^{\\infty} e^{i^{3/2}\\sqrt{-\\lambda_{k}+n\\omegai}|x|} A_{k,n} e^{-\\lambda_{k}t+n\\omega it}$, where $\\lambda_k$ represents the associated resonance. This expression defines Gamow vectors and resonances in a rigorous and physically relevant way for all frequencies and amplitudes in a time-de","authors_text":"Min Huang","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-04-26T17:30:42Z","title":"Gamow Vectors in a Periodically Perturbed Quantum System"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.4040","kind":"arxiv","version":1},"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:e9b6c823b2ca8de3e6b83cb4686e598428060b8912f60e262e8e3b6c0c8a857e","target":"record","created_at":"2026-05-18T02:13:57Z","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":"2b87087aef32d9f420b269ded57a93ccaa1ef72a4f9bb8e490ce3bb4b200a2f6","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-04-26T17:30:42Z","title_canon_sha256":"6391f3e27d427d659efaab542c5129a1ca0377cd99f09145bc8c399b0d81bf93"},"schema_version":"1.0","source":{"id":"0904.4040","kind":"arxiv","version":1}},"canonical_sha256":"69948db19484b978aba0dcad66024e0baf8a208105b515e194182b3a135d6a3d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"69948db19484b978aba0dcad66024e0baf8a208105b515e194182b3a135d6a3d","first_computed_at":"2026-05-18T02:13:57.281074Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:13:57.281074Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"watSMlGqBZWehm+sSxYNkkBW9bmniSjHNbLN5rPsUL/2cXejP36pPoPfFk28ddD93tEsOCzVDNndujBHDu91BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:13:57.281742Z","signed_message":"canonical_sha256_bytes"},"source_id":"0904.4040","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e9b6c823b2ca8de3e6b83cb4686e598428060b8912f60e262e8e3b6c0c8a857e","sha256:0f0c99407c6a671fa2486eda082d0c6b398152883a28340d425db5349e3a1527"],"state_sha256":"dd8b6b700063e0174051ceecbfb2fd4116e09c0ef12c2778e817c10267d5432d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4IBTRAj/TjZHOD38Mminla5fQKDV+sL0BYPTx7IdiK8TImT+9UHRRxznoJFEA8uLg9wwcFbi0vjlsogCUzDrCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T23:03:54.844825Z","bundle_sha256":"5cd03652b7add92f2ef1f642a08329cbc877941e68988c604a4f365cecad66c6"}}