{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:TK5WNYRVADRXGKHXEF2CENEN32","short_pith_number":"pith:TK5WNYRV","schema_version":"1.0","canonical_sha256":"9abb66e23500e37328f7217422348ddea1d81a389cabc0d7bc0b3972d99c35c1","source":{"kind":"arxiv","id":"2307.16191","version":1},"attestation_state":"computed","paper":{"title":"Energy transfer and radiation in Hamiltonian nonlinear Klein-Gordon equations: general case","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jie Liu, Zhaojie Yang, Zhen Lei","submitted_at":"2023-07-30T10:10:58Z","abstract_excerpt":"In this paper, we consider Klein-Gordon equations with cubic nonlinearity in three spatial dimensions, which are Hamiltonian perturbations of the linear one with potential. It is assumed that the corresponding Klein-Gordon operator $B = \\sqrt{-\\Delta + V(x) + m^2} $ admits an arbitrary number of possibly degenerate eigenvalues in $(0, m)$, and hence the unperturbed linear equation has multiple time-periodic solutions known as bound states. In \\cite{SW1999}, Soffer and Weinstein discovered a mechanism called Fermi's Golden Rule for this nonlinear system in the case of one simple but relatively "},"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":"2307.16191","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2023-07-30T10:10:58Z","cross_cats_sorted":[],"title_canon_sha256":"ae0346bcfc838e154cca7874dd7e31ec92a0816b02ef791de30153a59d5a3b00","abstract_canon_sha256":"86baeae36a3fd7b564274aff558ebc91c63347097c645c9bdef8d6194c22d9e3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:35:59.927639Z","signature_b64":"GuPLVoC8npVwHLVrAKB+Bkw2YZuSX/Rgft0HTHUXWcReowblKDU8R4EIqxH+YyG1uBvKcGItpRMJxCAGNAwxBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9abb66e23500e37328f7217422348ddea1d81a389cabc0d7bc0b3972d99c35c1","last_reissued_at":"2026-07-05T06:35:59.927173Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:35:59.927173Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Energy transfer and radiation in Hamiltonian nonlinear Klein-Gordon equations: general case","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jie Liu, Zhaojie Yang, Zhen Lei","submitted_at":"2023-07-30T10:10:58Z","abstract_excerpt":"In this paper, we consider Klein-Gordon equations with cubic nonlinearity in three spatial dimensions, which are Hamiltonian perturbations of the linear one with potential. It is assumed that the corresponding Klein-Gordon operator $B = \\sqrt{-\\Delta + V(x) + m^2} $ admits an arbitrary number of possibly degenerate eigenvalues in $(0, m)$, and hence the unperturbed linear equation has multiple time-periodic solutions known as bound states. In \\cite{SW1999}, Soffer and Weinstein discovered a mechanism called Fermi's Golden Rule for this nonlinear system in the case of one simple but relatively "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.16191","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2307.16191/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":"2307.16191","created_at":"2026-07-05T06:35:59.927229+00:00"},{"alias_kind":"arxiv_version","alias_value":"2307.16191v1","created_at":"2026-07-05T06:35:59.927229+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.16191","created_at":"2026-07-05T06:35:59.927229+00:00"},{"alias_kind":"pith_short_12","alias_value":"TK5WNYRVADRX","created_at":"2026-07-05T06:35:59.927229+00:00"},{"alias_kind":"pith_short_16","alias_value":"TK5WNYRVADRXGKHX","created_at":"2026-07-05T06:35:59.927229+00:00"},{"alias_kind":"pith_short_8","alias_value":"TK5WNYRV","created_at":"2026-07-05T06:35:59.927229+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/TK5WNYRVADRXGKHXEF2CENEN32","json":"https://pith.science/pith/TK5WNYRVADRXGKHXEF2CENEN32.json","graph_json":"https://pith.science/api/pith-number/TK5WNYRVADRXGKHXEF2CENEN32/graph.json","events_json":"https://pith.science/api/pith-number/TK5WNYRVADRXGKHXEF2CENEN32/events.json","paper":"https://pith.science/paper/TK5WNYRV"},"agent_actions":{"view_html":"https://pith.science/pith/TK5WNYRVADRXGKHXEF2CENEN32","download_json":"https://pith.science/pith/TK5WNYRVADRXGKHXEF2CENEN32.json","view_paper":"https://pith.science/paper/TK5WNYRV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2307.16191&json=true","fetch_graph":"https://pith.science/api/pith-number/TK5WNYRVADRXGKHXEF2CENEN32/graph.json","fetch_events":"https://pith.science/api/pith-number/TK5WNYRVADRXGKHXEF2CENEN32/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TK5WNYRVADRXGKHXEF2CENEN32/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TK5WNYRVADRXGKHXEF2CENEN32/action/storage_attestation","attest_author":"https://pith.science/pith/TK5WNYRVADRXGKHXEF2CENEN32/action/author_attestation","sign_citation":"https://pith.science/pith/TK5WNYRVADRXGKHXEF2CENEN32/action/citation_signature","submit_replication":"https://pith.science/pith/TK5WNYRVADRXGKHXEF2CENEN32/action/replication_record"}},"created_at":"2026-07-05T06:35:59.927229+00:00","updated_at":"2026-07-05T06:35:59.927229+00:00"}