{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:RQVGNGNBXDOJ6WJKQZCZALCKPW","short_pith_number":"pith:RQVGNGNB","canonical_record":{"source":{"id":"2201.06490","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-01-17T16:03:59Z","cross_cats_sorted":[],"title_canon_sha256":"7d487e40025a0b9d79e131304a4376dfc4a37d80a0d48f9c2f2c42d1cbcafa3d","abstract_canon_sha256":"2fa42b3ba5386b769e209615589c7b8b25cf6ced9ebdaf9f237f2a8bb0157912"},"schema_version":"1.0"},"canonical_sha256":"8c2a6699a1b8dc9f592a8645902c4a7db84be52419c3bfbef021a80f12365b0c","source":{"kind":"arxiv","id":"2201.06490","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2201.06490","created_at":"2026-07-05T04:59:39Z"},{"alias_kind":"arxiv_version","alias_value":"2201.06490v2","created_at":"2026-07-05T04:59:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2201.06490","created_at":"2026-07-05T04:59:39Z"},{"alias_kind":"pith_short_12","alias_value":"RQVGNGNBXDOJ","created_at":"2026-07-05T04:59:39Z"},{"alias_kind":"pith_short_16","alias_value":"RQVGNGNBXDOJ6WJK","created_at":"2026-07-05T04:59:39Z"},{"alias_kind":"pith_short_8","alias_value":"RQVGNGNB","created_at":"2026-07-05T04:59:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:RQVGNGNBXDOJ6WJKQZCZALCKPW","target":"record","payload":{"canonical_record":{"source":{"id":"2201.06490","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-01-17T16:03:59Z","cross_cats_sorted":[],"title_canon_sha256":"7d487e40025a0b9d79e131304a4376dfc4a37d80a0d48f9c2f2c42d1cbcafa3d","abstract_canon_sha256":"2fa42b3ba5386b769e209615589c7b8b25cf6ced9ebdaf9f237f2a8bb0157912"},"schema_version":"1.0"},"canonical_sha256":"8c2a6699a1b8dc9f592a8645902c4a7db84be52419c3bfbef021a80f12365b0c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:59:39.822967Z","signature_b64":"29sbJ9uWoM18YEEVe1ktYPgMUnSa/jos9m7WNRiSDejPyvCKdIjovEM95R82o62PyBCU9KVei1DTEJEy+K9BDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8c2a6699a1b8dc9f592a8645902c4a7db84be52419c3bfbef021a80f12365b0c","last_reissued_at":"2026-07-05T04:59:39.822491Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:59:39.822491Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2201.06490","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":"2026-07-05T04:59:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CsxqI9jg39iOC010ddDGXuIMOgAIp8Hj9IVQ9ZWMIf/T0dMV9be1MkgvpdZPRAXofE6TP4V8ZzEEo3xyNp2nCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T23:49:09.562578Z"},"content_sha256":"39e99f768bd5ede90a737af4b158acb38a2ae39c2a8ad9ac9eb1fb3142d5e784","schema_version":"1.0","event_id":"sha256:39e99f768bd5ede90a737af4b158acb38a2ae39c2a8ad9ac9eb1fb3142d5e784"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:RQVGNGNBXDOJ6WJKQZCZALCKPW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Energy transfer, weak resonance, and Fermi's golden rule in Hamiltonian nonlinear Klein-Gordon equations","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":"2022-01-17T16:03:59Z","abstract_excerpt":"This paper focuses on a class of nonlinear Klein-Gordon equations in three dimensions, which are Hamiltonian perturbations of the linear Klein-Gordon equation with potential. The unperturbed dynamical system has a bound state with frequency $\\omega$, a spatially localized and time periodic solution. In quantum mechanics, metastable states, which last longer than expected, have been observed. These metastable states are a consequence of the instability of the bound state under the nonlinear Fermi's Golden Rule.\n  In this study, we explore the underlying mathematical instability mechanism from t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.06490","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2201.06490/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:59:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LnGjkrBk4s+yfRmdWgPSImXVuCuOeP/ZwNjNxlv4b3SlgA5+Zk1bEhVl6ulEmpoRTqmYvtaJ6m4CXXeahjqNBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T23:49:09.563418Z"},"content_sha256":"418aefac7a5c5646e839f14e696273454dae8d37f88257dd6a4e6e9ac64ebeed","schema_version":"1.0","event_id":"sha256:418aefac7a5c5646e839f14e696273454dae8d37f88257dd6a4e6e9ac64ebeed"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RQVGNGNBXDOJ6WJKQZCZALCKPW/bundle.json","state_url":"https://pith.science/pith/RQVGNGNBXDOJ6WJKQZCZALCKPW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RQVGNGNBXDOJ6WJKQZCZALCKPW/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":"2026-08-17T23:49:09Z","links":{"resolver":"https://pith.science/pith/RQVGNGNBXDOJ6WJKQZCZALCKPW","bundle":"https://pith.science/pith/RQVGNGNBXDOJ6WJKQZCZALCKPW/bundle.json","state":"https://pith.science/pith/RQVGNGNBXDOJ6WJKQZCZALCKPW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RQVGNGNBXDOJ6WJKQZCZALCKPW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:RQVGNGNBXDOJ6WJKQZCZALCKPW","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":"2fa42b3ba5386b769e209615589c7b8b25cf6ced9ebdaf9f237f2a8bb0157912","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-01-17T16:03:59Z","title_canon_sha256":"7d487e40025a0b9d79e131304a4376dfc4a37d80a0d48f9c2f2c42d1cbcafa3d"},"schema_version":"1.0","source":{"id":"2201.06490","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2201.06490","created_at":"2026-07-05T04:59:39Z"},{"alias_kind":"arxiv_version","alias_value":"2201.06490v2","created_at":"2026-07-05T04:59:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2201.06490","created_at":"2026-07-05T04:59:39Z"},{"alias_kind":"pith_short_12","alias_value":"RQVGNGNBXDOJ","created_at":"2026-07-05T04:59:39Z"},{"alias_kind":"pith_short_16","alias_value":"RQVGNGNBXDOJ6WJK","created_at":"2026-07-05T04:59:39Z"},{"alias_kind":"pith_short_8","alias_value":"RQVGNGNB","created_at":"2026-07-05T04:59:39Z"}],"graph_snapshots":[{"event_id":"sha256:418aefac7a5c5646e839f14e696273454dae8d37f88257dd6a4e6e9ac64ebeed","target":"graph","created_at":"2026-07-05T04:59:39Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2201.06490/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper focuses on a class of nonlinear Klein-Gordon equations in three dimensions, which are Hamiltonian perturbations of the linear Klein-Gordon equation with potential. The unperturbed dynamical system has a bound state with frequency $\\omega$, a spatially localized and time periodic solution. In quantum mechanics, metastable states, which last longer than expected, have been observed. These metastable states are a consequence of the instability of the bound state under the nonlinear Fermi's Golden Rule.\n  In this study, we explore the underlying mathematical instability mechanism from t","authors_text":"Jie Liu, Zhaojie Yang, Zhen Lei","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-01-17T16:03:59Z","title":"Energy transfer, weak resonance, and Fermi's golden rule in Hamiltonian nonlinear Klein-Gordon equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.06490","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":"sha256:39e99f768bd5ede90a737af4b158acb38a2ae39c2a8ad9ac9eb1fb3142d5e784","target":"record","created_at":"2026-07-05T04:59:39Z","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":"2fa42b3ba5386b769e209615589c7b8b25cf6ced9ebdaf9f237f2a8bb0157912","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-01-17T16:03:59Z","title_canon_sha256":"7d487e40025a0b9d79e131304a4376dfc4a37d80a0d48f9c2f2c42d1cbcafa3d"},"schema_version":"1.0","source":{"id":"2201.06490","kind":"arxiv","version":2}},"canonical_sha256":"8c2a6699a1b8dc9f592a8645902c4a7db84be52419c3bfbef021a80f12365b0c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8c2a6699a1b8dc9f592a8645902c4a7db84be52419c3bfbef021a80f12365b0c","first_computed_at":"2026-07-05T04:59:39.822491Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:59:39.822491Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"29sbJ9uWoM18YEEVe1ktYPgMUnSa/jos9m7WNRiSDejPyvCKdIjovEM95R82o62PyBCU9KVei1DTEJEy+K9BDg==","signature_status":"signed_v1","signed_at":"2026-07-05T04:59:39.822967Z","signed_message":"canonical_sha256_bytes"},"source_id":"2201.06490","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:39e99f768bd5ede90a737af4b158acb38a2ae39c2a8ad9ac9eb1fb3142d5e784","sha256:418aefac7a5c5646e839f14e696273454dae8d37f88257dd6a4e6e9ac64ebeed"],"state_sha256":"50586c31ecdbacbcd803ebfdfef5251f473a4fc473ce085f1d7cc55c87db57f4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SoaGhf60WpIarVoSdfvup30CYc2EUGYXmElnJABDgtA95I1yV4u3lQL0b/nNT9VBxZ/FRR9yYZaEUkMXgHs+CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T23:49:09.571643Z","bundle_sha256":"434555d8d2072373f2cf9f696d452431b7a66fe164d52f8ae089d331d3ad59ae"}}