{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:52KFYTDTSHDWJNUDT3XSDMZY4B","short_pith_number":"pith:52KFYTDT","canonical_record":{"source":{"id":"2211.07929","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-11-15T06:25:16Z","cross_cats_sorted":[],"title_canon_sha256":"4623e9feeba0f7983b14a30928729478a0369eb70f514b604aec52c299a2f63c","abstract_canon_sha256":"0e1c9cfe0b94ea0fb5c133c7790f0b727316d79afc712b8743d1328233547caa"},"schema_version":"1.0"},"canonical_sha256":"ee945c4c7391c764b6839eef21b338e04995d47ee49a00bff87dd576f98632c6","source":{"kind":"arxiv","id":"2211.07929","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.07929","created_at":"2026-07-05T05:16:07Z"},{"alias_kind":"arxiv_version","alias_value":"2211.07929v1","created_at":"2026-07-05T05:16:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.07929","created_at":"2026-07-05T05:16:07Z"},{"alias_kind":"pith_short_12","alias_value":"52KFYTDTSHDW","created_at":"2026-07-05T05:16:07Z"},{"alias_kind":"pith_short_16","alias_value":"52KFYTDTSHDWJNUD","created_at":"2026-07-05T05:16:07Z"},{"alias_kind":"pith_short_8","alias_value":"52KFYTDT","created_at":"2026-07-05T05:16:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:52KFYTDTSHDWJNUDT3XSDMZY4B","target":"record","payload":{"canonical_record":{"source":{"id":"2211.07929","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-11-15T06:25:16Z","cross_cats_sorted":[],"title_canon_sha256":"4623e9feeba0f7983b14a30928729478a0369eb70f514b604aec52c299a2f63c","abstract_canon_sha256":"0e1c9cfe0b94ea0fb5c133c7790f0b727316d79afc712b8743d1328233547caa"},"schema_version":"1.0"},"canonical_sha256":"ee945c4c7391c764b6839eef21b338e04995d47ee49a00bff87dd576f98632c6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:16:07.859208Z","signature_b64":"vLXte9N8PDAJoCabqd4B18crFsWAGNQkMdK1TbkNWfldoQTCmqik+CLmk9nI4HQXA3OHOT8Syd+Fzj86Tm6RAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ee945c4c7391c764b6839eef21b338e04995d47ee49a00bff87dd576f98632c6","last_reissued_at":"2026-07-05T05:16:07.858746Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:16:07.858746Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2211.07929","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":"2026-07-05T05:16:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0abWsnGg8UI8tGDDC4EXdS29ZLuso7zfA9/Hd5GK8ld0DRqf3+RZe5bX0y4MeGTBKoZnOnD+Mbn3JQLZrHNvBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T21:31:26.398296Z"},"content_sha256":"5ccc25b202a1b5dad043f3e671d66a0001e0af6df86da450ba721d3b3b41acfa","schema_version":"1.0","event_id":"sha256:5ccc25b202a1b5dad043f3e671d66a0001e0af6df86da450ba721d3b3b41acfa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:52KFYTDTSHDWJNUDT3XSDMZY4B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A note on separation conditions of resonance sets in the instability analysis for high-frequency oscillations in geometric optics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jiaojiao Pan","submitted_at":"2022-11-15T06:25:16Z","abstract_excerpt":"In this paper, we study the instability of highly-oscillating solutions to semi-linear hyperbolic systems. A instability criterion was given in \\cite{Lu} under rather strong separation conditions of resonance sets: coupled resonance sets are pairwise disjoint. Here we show that such separation conditions in \\cite{Lu} can be relaxed: one of the coupled non-transparent resonance sets is allowed to intersect with at most two others. We obtain the same instability criterion as in \\cite{Lu}. Finally, we give some applications to coupled Klein-Gordon systems with equal masses and nonlinear terms spe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.07929","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/2211.07929/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":"2026-07-05T05:16:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hkmSH7K/W1GZcEWumTbb9m4m2lJjv7ozakg4BHsDQar4HwJ4mJkvQiKVOws1yxXViH4YqvL+L892k1lkPyFkCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T21:31:26.398833Z"},"content_sha256":"bac72877f84ba7fc243667fe6ad8c0b9b3dc0ba41a0aa5101cc890224142c1a1","schema_version":"1.0","event_id":"sha256:bac72877f84ba7fc243667fe6ad8c0b9b3dc0ba41a0aa5101cc890224142c1a1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/52KFYTDTSHDWJNUDT3XSDMZY4B/bundle.json","state_url":"https://pith.science/pith/52KFYTDTSHDWJNUDT3XSDMZY4B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/52KFYTDTSHDWJNUDT3XSDMZY4B/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":"2026-08-04T21:31:26Z","links":{"resolver":"https://pith.science/pith/52KFYTDTSHDWJNUDT3XSDMZY4B","bundle":"https://pith.science/pith/52KFYTDTSHDWJNUDT3XSDMZY4B/bundle.json","state":"https://pith.science/pith/52KFYTDTSHDWJNUDT3XSDMZY4B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/52KFYTDTSHDWJNUDT3XSDMZY4B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:52KFYTDTSHDWJNUDT3XSDMZY4B","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":"0e1c9cfe0b94ea0fb5c133c7790f0b727316d79afc712b8743d1328233547caa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-11-15T06:25:16Z","title_canon_sha256":"4623e9feeba0f7983b14a30928729478a0369eb70f514b604aec52c299a2f63c"},"schema_version":"1.0","source":{"id":"2211.07929","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.07929","created_at":"2026-07-05T05:16:07Z"},{"alias_kind":"arxiv_version","alias_value":"2211.07929v1","created_at":"2026-07-05T05:16:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.07929","created_at":"2026-07-05T05:16:07Z"},{"alias_kind":"pith_short_12","alias_value":"52KFYTDTSHDW","created_at":"2026-07-05T05:16:07Z"},{"alias_kind":"pith_short_16","alias_value":"52KFYTDTSHDWJNUD","created_at":"2026-07-05T05:16:07Z"},{"alias_kind":"pith_short_8","alias_value":"52KFYTDT","created_at":"2026-07-05T05:16:07Z"}],"graph_snapshots":[{"event_id":"sha256:bac72877f84ba7fc243667fe6ad8c0b9b3dc0ba41a0aa5101cc890224142c1a1","target":"graph","created_at":"2026-07-05T05:16:07Z","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/2211.07929/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we study the instability of highly-oscillating solutions to semi-linear hyperbolic systems. A instability criterion was given in \\cite{Lu} under rather strong separation conditions of resonance sets: coupled resonance sets are pairwise disjoint. Here we show that such separation conditions in \\cite{Lu} can be relaxed: one of the coupled non-transparent resonance sets is allowed to intersect with at most two others. We obtain the same instability criterion as in \\cite{Lu}. Finally, we give some applications to coupled Klein-Gordon systems with equal masses and nonlinear terms spe","authors_text":"Jiaojiao Pan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-11-15T06:25:16Z","title":"A note on separation conditions of resonance sets in the instability analysis for high-frequency oscillations in geometric optics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.07929","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":"sha256:5ccc25b202a1b5dad043f3e671d66a0001e0af6df86da450ba721d3b3b41acfa","target":"record","created_at":"2026-07-05T05:16:07Z","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":"0e1c9cfe0b94ea0fb5c133c7790f0b727316d79afc712b8743d1328233547caa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-11-15T06:25:16Z","title_canon_sha256":"4623e9feeba0f7983b14a30928729478a0369eb70f514b604aec52c299a2f63c"},"schema_version":"1.0","source":{"id":"2211.07929","kind":"arxiv","version":1}},"canonical_sha256":"ee945c4c7391c764b6839eef21b338e04995d47ee49a00bff87dd576f98632c6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ee945c4c7391c764b6839eef21b338e04995d47ee49a00bff87dd576f98632c6","first_computed_at":"2026-07-05T05:16:07.858746Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:16:07.858746Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vLXte9N8PDAJoCabqd4B18crFsWAGNQkMdK1TbkNWfldoQTCmqik+CLmk9nI4HQXA3OHOT8Syd+Fzj86Tm6RAw==","signature_status":"signed_v1","signed_at":"2026-07-05T05:16:07.859208Z","signed_message":"canonical_sha256_bytes"},"source_id":"2211.07929","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ccc25b202a1b5dad043f3e671d66a0001e0af6df86da450ba721d3b3b41acfa","sha256:bac72877f84ba7fc243667fe6ad8c0b9b3dc0ba41a0aa5101cc890224142c1a1"],"state_sha256":"5f4ce470fe2e62fee319e78125832a042e04b16c6b263ca769de3c367da71f55"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ab5OHYBU7ODnjQSgYvw+gujLkKk+3YMXXxBPMCzFj3xd60qbhgiWrQ/kWyzBfA8YXXBMgaK5x1YkxwzIl8n7Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T21:31:26.404014Z","bundle_sha256":"d74f00a7ab89d18a1058534df21d3021ba1b0ae31fa6081f4715efe912943be1"}}