{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:HS47JDUJHTQR6CST5PXVMN476Q","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":"7176c6b1874765cc8eff5be6f66b85ad3c197dc783f8fc2848d8d9f4bbb392a9","cross_cats_sorted":["math-ph","math.CA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-05-09T19:00:54Z","title_canon_sha256":"16764cae83a11629cf0f3e7d532e4487b4a8070180873321aee91583b280074f"},"schema_version":"1.0","source":{"id":"1205.2070","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.2070","created_at":"2026-05-18T01:57:35Z"},{"alias_kind":"arxiv_version","alias_value":"1205.2070v2","created_at":"2026-05-18T01:57:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.2070","created_at":"2026-05-18T01:57:35Z"},{"alias_kind":"pith_short_12","alias_value":"HS47JDUJHTQR","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HS47JDUJHTQR6CST","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HS47JDUJ","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:2f0340597b2effbb572b2d43f5d0c650bd8cd6be4fa0753625426d605762522d","target":"graph","created_at":"2026-05-18T01:57:35Z","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 consider multiscale Hamiltonian systems in which harmonic oscillators with several high frequencies are coupled to a slow system. It is shown that the oscillatory energy is nearly preserved over long times eps^{-N} for arbitrary N>1, where eps^{-1} is the size of the smallest high frequency. The result is uniform in the frequencies and does not require non-resonance conditions.","authors_text":"Christian Lubich, Ernst Hairer, Ludwig Gauckler","cross_cats":["math-ph","math.CA","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-05-09T19:00:54Z","title":"Energy separation in oscillatory Hamiltonian systems without any non-resonance condition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.2070","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":"sha256:5813a56f2cc72e28d23531a95df85e728cca9113402eb474cef19e243ed80ec4","target":"record","created_at":"2026-05-18T01:57:35Z","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":"7176c6b1874765cc8eff5be6f66b85ad3c197dc783f8fc2848d8d9f4bbb392a9","cross_cats_sorted":["math-ph","math.CA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-05-09T19:00:54Z","title_canon_sha256":"16764cae83a11629cf0f3e7d532e4487b4a8070180873321aee91583b280074f"},"schema_version":"1.0","source":{"id":"1205.2070","kind":"arxiv","version":2}},"canonical_sha256":"3cb9f48e893ce11f0a53ebef56379ff439323a4c8a1410fae743d9b5709d9b90","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3cb9f48e893ce11f0a53ebef56379ff439323a4c8a1410fae743d9b5709d9b90","first_computed_at":"2026-05-18T01:57:35.929234Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:57:35.929234Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4QryzoPjx+uQahNK8rWp1I7u3M92ToLqz/WF4m0vfYxQECZQgxfDIhRvW8gK1GykaFiriUOk1fcNQXKa61k6BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:57:35.929691Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.2070","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5813a56f2cc72e28d23531a95df85e728cca9113402eb474cef19e243ed80ec4","sha256:2f0340597b2effbb572b2d43f5d0c650bd8cd6be4fa0753625426d605762522d"],"state_sha256":"b5683ba3f412b53a8a9d5db3bc37b1a4c87af2d67b8574ab1689045776d17780"}