{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:MT2EAHRTDQIR3UYFAWHLHEY5B5","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":"4cc5cf32a71c02efe49467e339ddae3241cfd9b048910ff883951fa5d35c002d","cross_cats_sorted":["physics.class-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-12-16T20:01:57Z","title_canon_sha256":"55516d68a73c8cfe816cf6bbb6f31de869aded7254bb4d83e4a4d7b1a0e8f158"},"schema_version":"1.0","source":{"id":"1312.4492","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.4492","created_at":"2026-05-18T03:04:24Z"},{"alias_kind":"arxiv_version","alias_value":"1312.4492v1","created_at":"2026-05-18T03:04:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.4492","created_at":"2026-05-18T03:04:24Z"},{"alias_kind":"pith_short_12","alias_value":"MT2EAHRTDQIR","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MT2EAHRTDQIR3UYF","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MT2EAHRT","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:a95e2c88b7284730e1254ad3b029d78474ef812a407eec122b74c4b05c0dc2cc","target":"graph","created_at":"2026-05-18T03:04:24Z","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 {\\it small solutions} of a vibrating mechanical system with smooth non-linearities for which we provide an approximate solution by using a triple scale analysis; a rigorous proof of convergence of the triple scale method is included; for the forced response, a stability result is needed in order to prove convergence in a neighbourhood of a primary resonance. The amplitude of the response with respect to the frequency forcing is described and it is related to the frequency of a free periodic vibration.","authors_text":"Bernard Rousselet (JAD), Nadia Ben Brahim (LGC-ENIT)","cross_cats":["physics.class-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-12-16T20:01:57Z","title":"Triple scale analysis of periodic solutions and resonance of some asymmetric non linear vibrating systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.4492","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":"sha256:74d2d5cc14cb87cd53c4ab03a7b954145669c5fe21f975442df9517cedd7c8a4","target":"record","created_at":"2026-05-18T03:04:24Z","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":"4cc5cf32a71c02efe49467e339ddae3241cfd9b048910ff883951fa5d35c002d","cross_cats_sorted":["physics.class-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-12-16T20:01:57Z","title_canon_sha256":"55516d68a73c8cfe816cf6bbb6f31de869aded7254bb4d83e4a4d7b1a0e8f158"},"schema_version":"1.0","source":{"id":"1312.4492","kind":"arxiv","version":1}},"canonical_sha256":"64f4401e331c111dd305058eb3931d0f73e939714401189a8947819b2ebaa315","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"64f4401e331c111dd305058eb3931d0f73e939714401189a8947819b2ebaa315","first_computed_at":"2026-05-18T03:04:24.599382Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:04:24.599382Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GzflbGTKZvAz/Ti2qmlcX6CP9/t69f7OYVzVE05P5ohc/C/5CL2Be3OnJ2qqu/zqBfjGbViK1PbXhWQiBYpyCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:04:24.600080Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.4492","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:74d2d5cc14cb87cd53c4ab03a7b954145669c5fe21f975442df9517cedd7c8a4","sha256:a95e2c88b7284730e1254ad3b029d78474ef812a407eec122b74c4b05c0dc2cc"],"state_sha256":"3a8ccd73da5adaed8d7079d59a94c42b14c185400afea34252e8bcaa82397475"}