{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:AIOE4GUBB4HFO5W62U7JIX7GOQ","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":"3a0b3c03c45f8882c63a8b8a9b729705cfff072a5ab3dd6e221870fe1feba1d1","cross_cats_sorted":["astro-ph.CO","gr-qc","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-02-04T15:49:01Z","title_canon_sha256":"e08d7eb28b09d7938d2a27d693eaa912e46003e696296bf84978ed5aa89f4899"},"schema_version":"1.0","source":{"id":"1002.1014","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.1014","created_at":"2026-05-18T02:09:19Z"},{"alias_kind":"arxiv_version","alias_value":"1002.1014v1","created_at":"2026-05-18T02:09:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.1014","created_at":"2026-05-18T02:09:19Z"},{"alias_kind":"pith_short_12","alias_value":"AIOE4GUBB4HF","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"AIOE4GUBB4HFO5W6","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"AIOE4GUB","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:ffc986587143f9dc57a825f22bf06d382b086e7b42eb6434f56cf2fd80929eb9","target":"graph","created_at":"2026-05-18T02:09:19Z","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":"This paper derives expressions for the growth rates for the random 2 x 2 matrices that result from solutions to the random Hill's equation. The parameters that appear in Hill's equation include the forcing strength and oscillation frequency. The development of the solutions to this periodic differential equation can be described by a discrete map, where the matrix elements are given by the principal solutions for each cycle. Variations in the forcing strength and oscillation frequency lead to matrix elements that vary from cycle to cycle. This paper presents an analysis of the growth rates inc","authors_text":"Anthony M. Bloch, Fred C. Adams","cross_cats":["astro-ph.CO","gr-qc","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-02-04T15:49:01Z","title":"Hill's Equation with Random Forcing Parameters: Determination of Growth Rates through Random Matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.1014","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":"sha256:123cc201dad68fefa34d3eced4194ea22aa6f48eb503e1c32856ea689454a374","target":"record","created_at":"2026-05-18T02:09:19Z","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":"3a0b3c03c45f8882c63a8b8a9b729705cfff072a5ab3dd6e221870fe1feba1d1","cross_cats_sorted":["astro-ph.CO","gr-qc","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-02-04T15:49:01Z","title_canon_sha256":"e08d7eb28b09d7938d2a27d693eaa912e46003e696296bf84978ed5aa89f4899"},"schema_version":"1.0","source":{"id":"1002.1014","kind":"arxiv","version":1}},"canonical_sha256":"021c4e1a810f0e5776ded53e945fe6740c67f8c9b3346ba3dfdb65a1c069fd0f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"021c4e1a810f0e5776ded53e945fe6740c67f8c9b3346ba3dfdb65a1c069fd0f","first_computed_at":"2026-05-18T02:09:19.525229Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:09:19.525229Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ufrULO01YOV7D+jT+VIWpyPEcAen8r9JoAfa6gs9a3Ax7NOSsWnbKbCFnzecNSnTnawZFCw1cFy+IPxd1AXBBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:09:19.526048Z","signed_message":"canonical_sha256_bytes"},"source_id":"1002.1014","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:123cc201dad68fefa34d3eced4194ea22aa6f48eb503e1c32856ea689454a374","sha256:ffc986587143f9dc57a825f22bf06d382b086e7b42eb6434f56cf2fd80929eb9"],"state_sha256":"a45234041a8cf9a705fd0ffe66e745d77c3cd49e53e8bb552b8b2411c148b5d3"}