{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:XEXW6HXQYY6RKCHZHS22I4KDH3","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":"4c60096d1b0473345a695ea1891a294d34b675f6f8450f930433363a71a22b6f","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-11-08T09:19:44Z","title_canon_sha256":"26dac93eb165016cac00f984887e6d52a66c27318192c447c61837ed77d294ef"},"schema_version":"1.0","source":{"id":"0911.1501","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.1501","created_at":"2026-05-18T02:00:02Z"},{"alias_kind":"arxiv_version","alias_value":"0911.1501v1","created_at":"2026-05-18T02:00:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.1501","created_at":"2026-05-18T02:00:02Z"},{"alias_kind":"pith_short_12","alias_value":"XEXW6HXQYY6R","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"XEXW6HXQYY6RKCHZ","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"XEXW6HXQ","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:8a48470c4576750196194f3625248018a61fca557355ca61a53c3546dede7510","target":"graph","created_at":"2026-05-18T02:00:02Z","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":"The response function of a network of springs and masses, an elastodynamic network, is the matrix valued function $W(\\omega)$, depending on the frequency $\\omega$, mapping the displacements of some accessible or terminal nodes to the net forces at the terminals. We give necessary and sufficient conditions for a given function $W(\\omega)$ to be the response function of an elastodynamic network, assuming there is no damping. In particular we construct an elastodynamic network that can mimic a suitable response in the frequency or time domain. Our characterization is valid for networks in three d","authors_text":"Daniel Onofrei, Fernando Guevara Vasquez, Graeme W. Milton","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-11-08T09:19:44Z","title":"Complete characterization and synthesis of the response function of elastodynamic networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.1501","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":"sha256:04d20c875f5d1d289c80f090642b2206d3459d7a5e1b37f2c14423026ed67c59","target":"record","created_at":"2026-05-18T02:00:02Z","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":"4c60096d1b0473345a695ea1891a294d34b675f6f8450f930433363a71a22b6f","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-11-08T09:19:44Z","title_canon_sha256":"26dac93eb165016cac00f984887e6d52a66c27318192c447c61837ed77d294ef"},"schema_version":"1.0","source":{"id":"0911.1501","kind":"arxiv","version":1}},"canonical_sha256":"b92f6f1ef0c63d1508f93cb5a471433ee5c27715698244b836f08b040c615e12","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b92f6f1ef0c63d1508f93cb5a471433ee5c27715698244b836f08b040c615e12","first_computed_at":"2026-05-18T02:00:02.960968Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:00:02.960968Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oxEKYfzvYppPwfIWZXX9YGTxwRyRj/LhHkYptisHkeD1eqeRICVfuq/tDfyhBediV82XFWyUHlfFqHZP7ld+Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:00:02.961485Z","signed_message":"canonical_sha256_bytes"},"source_id":"0911.1501","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:04d20c875f5d1d289c80f090642b2206d3459d7a5e1b37f2c14423026ed67c59","sha256:8a48470c4576750196194f3625248018a61fca557355ca61a53c3546dede7510"],"state_sha256":"2ab60d6044b547887fbdf8ca67924df9af57d7d256897b85c259119f8ecb1f17"}