{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:T5AMOT7AJTK6LP6U4D2U4WFFRE","short_pith_number":"pith:T5AMOT7A","canonical_record":{"source":{"id":"1310.7089","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-26T09:35:14Z","cross_cats_sorted":[],"title_canon_sha256":"73ee29f2f07b5b2bfc854aeb45b1e42fbd4e432b65f60bb607d35f5d55cdebd5","abstract_canon_sha256":"55a4902712e1d69ebef48d5c7fbf2d67c66729545f12ed79957c83976e6afec4"},"schema_version":"1.0"},"canonical_sha256":"9f40c74fe04cd5e5bfd4e0f54e58a589260ebec1c5f7318f962c139e63f83888","source":{"kind":"arxiv","id":"1310.7089","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.7089","created_at":"2026-05-18T03:08:46Z"},{"alias_kind":"arxiv_version","alias_value":"1310.7089v1","created_at":"2026-05-18T03:08:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.7089","created_at":"2026-05-18T03:08:46Z"},{"alias_kind":"pith_short_12","alias_value":"T5AMOT7AJTK6","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"T5AMOT7AJTK6LP6U","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"T5AMOT7A","created_at":"2026-05-18T12:27:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:T5AMOT7AJTK6LP6U4D2U4WFFRE","target":"record","payload":{"canonical_record":{"source":{"id":"1310.7089","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-26T09:35:14Z","cross_cats_sorted":[],"title_canon_sha256":"73ee29f2f07b5b2bfc854aeb45b1e42fbd4e432b65f60bb607d35f5d55cdebd5","abstract_canon_sha256":"55a4902712e1d69ebef48d5c7fbf2d67c66729545f12ed79957c83976e6afec4"},"schema_version":"1.0"},"canonical_sha256":"9f40c74fe04cd5e5bfd4e0f54e58a589260ebec1c5f7318f962c139e63f83888","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:08:46.279446Z","signature_b64":"gRowq3nE8TieqycF6yp/QToNLi5HGPUoCLPyDw97cKtq+kpgt6XA0wRgL2zyyl92q6ig4VipYSTteTXzyUdLAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f40c74fe04cd5e5bfd4e0f54e58a589260ebec1c5f7318f962c139e63f83888","last_reissued_at":"2026-05-18T03:08:46.279019Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:08:46.279019Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.7089","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":"2026-05-18T03:08:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0MqNcYiw8l3RMAf7Rcm1TYOwOGl9D5pVdtCx2Zn4TW/DRB9rNrOShHBjNZnLt/6j8Bh0LEsyA+ubF36pHRd/Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T23:39:42.825756Z"},"content_sha256":"eda58f9fac49b0872688e5bea2ad20ec59f3496ec04645a5dfea70216f243ecf","schema_version":"1.0","event_id":"sha256:eda58f9fac49b0872688e5bea2ad20ec59f3496ec04645a5dfea70216f243ecf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:T5AMOT7AJTK6LP6U4D2U4WFFRE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Resonant waves in elastic structured media: dynamic homogenisation versus Green's functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alexander Movchan, Leonid Slepyan","submitted_at":"2013-10-26T09:35:14Z","abstract_excerpt":"We address an important issue of a dynamic homogenisation in vector elasticity for a doubly periodic mass-spring elastic lattice. The notion of logarithmically growing resonant waves is used in a complete analysis of star-shaped wave forms induced by an oscillating point force. We note that the dispersion surfaces for Floquet-Bloch waves in an elastic lattice main contain critical points of the saddle type. Based on the local quadratic approximations of the frequency, as a function of wave vector components, we deduce properties of a transient asymptotic solution as the contribution of the poi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7089","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":""},"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":"2026-05-18T03:08:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q+OH1cldeMVJqzo5Yc2EF3qdsXf7zI05CgviR91/6ZK/nAyCYpOzCfQGqjp6rAzQUeZwS/SddTVX4PiIFqSgBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T23:39:42.826122Z"},"content_sha256":"3691a10ccb6537a5ffcf35589a5ce69785e8cee13eec9bba999bd3f1bdfefafe","schema_version":"1.0","event_id":"sha256:3691a10ccb6537a5ffcf35589a5ce69785e8cee13eec9bba999bd3f1bdfefafe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T5AMOT7AJTK6LP6U4D2U4WFFRE/bundle.json","state_url":"https://pith.science/pith/T5AMOT7AJTK6LP6U4D2U4WFFRE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T5AMOT7AJTK6LP6U4D2U4WFFRE/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":"2026-07-01T23:39:42Z","links":{"resolver":"https://pith.science/pith/T5AMOT7AJTK6LP6U4D2U4WFFRE","bundle":"https://pith.science/pith/T5AMOT7AJTK6LP6U4D2U4WFFRE/bundle.json","state":"https://pith.science/pith/T5AMOT7AJTK6LP6U4D2U4WFFRE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T5AMOT7AJTK6LP6U4D2U4WFFRE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:T5AMOT7AJTK6LP6U4D2U4WFFRE","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":"55a4902712e1d69ebef48d5c7fbf2d67c66729545f12ed79957c83976e6afec4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-26T09:35:14Z","title_canon_sha256":"73ee29f2f07b5b2bfc854aeb45b1e42fbd4e432b65f60bb607d35f5d55cdebd5"},"schema_version":"1.0","source":{"id":"1310.7089","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.7089","created_at":"2026-05-18T03:08:46Z"},{"alias_kind":"arxiv_version","alias_value":"1310.7089v1","created_at":"2026-05-18T03:08:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.7089","created_at":"2026-05-18T03:08:46Z"},{"alias_kind":"pith_short_12","alias_value":"T5AMOT7AJTK6","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"T5AMOT7AJTK6LP6U","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"T5AMOT7A","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:3691a10ccb6537a5ffcf35589a5ce69785e8cee13eec9bba999bd3f1bdfefafe","target":"graph","created_at":"2026-05-18T03:08:46Z","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 address an important issue of a dynamic homogenisation in vector elasticity for a doubly periodic mass-spring elastic lattice. The notion of logarithmically growing resonant waves is used in a complete analysis of star-shaped wave forms induced by an oscillating point force. We note that the dispersion surfaces for Floquet-Bloch waves in an elastic lattice main contain critical points of the saddle type. Based on the local quadratic approximations of the frequency, as a function of wave vector components, we deduce properties of a transient asymptotic solution as the contribution of the poi","authors_text":"Alexander Movchan, Leonid Slepyan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-26T09:35:14Z","title":"Resonant waves in elastic structured media: dynamic homogenisation versus Green's functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7089","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:eda58f9fac49b0872688e5bea2ad20ec59f3496ec04645a5dfea70216f243ecf","target":"record","created_at":"2026-05-18T03:08:46Z","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":"55a4902712e1d69ebef48d5c7fbf2d67c66729545f12ed79957c83976e6afec4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-26T09:35:14Z","title_canon_sha256":"73ee29f2f07b5b2bfc854aeb45b1e42fbd4e432b65f60bb607d35f5d55cdebd5"},"schema_version":"1.0","source":{"id":"1310.7089","kind":"arxiv","version":1}},"canonical_sha256":"9f40c74fe04cd5e5bfd4e0f54e58a589260ebec1c5f7318f962c139e63f83888","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f40c74fe04cd5e5bfd4e0f54e58a589260ebec1c5f7318f962c139e63f83888","first_computed_at":"2026-05-18T03:08:46.279019Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:08:46.279019Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gRowq3nE8TieqycF6yp/QToNLi5HGPUoCLPyDw97cKtq+kpgt6XA0wRgL2zyyl92q6ig4VipYSTteTXzyUdLAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:08:46.279446Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.7089","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eda58f9fac49b0872688e5bea2ad20ec59f3496ec04645a5dfea70216f243ecf","sha256:3691a10ccb6537a5ffcf35589a5ce69785e8cee13eec9bba999bd3f1bdfefafe"],"state_sha256":"ce0a0550bacfc60e2c3b95609c7f9166f0a8f2710a808fba1350daeb60a8d7d9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cgIwSLVPT+srnLRPBGwuUT5tPCCFe3YN7XOKY8Clsi6Y6sDGh8UvQXdeUfO9rON6PJs4Nny+nhgNwlKRHL29BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T23:39:42.828549Z","bundle_sha256":"ee13dda31aa5814e27d405c3783ab53e263dfceefaffaeed057d37b659136cc7"}}