{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:2LYJTCXKMSQFEUSQBIJ6ISUVWC","short_pith_number":"pith:2LYJTCXK","canonical_record":{"source":{"id":"1509.05522","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2015-09-18T07:24:40Z","cross_cats_sorted":[],"title_canon_sha256":"4ea662be5d6bf73f9fb428e331a947f4ff312f36d4c1989d666e9410cf908bb8","abstract_canon_sha256":"2bfd3ff929a18209535a969a9dc04b97cdb4fb22ba80b04442cf71ea419693c1"},"schema_version":"1.0"},"canonical_sha256":"d2f0998aea64a05252500a13e44a95b0a9e41a002f3a2d8bacc1a379d0820617","source":{"kind":"arxiv","id":"1509.05522","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.05522","created_at":"2026-05-18T01:24:52Z"},{"alias_kind":"arxiv_version","alias_value":"1509.05522v1","created_at":"2026-05-18T01:24:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.05522","created_at":"2026-05-18T01:24:52Z"},{"alias_kind":"pith_short_12","alias_value":"2LYJTCXKMSQF","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2LYJTCXKMSQFEUSQ","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2LYJTCXK","created_at":"2026-05-18T12:29:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:2LYJTCXKMSQFEUSQBIJ6ISUVWC","target":"record","payload":{"canonical_record":{"source":{"id":"1509.05522","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2015-09-18T07:24:40Z","cross_cats_sorted":[],"title_canon_sha256":"4ea662be5d6bf73f9fb428e331a947f4ff312f36d4c1989d666e9410cf908bb8","abstract_canon_sha256":"2bfd3ff929a18209535a969a9dc04b97cdb4fb22ba80b04442cf71ea419693c1"},"schema_version":"1.0"},"canonical_sha256":"d2f0998aea64a05252500a13e44a95b0a9e41a002f3a2d8bacc1a379d0820617","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:52.240339Z","signature_b64":"o4cJoLNIqekSS3ofKjwzGc9R2qFyI2asr7XB9MFwVNm8H7LHPzA8QD7hFRKzplqSWQNMtknOs2QzNtN9167DAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d2f0998aea64a05252500a13e44a95b0a9e41a002f3a2d8bacc1a379d0820617","last_reissued_at":"2026-05-18T01:24:52.239581Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:52.239581Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.05522","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":"2026-05-18T01:24:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XzoMNvR+MOGjsWuKSu6euzCiK2HHvsSmPBp7g/bqLRspRdHAe+QgHgr3sWfFnbI6SnLJPJiUTWLa8gl+0FLDBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T18:31:31.737069Z"},"content_sha256":"65affd56481127baa5552f4769beb72892d19990e1c082713b227f78d868c692","schema_version":"1.0","event_id":"sha256:65affd56481127baa5552f4769beb72892d19990e1c082713b227f78d868c692"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:2LYJTCXKMSQFEUSQBIJ6ISUVWC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Resonant and Non-Local Properties of Phononic Metasolids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.mtrl-sci","authors_text":"Bahram Djafari-Rouhani, Daniel Torrent, Yan Pennec","submitted_at":"2015-09-18T07:24:40Z","abstract_excerpt":"We derive a general theory of effective properties in metasolids based on phononic crystals with low frequency resonances. We demonstrate that in general these structures need to be described by means of a frequency-dependent and non-local anisotropic mass density, stiffness tensor and a third- rank coupling tensor, which shows that they behave like a non-local Willis medium. The effect of non-locality and coupling tensor manifest themselves for some particular resonances whereas they become negligible for other resonances. Considering the example of a two-dimensional phononic crystal, consist"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05522","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":"2026-05-18T01:24:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YVwuYUJh292sQWeUEe5Lgt09BSXYj1tP1fI/3M5hoT8IcSRmj9LNmhfy3N9RW1eJOZomx1KsjzD9jd6aYJdJDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T18:31:31.737752Z"},"content_sha256":"7d765062769cf8748da61854c89f64062ca9a1c8ad404fae340a92fddf881f5e","schema_version":"1.0","event_id":"sha256:7d765062769cf8748da61854c89f64062ca9a1c8ad404fae340a92fddf881f5e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2LYJTCXKMSQFEUSQBIJ6ISUVWC/bundle.json","state_url":"https://pith.science/pith/2LYJTCXKMSQFEUSQBIJ6ISUVWC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2LYJTCXKMSQFEUSQBIJ6ISUVWC/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":"2026-05-25T18:31:31Z","links":{"resolver":"https://pith.science/pith/2LYJTCXKMSQFEUSQBIJ6ISUVWC","bundle":"https://pith.science/pith/2LYJTCXKMSQFEUSQBIJ6ISUVWC/bundle.json","state":"https://pith.science/pith/2LYJTCXKMSQFEUSQBIJ6ISUVWC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2LYJTCXKMSQFEUSQBIJ6ISUVWC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:2LYJTCXKMSQFEUSQBIJ6ISUVWC","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":"2bfd3ff929a18209535a969a9dc04b97cdb4fb22ba80b04442cf71ea419693c1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2015-09-18T07:24:40Z","title_canon_sha256":"4ea662be5d6bf73f9fb428e331a947f4ff312f36d4c1989d666e9410cf908bb8"},"schema_version":"1.0","source":{"id":"1509.05522","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.05522","created_at":"2026-05-18T01:24:52Z"},{"alias_kind":"arxiv_version","alias_value":"1509.05522v1","created_at":"2026-05-18T01:24:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.05522","created_at":"2026-05-18T01:24:52Z"},{"alias_kind":"pith_short_12","alias_value":"2LYJTCXKMSQF","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2LYJTCXKMSQFEUSQ","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2LYJTCXK","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:7d765062769cf8748da61854c89f64062ca9a1c8ad404fae340a92fddf881f5e","target":"graph","created_at":"2026-05-18T01:24:52Z","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 derive a general theory of effective properties in metasolids based on phononic crystals with low frequency resonances. We demonstrate that in general these structures need to be described by means of a frequency-dependent and non-local anisotropic mass density, stiffness tensor and a third- rank coupling tensor, which shows that they behave like a non-local Willis medium. The effect of non-locality and coupling tensor manifest themselves for some particular resonances whereas they become negligible for other resonances. Considering the example of a two-dimensional phononic crystal, consist","authors_text":"Bahram Djafari-Rouhani, Daniel Torrent, Yan Pennec","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2015-09-18T07:24:40Z","title":"Resonant and Non-Local Properties of Phononic Metasolids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05522","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":"sha256:65affd56481127baa5552f4769beb72892d19990e1c082713b227f78d868c692","target":"record","created_at":"2026-05-18T01:24:52Z","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":"2bfd3ff929a18209535a969a9dc04b97cdb4fb22ba80b04442cf71ea419693c1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2015-09-18T07:24:40Z","title_canon_sha256":"4ea662be5d6bf73f9fb428e331a947f4ff312f36d4c1989d666e9410cf908bb8"},"schema_version":"1.0","source":{"id":"1509.05522","kind":"arxiv","version":1}},"canonical_sha256":"d2f0998aea64a05252500a13e44a95b0a9e41a002f3a2d8bacc1a379d0820617","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d2f0998aea64a05252500a13e44a95b0a9e41a002f3a2d8bacc1a379d0820617","first_computed_at":"2026-05-18T01:24:52.239581Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:52.239581Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o4cJoLNIqekSS3ofKjwzGc9R2qFyI2asr7XB9MFwVNm8H7LHPzA8QD7hFRKzplqSWQNMtknOs2QzNtN9167DAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:52.240339Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.05522","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:65affd56481127baa5552f4769beb72892d19990e1c082713b227f78d868c692","sha256:7d765062769cf8748da61854c89f64062ca9a1c8ad404fae340a92fddf881f5e"],"state_sha256":"6d493a851ddac76b7134fa212eeffe1c915b70e138cd17057abe7451cd9cae77"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GA4kvv45Kb2n7rFtyhTdkwYTfQ5IoTGgReggog+Pdx0DVlu20emY3Sn/0Kh4Qa5qsWxfwayhYz/F+c8SYT4qAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T18:31:31.741430Z","bundle_sha256":"cde20918f4a32163e16467c3993de28bbf20602d11461aa9b51ee50add1197d8"}}