{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:TEEHVYG2BDOVSX6KW6VEY54GJ3","short_pith_number":"pith:TEEHVYG2","canonical_record":{"source":{"id":"1602.04315","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-02-13T11:03:09Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"28210cb32421be35ea4dd682aefeb509710d1ededca033df8b62f27e1b2620b2","abstract_canon_sha256":"c481438246ad65aab4073953da6b561cadfc3434a875f095e62e1fbc315306ae"},"schema_version":"1.0"},"canonical_sha256":"99087ae0da08dd595fcab7aa4c77864ee1487764e9c442b906e67ad13ad8275f","source":{"kind":"arxiv","id":"1602.04315","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.04315","created_at":"2026-05-18T00:54:20Z"},{"alias_kind":"arxiv_version","alias_value":"1602.04315v1","created_at":"2026-05-18T00:54:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.04315","created_at":"2026-05-18T00:54:20Z"},{"alias_kind":"pith_short_12","alias_value":"TEEHVYG2BDOV","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"TEEHVYG2BDOVSX6K","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"TEEHVYG2","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:TEEHVYG2BDOVSX6KW6VEY54GJ3","target":"record","payload":{"canonical_record":{"source":{"id":"1602.04315","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-02-13T11:03:09Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"28210cb32421be35ea4dd682aefeb509710d1ededca033df8b62f27e1b2620b2","abstract_canon_sha256":"c481438246ad65aab4073953da6b561cadfc3434a875f095e62e1fbc315306ae"},"schema_version":"1.0"},"canonical_sha256":"99087ae0da08dd595fcab7aa4c77864ee1487764e9c442b906e67ad13ad8275f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:20.611191Z","signature_b64":"INajYEg12wIE86iW5hvbj0uIe/khJWKphK2zKvK1Zbm9Qi/UWtayLl+PbsRsevvvLSL8RYXgqT/iNEveSQrnDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"99087ae0da08dd595fcab7aa4c77864ee1487764e9c442b906e67ad13ad8275f","last_reissued_at":"2026-05-18T00:54:20.610857Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:20.610857Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.04315","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":"2026-05-18T00:54:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tiw67OOLo5twHWv7CuGlQOEjeufPWG0Gg64lVScnJMuHBGZhsaW6xFQoqhQyKN3MjxFUQKXRiQ5tYib9lrzaBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T13:49:39.645231Z"},"content_sha256":"985a5b46e6be438fef3f0ec70d1da5bb655ed663721cff756d96553217b988fd","schema_version":"1.0","event_id":"sha256:985a5b46e6be438fef3f0ec70d1da5bb655ed663721cff756d96553217b988fd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:TEEHVYG2BDOVSX6KW6VEY54GJ3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Complete band gaps including non-local effects occur only in the relaxed micromorphic model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Angela Madeo, Gabriele Barbagallo, Marco Valerio D'Agostino, Patrizio Neff","submitted_at":"2016-02-13T11:03:09Z","abstract_excerpt":"In this paper we substantiate the claim implicitly made in previous works that the relaxed micromorphic model is the only linear, isotropic, reversibly elastic, nonlocal generalized continuum model able to describe complete band-gaps on a phenomenological level. To this end, we recapitulate the response of the standard Mindlin-Eringen micromorphic model with the full micro-distortion gradient of P, the relaxed micromorphic model depending only on the Curl P of the micro-distortion P, and a variant of the standard micromorphic model in which the curvature depends only on the divergence Div P of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.04315","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":"2026-05-18T00:54:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MXuhAHy/we1tfsx+kNN+7c35/jdZNcN1IZpPQoh8HHfJ8dF/luwMM+U7rgcBxdo/xJtVOWlMFa38OSnT3LWiCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T13:49:39.645620Z"},"content_sha256":"a8012c6fb03ced5f7dabd684e5b3bd736a8ae505419f3a3818d5eefdf8254de3","schema_version":"1.0","event_id":"sha256:a8012c6fb03ced5f7dabd684e5b3bd736a8ae505419f3a3818d5eefdf8254de3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TEEHVYG2BDOVSX6KW6VEY54GJ3/bundle.json","state_url":"https://pith.science/pith/TEEHVYG2BDOVSX6KW6VEY54GJ3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TEEHVYG2BDOVSX6KW6VEY54GJ3/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":"2026-06-01T13:49:39Z","links":{"resolver":"https://pith.science/pith/TEEHVYG2BDOVSX6KW6VEY54GJ3","bundle":"https://pith.science/pith/TEEHVYG2BDOVSX6KW6VEY54GJ3/bundle.json","state":"https://pith.science/pith/TEEHVYG2BDOVSX6KW6VEY54GJ3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TEEHVYG2BDOVSX6KW6VEY54GJ3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TEEHVYG2BDOVSX6KW6VEY54GJ3","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":"c481438246ad65aab4073953da6b561cadfc3434a875f095e62e1fbc315306ae","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-02-13T11:03:09Z","title_canon_sha256":"28210cb32421be35ea4dd682aefeb509710d1ededca033df8b62f27e1b2620b2"},"schema_version":"1.0","source":{"id":"1602.04315","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.04315","created_at":"2026-05-18T00:54:20Z"},{"alias_kind":"arxiv_version","alias_value":"1602.04315v1","created_at":"2026-05-18T00:54:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.04315","created_at":"2026-05-18T00:54:20Z"},{"alias_kind":"pith_short_12","alias_value":"TEEHVYG2BDOV","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"TEEHVYG2BDOVSX6K","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"TEEHVYG2","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:a8012c6fb03ced5f7dabd684e5b3bd736a8ae505419f3a3818d5eefdf8254de3","target":"graph","created_at":"2026-05-18T00:54:20Z","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":"In this paper we substantiate the claim implicitly made in previous works that the relaxed micromorphic model is the only linear, isotropic, reversibly elastic, nonlocal generalized continuum model able to describe complete band-gaps on a phenomenological level. To this end, we recapitulate the response of the standard Mindlin-Eringen micromorphic model with the full micro-distortion gradient of P, the relaxed micromorphic model depending only on the Curl P of the micro-distortion P, and a variant of the standard micromorphic model in which the curvature depends only on the divergence Div P of","authors_text":"Angela Madeo, Gabriele Barbagallo, Marco Valerio D'Agostino, Patrizio Neff","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-02-13T11:03:09Z","title":"Complete band gaps including non-local effects occur only in the relaxed micromorphic model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.04315","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":"sha256:985a5b46e6be438fef3f0ec70d1da5bb655ed663721cff756d96553217b988fd","target":"record","created_at":"2026-05-18T00:54:20Z","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":"c481438246ad65aab4073953da6b561cadfc3434a875f095e62e1fbc315306ae","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-02-13T11:03:09Z","title_canon_sha256":"28210cb32421be35ea4dd682aefeb509710d1ededca033df8b62f27e1b2620b2"},"schema_version":"1.0","source":{"id":"1602.04315","kind":"arxiv","version":1}},"canonical_sha256":"99087ae0da08dd595fcab7aa4c77864ee1487764e9c442b906e67ad13ad8275f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"99087ae0da08dd595fcab7aa4c77864ee1487764e9c442b906e67ad13ad8275f","first_computed_at":"2026-05-18T00:54:20.610857Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:20.610857Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"INajYEg12wIE86iW5hvbj0uIe/khJWKphK2zKvK1Zbm9Qi/UWtayLl+PbsRsevvvLSL8RYXgqT/iNEveSQrnDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:20.611191Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.04315","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:985a5b46e6be438fef3f0ec70d1da5bb655ed663721cff756d96553217b988fd","sha256:a8012c6fb03ced5f7dabd684e5b3bd736a8ae505419f3a3818d5eefdf8254de3"],"state_sha256":"1063d6a5f351d25785bbb5b027d471d064fdabb872c33469ad4e7c3da1b93d3c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZbNWFEqlarSH0te8Qh/nd16Xpybw3Z/drqCDVSmb1D1Fjs9xFNCc9HAhQz4zjceLfnYbo2c+E5eY3pez22+0Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T13:49:39.647456Z","bundle_sha256":"548ba287fecd3b519a6b671011c7ad7611d87d4ae99211fb648e32cbfc35a5e3"}}