{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:WKDWT45LTS426GMXZEAJXQKM3Q","short_pith_number":"pith:WKDWT45L","canonical_record":{"source":{"id":"1907.00447","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-06-30T20:16:44Z","cross_cats_sorted":["cond-mat.mtrl-sci"],"title_canon_sha256":"d4e289fa03b5a907c7d8c67a0842384d4249bbd665cf59e34f1f7743b4a20c85","abstract_canon_sha256":"7b39c1228206a9341872063c0ef31fbf0ed0475b151a092e99075d0d05d88382"},"schema_version":"1.0"},"canonical_sha256":"b28769f3ab9cb9af1997c9009bc14cdc04bc3f6c1df540b28eac4fbab42e287d","source":{"kind":"arxiv","id":"1907.00447","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.00447","created_at":"2026-05-17T23:41:51Z"},{"alias_kind":"arxiv_version","alias_value":"1907.00447v1","created_at":"2026-05-17T23:41:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.00447","created_at":"2026-05-17T23:41:51Z"},{"alias_kind":"pith_short_12","alias_value":"WKDWT45LTS42","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"WKDWT45LTS426GMX","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"WKDWT45L","created_at":"2026-05-18T12:33:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:WKDWT45LTS426GMXZEAJXQKM3Q","target":"record","payload":{"canonical_record":{"source":{"id":"1907.00447","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-06-30T20:16:44Z","cross_cats_sorted":["cond-mat.mtrl-sci"],"title_canon_sha256":"d4e289fa03b5a907c7d8c67a0842384d4249bbd665cf59e34f1f7743b4a20c85","abstract_canon_sha256":"7b39c1228206a9341872063c0ef31fbf0ed0475b151a092e99075d0d05d88382"},"schema_version":"1.0"},"canonical_sha256":"b28769f3ab9cb9af1997c9009bc14cdc04bc3f6c1df540b28eac4fbab42e287d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:51.668327Z","signature_b64":"xxX9Ersfmi1DnFcoaSKLcUjOkQB0+EGaxM9abmF9DLSPO7N9mZnoHWw6avBcrssbr0LgnvyQWbdmdBtZ0jL7DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b28769f3ab9cb9af1997c9009bc14cdc04bc3f6c1df540b28eac4fbab42e287d","last_reissued_at":"2026-05-17T23:41:51.667664Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:51.667664Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1907.00447","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":"2026-05-17T23:41:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MKmv95T2GlXwO0+/yvVEiruWy9MQjLLcf24qCZ8q7cHWLUWLg7thGdoyjZcXRSGlcTCiC6mwVGeooT6R75dXCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T11:37:20.619728Z"},"content_sha256":"e7ce472d9d26f1729e946dc6010d9c9787c26665a454973ac2be44cb92a4a714","schema_version":"1.0","event_id":"sha256:e7ce472d9d26f1729e946dc6010d9c9787c26665a454973ac2be44cb92a4a714"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:WKDWT45LTS426GMXZEAJXQKM3Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Energy minimising configurations of pre-strained multilayers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mtrl-sci"],"primary_cat":"math.AP","authors_text":"Bernd Schmidt, Miguel de Benito Delgado","submitted_at":"2019-06-30T20:16:44Z","abstract_excerpt":"We investigate energetically optimal configurations of thin structures with a pre-strain. Depending on the strength of the pre-strain we consider a whole hierarchy of effective plate theories with a spontaneous curvature term, ranging from linearised Kirchhoff to von K\\'arm\\'an to linearised von K\\'arm\\'an theories. While explicit formulae are available in the linearised regimes, the von K\\'arm\\'an theory turns out to be critical and a phase transition from cylindrical (as in linearised Kirchhoff) to spherical (as in von linearised K\\'arm\\'an) configurations is observed there. We analyse this "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.00447","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":"2026-05-17T23:41:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uXge9tpZ/wER99zIN6aXhIG25WowaYN9AtLQmstA9d47hWnViGi1IcKAthfpsMUbqTAGqP/vf9jGxH/jVM44Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T11:37:20.620453Z"},"content_sha256":"8df8472302af2c419ac683820c99f9d08aad9ac0e10ffa2bf887df836e4c4a54","schema_version":"1.0","event_id":"sha256:8df8472302af2c419ac683820c99f9d08aad9ac0e10ffa2bf887df836e4c4a54"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WKDWT45LTS426GMXZEAJXQKM3Q/bundle.json","state_url":"https://pith.science/pith/WKDWT45LTS426GMXZEAJXQKM3Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WKDWT45LTS426GMXZEAJXQKM3Q/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":"2026-06-10T11:37:20Z","links":{"resolver":"https://pith.science/pith/WKDWT45LTS426GMXZEAJXQKM3Q","bundle":"https://pith.science/pith/WKDWT45LTS426GMXZEAJXQKM3Q/bundle.json","state":"https://pith.science/pith/WKDWT45LTS426GMXZEAJXQKM3Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WKDWT45LTS426GMXZEAJXQKM3Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:WKDWT45LTS426GMXZEAJXQKM3Q","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":"7b39c1228206a9341872063c0ef31fbf0ed0475b151a092e99075d0d05d88382","cross_cats_sorted":["cond-mat.mtrl-sci"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-06-30T20:16:44Z","title_canon_sha256":"d4e289fa03b5a907c7d8c67a0842384d4249bbd665cf59e34f1f7743b4a20c85"},"schema_version":"1.0","source":{"id":"1907.00447","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.00447","created_at":"2026-05-17T23:41:51Z"},{"alias_kind":"arxiv_version","alias_value":"1907.00447v1","created_at":"2026-05-17T23:41:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.00447","created_at":"2026-05-17T23:41:51Z"},{"alias_kind":"pith_short_12","alias_value":"WKDWT45LTS42","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"WKDWT45LTS426GMX","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"WKDWT45L","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:8df8472302af2c419ac683820c99f9d08aad9ac0e10ffa2bf887df836e4c4a54","target":"graph","created_at":"2026-05-17T23:41:51Z","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 investigate energetically optimal configurations of thin structures with a pre-strain. Depending on the strength of the pre-strain we consider a whole hierarchy of effective plate theories with a spontaneous curvature term, ranging from linearised Kirchhoff to von K\\'arm\\'an to linearised von K\\'arm\\'an theories. While explicit formulae are available in the linearised regimes, the von K\\'arm\\'an theory turns out to be critical and a phase transition from cylindrical (as in linearised Kirchhoff) to spherical (as in von linearised K\\'arm\\'an) configurations is observed there. We analyse this ","authors_text":"Bernd Schmidt, Miguel de Benito Delgado","cross_cats":["cond-mat.mtrl-sci"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-06-30T20:16:44Z","title":"Energy minimising configurations of pre-strained multilayers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.00447","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:e7ce472d9d26f1729e946dc6010d9c9787c26665a454973ac2be44cb92a4a714","target":"record","created_at":"2026-05-17T23:41:51Z","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":"7b39c1228206a9341872063c0ef31fbf0ed0475b151a092e99075d0d05d88382","cross_cats_sorted":["cond-mat.mtrl-sci"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-06-30T20:16:44Z","title_canon_sha256":"d4e289fa03b5a907c7d8c67a0842384d4249bbd665cf59e34f1f7743b4a20c85"},"schema_version":"1.0","source":{"id":"1907.00447","kind":"arxiv","version":1}},"canonical_sha256":"b28769f3ab9cb9af1997c9009bc14cdc04bc3f6c1df540b28eac4fbab42e287d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b28769f3ab9cb9af1997c9009bc14cdc04bc3f6c1df540b28eac4fbab42e287d","first_computed_at":"2026-05-17T23:41:51.667664Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:51.667664Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xxX9Ersfmi1DnFcoaSKLcUjOkQB0+EGaxM9abmF9DLSPO7N9mZnoHWw6avBcrssbr0LgnvyQWbdmdBtZ0jL7DA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:51.668327Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.00447","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e7ce472d9d26f1729e946dc6010d9c9787c26665a454973ac2be44cb92a4a714","sha256:8df8472302af2c419ac683820c99f9d08aad9ac0e10ffa2bf887df836e4c4a54"],"state_sha256":"3747ce47ce9290ff24858731ae13e4857c29f5393c18403bd31b978d28f93006"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yfxRHwLMRRqNQ0GcPoCVUxidySwYgs7sF4tsIT8XqCQbg3a1XLU2zov7Lel0phr7X20qZGlmsQqMf1MmYuMFCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T11:37:20.624893Z","bundle_sha256":"f4d8f5eb27f84e8ba6a36ddb426134d34a13d7f92daca46166b8ea61dda2ebda"}}