{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:I7GGR4FOECBQEVUCSIQXH6HDZG","short_pith_number":"pith:I7GGR4FO","canonical_record":{"source":{"id":"1305.3170","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-05-14T14:44:13Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"4c50d018c92a4dcd8c34261577471d5de755dcce72ba5419abb59dae38804025","abstract_canon_sha256":"8724a51c7782f4bd3d1cebd8b31932ab0c15254ca1ec61cabd91106b916b3461"},"schema_version":"1.0"},"canonical_sha256":"47cc68f0ae2083025682922173f8e3c9addbd103346a089d3fa444e962d6f60a","source":{"kind":"arxiv","id":"1305.3170","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.3170","created_at":"2026-05-18T03:25:44Z"},{"alias_kind":"arxiv_version","alias_value":"1305.3170v1","created_at":"2026-05-18T03:25:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.3170","created_at":"2026-05-18T03:25:44Z"},{"alias_kind":"pith_short_12","alias_value":"I7GGR4FOECBQ","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"I7GGR4FOECBQEVUC","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"I7GGR4FO","created_at":"2026-05-18T12:27:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:I7GGR4FOECBQEVUCSIQXH6HDZG","target":"record","payload":{"canonical_record":{"source":{"id":"1305.3170","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-05-14T14:44:13Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"4c50d018c92a4dcd8c34261577471d5de755dcce72ba5419abb59dae38804025","abstract_canon_sha256":"8724a51c7782f4bd3d1cebd8b31932ab0c15254ca1ec61cabd91106b916b3461"},"schema_version":"1.0"},"canonical_sha256":"47cc68f0ae2083025682922173f8e3c9addbd103346a089d3fa444e962d6f60a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:25:44.597885Z","signature_b64":"N0l2GdelKLXnO5r1ivYpiI6zaU/x+Kszt5A9f6/dSpWYeGYiGXAFIdDXUQU5Dp2nTvzFB2V9LHItBsitPNDADw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"47cc68f0ae2083025682922173f8e3c9addbd103346a089d3fa444e962d6f60a","last_reissued_at":"2026-05-18T03:25:44.597140Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:25:44.597140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.3170","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":"2026-05-18T03:25:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EhMdJiPOtPVI6bCXL9OoKLsOgI9f4+FLbKn4eK2LLanN4W0KNe8xRGmCFBtiy2I3Rlk9s445rx9Ao4PD/hJCCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T15:18:31.769776Z"},"content_sha256":"32fa6561d1da58bf5c0ff9745bf8c3c5d3111cf47f13afb9f3554031ac65a8ed","schema_version":"1.0","event_id":"sha256:32fa6561d1da58bf5c0ff9745bf8c3c5d3111cf47f13afb9f3554031ac65a8ed"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:I7GGR4FOECBQEVUCSIQXH6HDZG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On variational dimension reduction in structure mechanics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Paolo Podio-Guidugli, Roberto Paroni","submitted_at":"2013-05-14T14:44:13Z","abstract_excerpt":"The classical low-dimensional models of thin structures are based on certain a priori assumptions on the three-dimensional deformation and/or stress fields, diverse in nature but all motivated by the smallness of certain dimensions with respect to others. In recent years, a considerable amount of work has been done in order to rigorously justify these a priori assumptions; in particular, several techniques have been introduced to make dimension re- duction rigorous. We here review, and to some extent reformulate, the main ideas common to these techniques, using some explicit dimension-reductio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.3170","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":"2026-05-18T03:25:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qbbnDEQhCoT3zAtu+A91C+MqQmbjGrFPEfd/aQTw5+rs1mFZ7amTjByl0Zhsv1C0RxgVd6yytfxJtvuQ6huyBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T15:18:31.770426Z"},"content_sha256":"f1c5e044aba17af412412d7ef2eacbd7a28eae180f254abc4696ca8ea1a61984","schema_version":"1.0","event_id":"sha256:f1c5e044aba17af412412d7ef2eacbd7a28eae180f254abc4696ca8ea1a61984"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I7GGR4FOECBQEVUCSIQXH6HDZG/bundle.json","state_url":"https://pith.science/pith/I7GGR4FOECBQEVUCSIQXH6HDZG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I7GGR4FOECBQEVUCSIQXH6HDZG/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":"2026-06-06T15:18:31Z","links":{"resolver":"https://pith.science/pith/I7GGR4FOECBQEVUCSIQXH6HDZG","bundle":"https://pith.science/pith/I7GGR4FOECBQEVUCSIQXH6HDZG/bundle.json","state":"https://pith.science/pith/I7GGR4FOECBQEVUCSIQXH6HDZG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I7GGR4FOECBQEVUCSIQXH6HDZG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:I7GGR4FOECBQEVUCSIQXH6HDZG","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":"8724a51c7782f4bd3d1cebd8b31932ab0c15254ca1ec61cabd91106b916b3461","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-05-14T14:44:13Z","title_canon_sha256":"4c50d018c92a4dcd8c34261577471d5de755dcce72ba5419abb59dae38804025"},"schema_version":"1.0","source":{"id":"1305.3170","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.3170","created_at":"2026-05-18T03:25:44Z"},{"alias_kind":"arxiv_version","alias_value":"1305.3170v1","created_at":"2026-05-18T03:25:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.3170","created_at":"2026-05-18T03:25:44Z"},{"alias_kind":"pith_short_12","alias_value":"I7GGR4FOECBQ","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"I7GGR4FOECBQEVUC","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"I7GGR4FO","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:f1c5e044aba17af412412d7ef2eacbd7a28eae180f254abc4696ca8ea1a61984","target":"graph","created_at":"2026-05-18T03:25:44Z","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 classical low-dimensional models of thin structures are based on certain a priori assumptions on the three-dimensional deformation and/or stress fields, diverse in nature but all motivated by the smallness of certain dimensions with respect to others. In recent years, a considerable amount of work has been done in order to rigorously justify these a priori assumptions; in particular, several techniques have been introduced to make dimension re- duction rigorous. We here review, and to some extent reformulate, the main ideas common to these techniques, using some explicit dimension-reductio","authors_text":"Paolo Podio-Guidugli, Roberto Paroni","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-05-14T14:44:13Z","title":"On variational dimension reduction in structure mechanics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.3170","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":"sha256:32fa6561d1da58bf5c0ff9745bf8c3c5d3111cf47f13afb9f3554031ac65a8ed","target":"record","created_at":"2026-05-18T03:25:44Z","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":"8724a51c7782f4bd3d1cebd8b31932ab0c15254ca1ec61cabd91106b916b3461","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-05-14T14:44:13Z","title_canon_sha256":"4c50d018c92a4dcd8c34261577471d5de755dcce72ba5419abb59dae38804025"},"schema_version":"1.0","source":{"id":"1305.3170","kind":"arxiv","version":1}},"canonical_sha256":"47cc68f0ae2083025682922173f8e3c9addbd103346a089d3fa444e962d6f60a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"47cc68f0ae2083025682922173f8e3c9addbd103346a089d3fa444e962d6f60a","first_computed_at":"2026-05-18T03:25:44.597140Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:25:44.597140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N0l2GdelKLXnO5r1ivYpiI6zaU/x+Kszt5A9f6/dSpWYeGYiGXAFIdDXUQU5Dp2nTvzFB2V9LHItBsitPNDADw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:25:44.597885Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.3170","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:32fa6561d1da58bf5c0ff9745bf8c3c5d3111cf47f13afb9f3554031ac65a8ed","sha256:f1c5e044aba17af412412d7ef2eacbd7a28eae180f254abc4696ca8ea1a61984"],"state_sha256":"2b20ac56fb959e8b1fab3e10c8b0345d0b75e2aca46fc74d4c1a9ad3edb98a97"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IjWLFsXntRqhpiDpHa56xus2qnwbIXQJPRUL9g1zrhpwjh5MmOQTmVqfb/4GtulhJMkAdcl2pLTiIHQ3v9d3BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T15:18:31.773856Z","bundle_sha256":"ed193181ef3d7eff8218ea89e8e4be349c969587c10536fc851b34a04b99a839"}}