{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:PJDZDEQLBFTPRCZ6WWDFSTPHIR","short_pith_number":"pith:PJDZDEQL","canonical_record":{"source":{"id":"1610.09155","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.OC","submitted_at":"2016-10-28T10:21:48Z","cross_cats_sorted":[],"title_canon_sha256":"8e635d077bc9c46ec3e918cde0f5b5150b0e1831aec88b572206441e9f83a439","abstract_canon_sha256":"cdc0890de03abaee101dfa09518109ae20cf4e172f8f5b61e0ee48210d0e1d2d"},"schema_version":"1.0"},"canonical_sha256":"7a4791920b0966f88b3eb586594de7446f2f80d35b2c95e7bea0e0abd056acc8","source":{"kind":"arxiv","id":"1610.09155","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.09155","created_at":"2026-05-18T01:00:58Z"},{"alias_kind":"arxiv_version","alias_value":"1610.09155v1","created_at":"2026-05-18T01:00:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.09155","created_at":"2026-05-18T01:00:58Z"},{"alias_kind":"pith_short_12","alias_value":"PJDZDEQLBFTP","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PJDZDEQLBFTPRCZ6","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PJDZDEQL","created_at":"2026-05-18T12:30:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:PJDZDEQLBFTPRCZ6WWDFSTPHIR","target":"record","payload":{"canonical_record":{"source":{"id":"1610.09155","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.OC","submitted_at":"2016-10-28T10:21:48Z","cross_cats_sorted":[],"title_canon_sha256":"8e635d077bc9c46ec3e918cde0f5b5150b0e1831aec88b572206441e9f83a439","abstract_canon_sha256":"cdc0890de03abaee101dfa09518109ae20cf4e172f8f5b61e0ee48210d0e1d2d"},"schema_version":"1.0"},"canonical_sha256":"7a4791920b0966f88b3eb586594de7446f2f80d35b2c95e7bea0e0abd056acc8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:58.985302Z","signature_b64":"0+x8FxOBcmowzIBZdARXIfhEC2lPm/2XWAJqqs/6TG+YNlBg/dH6+NKNGzLoMj9D1s8l5NaTUaFuhEDMO/07DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7a4791920b0966f88b3eb586594de7446f2f80d35b2c95e7bea0e0abd056acc8","last_reissued_at":"2026-05-18T01:00:58.984627Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:58.984627Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.09155","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":"2026-05-18T01:00:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nWLYz53Wie1Fmy0o9Oc50P59ZLeGV62l/zMhZLZ3AbGiaDJa75wc/KTh/TjXEOMfg0uSVW1vo0XCskdPscsIDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T01:23:33.645915Z"},"content_sha256":"0f259ebf337f8f00ca0ec7695fddf36604aba6a4ebc3d2a0ec8d178f4e39c53b","schema_version":"1.0","event_id":"sha256:0f259ebf337f8f00ca0ec7695fddf36604aba6a4ebc3d2a0ec8d178f4e39c53b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:PJDZDEQLBFTPRCZ6WWDFSTPHIR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal Design of Helical Springs of Power Law Materials","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Adilet Otemissov, Dongming Wei, Marios Fyrillas, Rustam Bekishev","submitted_at":"2016-10-28T10:21:48Z","abstract_excerpt":"In this paper the geometric dimensions of a compressive helical spring made of power law materials are optimized to reduce the amount of material. The mechanical constraints are derived to form the geometric programming problem. Both the prime and the dual problem are examined and solved semi-analytically for a range of spring index. A numerical example is provided to validate the solutions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09155","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":"2026-05-18T01:00:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ElW8b4KO+3QQLW+mFmQ1RN9FmnrnDE9bEHJmIE4fXgpMcD1GWoB+JNy2Tn+F1Sq5GWIaYNtVJMrR2SMTf/WIAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T01:23:33.646416Z"},"content_sha256":"1aea96ec4dcf35c00ab9a4a9e9014a4abadef482816fdf7d52de963ea38fb367","schema_version":"1.0","event_id":"sha256:1aea96ec4dcf35c00ab9a4a9e9014a4abadef482816fdf7d52de963ea38fb367"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PJDZDEQLBFTPRCZ6WWDFSTPHIR/bundle.json","state_url":"https://pith.science/pith/PJDZDEQLBFTPRCZ6WWDFSTPHIR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PJDZDEQLBFTPRCZ6WWDFSTPHIR/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":"2026-06-23T01:23:33Z","links":{"resolver":"https://pith.science/pith/PJDZDEQLBFTPRCZ6WWDFSTPHIR","bundle":"https://pith.science/pith/PJDZDEQLBFTPRCZ6WWDFSTPHIR/bundle.json","state":"https://pith.science/pith/PJDZDEQLBFTPRCZ6WWDFSTPHIR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PJDZDEQLBFTPRCZ6WWDFSTPHIR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:PJDZDEQLBFTPRCZ6WWDFSTPHIR","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":"cdc0890de03abaee101dfa09518109ae20cf4e172f8f5b61e0ee48210d0e1d2d","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.OC","submitted_at":"2016-10-28T10:21:48Z","title_canon_sha256":"8e635d077bc9c46ec3e918cde0f5b5150b0e1831aec88b572206441e9f83a439"},"schema_version":"1.0","source":{"id":"1610.09155","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.09155","created_at":"2026-05-18T01:00:58Z"},{"alias_kind":"arxiv_version","alias_value":"1610.09155v1","created_at":"2026-05-18T01:00:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.09155","created_at":"2026-05-18T01:00:58Z"},{"alias_kind":"pith_short_12","alias_value":"PJDZDEQLBFTP","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PJDZDEQLBFTPRCZ6","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PJDZDEQL","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:1aea96ec4dcf35c00ab9a4a9e9014a4abadef482816fdf7d52de963ea38fb367","target":"graph","created_at":"2026-05-18T01:00:58Z","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 the geometric dimensions of a compressive helical spring made of power law materials are optimized to reduce the amount of material. The mechanical constraints are derived to form the geometric programming problem. Both the prime and the dual problem are examined and solved semi-analytically for a range of spring index. A numerical example is provided to validate the solutions.","authors_text":"Adilet Otemissov, Dongming Wei, Marios Fyrillas, Rustam Bekishev","cross_cats":[],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.OC","submitted_at":"2016-10-28T10:21:48Z","title":"Optimal Design of Helical Springs of Power Law Materials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09155","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":"sha256:0f259ebf337f8f00ca0ec7695fddf36604aba6a4ebc3d2a0ec8d178f4e39c53b","target":"record","created_at":"2026-05-18T01:00:58Z","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":"cdc0890de03abaee101dfa09518109ae20cf4e172f8f5b61e0ee48210d0e1d2d","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.OC","submitted_at":"2016-10-28T10:21:48Z","title_canon_sha256":"8e635d077bc9c46ec3e918cde0f5b5150b0e1831aec88b572206441e9f83a439"},"schema_version":"1.0","source":{"id":"1610.09155","kind":"arxiv","version":1}},"canonical_sha256":"7a4791920b0966f88b3eb586594de7446f2f80d35b2c95e7bea0e0abd056acc8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7a4791920b0966f88b3eb586594de7446f2f80d35b2c95e7bea0e0abd056acc8","first_computed_at":"2026-05-18T01:00:58.984627Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:00:58.984627Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0+x8FxOBcmowzIBZdARXIfhEC2lPm/2XWAJqqs/6TG+YNlBg/dH6+NKNGzLoMj9D1s8l5NaTUaFuhEDMO/07DA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:00:58.985302Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.09155","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f259ebf337f8f00ca0ec7695fddf36604aba6a4ebc3d2a0ec8d178f4e39c53b","sha256:1aea96ec4dcf35c00ab9a4a9e9014a4abadef482816fdf7d52de963ea38fb367"],"state_sha256":"70103f5d333968db6d74dfd9d243ea570b927922ff2f68f900e9b097301e50c3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zbPkUAQ8bWwouwXl1kELthzbG52p3H8Xi68MCuYyTY1HENa1V9zhw3m31qY70ZPAz0nAyN6DLYpyo9ZuUSaxAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T01:23:33.649215Z","bundle_sha256":"82bbb9f10a31d162263427b8c6db504d6944712e7b1cdb9c7220d5d87dfd04a5"}}