{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:MNTAPNTWSXJQ6CF6BQLCKDFZNW","short_pith_number":"pith:MNTAPNTW","canonical_record":{"source":{"id":"1811.12057","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-11-29T10:52:02Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"076cd25e414ddeb9edb4578fa946ec78d73513b18d4415161981b88a6418943d","abstract_canon_sha256":"1b0b43e88b9885dbf1028440aba207a6ef437f932d797270e2483f7e82d0b491"},"schema_version":"1.0"},"canonical_sha256":"636607b67695d30f08be0c16250cb96db86f1b3f048ba993d0f5b9e2ac5b9755","source":{"kind":"arxiv","id":"1811.12057","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.12057","created_at":"2026-05-17T23:40:08Z"},{"alias_kind":"arxiv_version","alias_value":"1811.12057v1","created_at":"2026-05-17T23:40:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.12057","created_at":"2026-05-17T23:40:08Z"},{"alias_kind":"pith_short_12","alias_value":"MNTAPNTWSXJQ","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"MNTAPNTWSXJQ6CF6","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"MNTAPNTW","created_at":"2026-05-18T12:32:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:MNTAPNTWSXJQ6CF6BQLCKDFZNW","target":"record","payload":{"canonical_record":{"source":{"id":"1811.12057","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-11-29T10:52:02Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"076cd25e414ddeb9edb4578fa946ec78d73513b18d4415161981b88a6418943d","abstract_canon_sha256":"1b0b43e88b9885dbf1028440aba207a6ef437f932d797270e2483f7e82d0b491"},"schema_version":"1.0"},"canonical_sha256":"636607b67695d30f08be0c16250cb96db86f1b3f048ba993d0f5b9e2ac5b9755","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:08.841042Z","signature_b64":"2imgo45AgSWZAMb26sO3eu/x2sA5sy0nliR/GyOpWZQlgdZspguDxc/LAUo+t8hoE5T7IqXI0nP+7H7Vtr42Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"636607b67695d30f08be0c16250cb96db86f1b3f048ba993d0f5b9e2ac5b9755","last_reissued_at":"2026-05-17T23:40:08.840519Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:08.840519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.12057","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":"2026-05-17T23:40:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wGnCCR1Y9wt6j3MrCNmN+IDjSzv3RAymp4Hl4ogPhuxe3H7+NE6ZodjzOE9vwMBxFAZHwpx8sKChDEer5+NiCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T06:54:16.271972Z"},"content_sha256":"05136a76381857bc035319e65e2c4127548b1de7febd9a9bcbde9522549428d3","schema_version":"1.0","event_id":"sha256:05136a76381857bc035319e65e2c4127548b1de7febd9a9bcbde9522549428d3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:MNTAPNTWSXJQ6CF6BQLCKDFZNW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bifurcation analysis of rotating axially compressed imperfect nano-rod","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Du\\v{s}an Zorica, Ljubica Oparnica, Teodor M. Atanackovi\\'c","submitted_at":"2018-11-29T10:52:02Z","abstract_excerpt":"Static stability problem for axially compressed rotating nano-rod clamped at one and free at the other end is analyzed by the use of bifurcation theory. It is obtained that the pitchfork bifurcation may be either super- or sub-critical. Considering the imperfections in rod's shape and loading, it is proved that they constitute the two-parameter universal unfolding of the problem. Numerical analysis also revealed that for non-locality parameters having higher value than the critical one interaction curves have two branches, so that for a single critical value of angular velocity there exist two"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.12057","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":"2026-05-17T23:40:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WrxH606I9cLjGBg0LQp3OY/1EmzSZZeFcEV7CkXFhOJjz1dnzNgIss3sLa3t4IXEtj8SeyFdUwZu8UUOVbWKDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T06:54:16.272640Z"},"content_sha256":"d0f7f483769c3351f6ddd10885f7a258400d349fc78aa7d41df910559a8e5710","schema_version":"1.0","event_id":"sha256:d0f7f483769c3351f6ddd10885f7a258400d349fc78aa7d41df910559a8e5710"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MNTAPNTWSXJQ6CF6BQLCKDFZNW/bundle.json","state_url":"https://pith.science/pith/MNTAPNTWSXJQ6CF6BQLCKDFZNW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MNTAPNTWSXJQ6CF6BQLCKDFZNW/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":"2026-06-05T06:54:16Z","links":{"resolver":"https://pith.science/pith/MNTAPNTWSXJQ6CF6BQLCKDFZNW","bundle":"https://pith.science/pith/MNTAPNTWSXJQ6CF6BQLCKDFZNW/bundle.json","state":"https://pith.science/pith/MNTAPNTWSXJQ6CF6BQLCKDFZNW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MNTAPNTWSXJQ6CF6BQLCKDFZNW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:MNTAPNTWSXJQ6CF6BQLCKDFZNW","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":"1b0b43e88b9885dbf1028440aba207a6ef437f932d797270e2483f7e82d0b491","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-11-29T10:52:02Z","title_canon_sha256":"076cd25e414ddeb9edb4578fa946ec78d73513b18d4415161981b88a6418943d"},"schema_version":"1.0","source":{"id":"1811.12057","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.12057","created_at":"2026-05-17T23:40:08Z"},{"alias_kind":"arxiv_version","alias_value":"1811.12057v1","created_at":"2026-05-17T23:40:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.12057","created_at":"2026-05-17T23:40:08Z"},{"alias_kind":"pith_short_12","alias_value":"MNTAPNTWSXJQ","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"MNTAPNTWSXJQ6CF6","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"MNTAPNTW","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:d0f7f483769c3351f6ddd10885f7a258400d349fc78aa7d41df910559a8e5710","target":"graph","created_at":"2026-05-17T23:40:08Z","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":"Static stability problem for axially compressed rotating nano-rod clamped at one and free at the other end is analyzed by the use of bifurcation theory. It is obtained that the pitchfork bifurcation may be either super- or sub-critical. Considering the imperfections in rod's shape and loading, it is proved that they constitute the two-parameter universal unfolding of the problem. Numerical analysis also revealed that for non-locality parameters having higher value than the critical one interaction curves have two branches, so that for a single critical value of angular velocity there exist two","authors_text":"Du\\v{s}an Zorica, Ljubica Oparnica, Teodor M. Atanackovi\\'c","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-11-29T10:52:02Z","title":"Bifurcation analysis of rotating axially compressed imperfect nano-rod"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.12057","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":"sha256:05136a76381857bc035319e65e2c4127548b1de7febd9a9bcbde9522549428d3","target":"record","created_at":"2026-05-17T23:40:08Z","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":"1b0b43e88b9885dbf1028440aba207a6ef437f932d797270e2483f7e82d0b491","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-11-29T10:52:02Z","title_canon_sha256":"076cd25e414ddeb9edb4578fa946ec78d73513b18d4415161981b88a6418943d"},"schema_version":"1.0","source":{"id":"1811.12057","kind":"arxiv","version":1}},"canonical_sha256":"636607b67695d30f08be0c16250cb96db86f1b3f048ba993d0f5b9e2ac5b9755","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"636607b67695d30f08be0c16250cb96db86f1b3f048ba993d0f5b9e2ac5b9755","first_computed_at":"2026-05-17T23:40:08.840519Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:08.840519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2imgo45AgSWZAMb26sO3eu/x2sA5sy0nliR/GyOpWZQlgdZspguDxc/LAUo+t8hoE5T7IqXI0nP+7H7Vtr42Bg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:08.841042Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.12057","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:05136a76381857bc035319e65e2c4127548b1de7febd9a9bcbde9522549428d3","sha256:d0f7f483769c3351f6ddd10885f7a258400d349fc78aa7d41df910559a8e5710"],"state_sha256":"8a056792a6e4a09d1584d40b94317dce6314bb64e3aacea5f2c28fb65dc54e91"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t9gMCPFP7Nn1N77X4u1ErErhAaMzCIsmCJlrWGIX/KSzcYmHSWp4CQBjHaq8hwqh8mC2L+KBND0/jk8CUJ1kDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T06:54:16.276232Z","bundle_sha256":"eb51ad774649d68df96cee644c88215a3c85d9410d507b4f3195aa47b137dad2"}}