{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:WARYBJR3PM3PE5YQ2DUYMXK5RM","short_pith_number":"pith:WARYBJR3","canonical_record":{"source":{"id":"math/0502214","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.NT","submitted_at":"2005-02-10T16:18:54Z","cross_cats_sorted":[],"title_canon_sha256":"578412d5ca0e83e4a9676c49121f5b26b68beaa04e25302ed411005980f9cefb","abstract_canon_sha256":"90f044e15b939095fce84794f822ea08b8670c201887c020c2c10e1d4bbabae4"},"schema_version":"1.0"},"canonical_sha256":"b02380a63b7b36f27710d0e9865d5d8b0ed4ba196dc64408927b46b647d70ef6","source":{"kind":"arxiv","id":"math/0502214","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0502214","created_at":"2026-07-04T14:39:36Z"},{"alias_kind":"arxiv_version","alias_value":"math/0502214v2","created_at":"2026-07-04T14:39:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0502214","created_at":"2026-07-04T14:39:36Z"},{"alias_kind":"pith_short_12","alias_value":"WARYBJR3PM3P","created_at":"2026-07-04T14:39:36Z"},{"alias_kind":"pith_short_16","alias_value":"WARYBJR3PM3PE5YQ","created_at":"2026-07-04T14:39:36Z"},{"alias_kind":"pith_short_8","alias_value":"WARYBJR3","created_at":"2026-07-04T14:39:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:WARYBJR3PM3PE5YQ2DUYMXK5RM","target":"record","payload":{"canonical_record":{"source":{"id":"math/0502214","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.NT","submitted_at":"2005-02-10T16:18:54Z","cross_cats_sorted":[],"title_canon_sha256":"578412d5ca0e83e4a9676c49121f5b26b68beaa04e25302ed411005980f9cefb","abstract_canon_sha256":"90f044e15b939095fce84794f822ea08b8670c201887c020c2c10e1d4bbabae4"},"schema_version":"1.0"},"canonical_sha256":"b02380a63b7b36f27710d0e9865d5d8b0ed4ba196dc64408927b46b647d70ef6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:39:36.088369Z","signature_b64":"clSRAprUflVUIZmKn+MvAB7GF4cJV3EOysE3XZi/vFVWfimtH0YwAN/F/kR/i697AN05jRZmFuumSLku2NvzCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b02380a63b7b36f27710d0e9865d5d8b0ed4ba196dc64408927b46b647d70ef6","last_reissued_at":"2026-07-04T14:39:36.088000Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:39:36.088000Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0502214","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T14:39:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I3q6fbLcxqTXTxzuU3kPKYRPSAxblR4hXG/ggso1yvhjNiVumKacJhPy2aO0cLd8u3ZN9jpsYG+N//qqtI25Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T14:19:39.790302Z"},"content_sha256":"20b0c98cac9843cd7cb17bbde1a4c68f864c61aa55ad65500559c0e8105d1ad9","schema_version":"1.0","event_id":"sha256:20b0c98cac9843cd7cb17bbde1a4c68f864c61aa55ad65500559c0e8105d1ad9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:WARYBJR3PM3PE5YQ2DUYMXK5RM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Complexity of Computing Quadratic Nonresidues","license":"","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"N.A. Carella","submitted_at":"2005-02-10T16:18:54Z","abstract_excerpt":"This note provides new methods for constructing quadratic nonresidues in finite fields of characteristic p. It will be shown that there is an effective deterministic polynomial time algorithm for constructing quadratic nonresidues in finite fields."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0502214","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0502214/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T14:39:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EW5Erg0OFOvcp9+bgdfFEtssZwQv6KjqRs+NwE+T4ETKUy+vijaagnk+WG5XBVvs+xqqQkkl/A22HGpsFhgTBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T14:19:39.790815Z"},"content_sha256":"f306f344ffd4a4df181b66e58bad67c5d43abf93f1302c2ba684ee68665fda63","schema_version":"1.0","event_id":"sha256:f306f344ffd4a4df181b66e58bad67c5d43abf93f1302c2ba684ee68665fda63"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WARYBJR3PM3PE5YQ2DUYMXK5RM/bundle.json","state_url":"https://pith.science/pith/WARYBJR3PM3PE5YQ2DUYMXK5RM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WARYBJR3PM3PE5YQ2DUYMXK5RM/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":"2026-08-16T14:19:39Z","links":{"resolver":"https://pith.science/pith/WARYBJR3PM3PE5YQ2DUYMXK5RM","bundle":"https://pith.science/pith/WARYBJR3PM3PE5YQ2DUYMXK5RM/bundle.json","state":"https://pith.science/pith/WARYBJR3PM3PE5YQ2DUYMXK5RM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WARYBJR3PM3PE5YQ2DUYMXK5RM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:WARYBJR3PM3PE5YQ2DUYMXK5RM","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":"90f044e15b939095fce84794f822ea08b8670c201887c020c2c10e1d4bbabae4","cross_cats_sorted":[],"license":"","primary_cat":"math.NT","submitted_at":"2005-02-10T16:18:54Z","title_canon_sha256":"578412d5ca0e83e4a9676c49121f5b26b68beaa04e25302ed411005980f9cefb"},"schema_version":"1.0","source":{"id":"math/0502214","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0502214","created_at":"2026-07-04T14:39:36Z"},{"alias_kind":"arxiv_version","alias_value":"math/0502214v2","created_at":"2026-07-04T14:39:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0502214","created_at":"2026-07-04T14:39:36Z"},{"alias_kind":"pith_short_12","alias_value":"WARYBJR3PM3P","created_at":"2026-07-04T14:39:36Z"},{"alias_kind":"pith_short_16","alias_value":"WARYBJR3PM3PE5YQ","created_at":"2026-07-04T14:39:36Z"},{"alias_kind":"pith_short_8","alias_value":"WARYBJR3","created_at":"2026-07-04T14:39:36Z"}],"graph_snapshots":[{"event_id":"sha256:f306f344ffd4a4df181b66e58bad67c5d43abf93f1302c2ba684ee68665fda63","target":"graph","created_at":"2026-07-04T14:39:36Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0502214/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This note provides new methods for constructing quadratic nonresidues in finite fields of characteristic p. It will be shown that there is an effective deterministic polynomial time algorithm for constructing quadratic nonresidues in finite fields.","authors_text":"N.A. Carella","cross_cats":[],"headline":"","license":"","primary_cat":"math.NT","submitted_at":"2005-02-10T16:18:54Z","title":"Complexity of Computing Quadratic Nonresidues"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0502214","kind":"arxiv","version":2},"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":"sha256:20b0c98cac9843cd7cb17bbde1a4c68f864c61aa55ad65500559c0e8105d1ad9","target":"record","created_at":"2026-07-04T14:39:36Z","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":"90f044e15b939095fce84794f822ea08b8670c201887c020c2c10e1d4bbabae4","cross_cats_sorted":[],"license":"","primary_cat":"math.NT","submitted_at":"2005-02-10T16:18:54Z","title_canon_sha256":"578412d5ca0e83e4a9676c49121f5b26b68beaa04e25302ed411005980f9cefb"},"schema_version":"1.0","source":{"id":"math/0502214","kind":"arxiv","version":2}},"canonical_sha256":"b02380a63b7b36f27710d0e9865d5d8b0ed4ba196dc64408927b46b647d70ef6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b02380a63b7b36f27710d0e9865d5d8b0ed4ba196dc64408927b46b647d70ef6","first_computed_at":"2026-07-04T14:39:36.088000Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:39:36.088000Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"clSRAprUflVUIZmKn+MvAB7GF4cJV3EOysE3XZi/vFVWfimtH0YwAN/F/kR/i697AN05jRZmFuumSLku2NvzCg==","signature_status":"signed_v1","signed_at":"2026-07-04T14:39:36.088369Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0502214","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:20b0c98cac9843cd7cb17bbde1a4c68f864c61aa55ad65500559c0e8105d1ad9","sha256:f306f344ffd4a4df181b66e58bad67c5d43abf93f1302c2ba684ee68665fda63"],"state_sha256":"6aa18a7a4c4266bc223d7e8524d57278ae838af05388a5004f3f919a9dedc368"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AVw1DcxBq76VxSulUG/uSBgY8Q6uu1B1Q8GWE7sW09QVgqfw+c8giE1Rcxnr+W5h/zgJ8Rf5vQ+zWun5hKNPCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T14:19:39.796186Z","bundle_sha256":"bc79cc609954557176c95499bdcf89ba2a96572b25efd0648ffbc95021c73a2f"}}