{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:FMDFVWSAJIJM275WBTFH7VWASM","short_pith_number":"pith:FMDFVWSA","canonical_record":{"source":{"id":"1512.06480","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-12-21T03:10:40Z","cross_cats_sorted":[],"title_canon_sha256":"36ecdf2db867674dfc4181ccadcbc07eb65dda3373120c2c371cd3e81e0eec02","abstract_canon_sha256":"4a7a28def8b32379279e5668f260bb0f19cb4e866b9cba46750c40bf89bf9f1b"},"schema_version":"1.0"},"canonical_sha256":"2b065ada404a12cd7fb60cca7fd6c0932bf61093f1253b308ebc579879a06932","source":{"kind":"arxiv","id":"1512.06480","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.06480","created_at":"2026-05-18T01:24:00Z"},{"alias_kind":"arxiv_version","alias_value":"1512.06480v1","created_at":"2026-05-18T01:24:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.06480","created_at":"2026-05-18T01:24:00Z"},{"alias_kind":"pith_short_12","alias_value":"FMDFVWSAJIJM","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FMDFVWSAJIJM275W","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FMDFVWSA","created_at":"2026-05-18T12:29:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:FMDFVWSAJIJM275WBTFH7VWASM","target":"record","payload":{"canonical_record":{"source":{"id":"1512.06480","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-12-21T03:10:40Z","cross_cats_sorted":[],"title_canon_sha256":"36ecdf2db867674dfc4181ccadcbc07eb65dda3373120c2c371cd3e81e0eec02","abstract_canon_sha256":"4a7a28def8b32379279e5668f260bb0f19cb4e866b9cba46750c40bf89bf9f1b"},"schema_version":"1.0"},"canonical_sha256":"2b065ada404a12cd7fb60cca7fd6c0932bf61093f1253b308ebc579879a06932","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:00.446678Z","signature_b64":"Jw+IFexyuWGMcNjVUoSG62+ZoHDBaGW5h/GEinwLBsIOsNxBXAudC8WjKT3Bl5Kfwj+/vth+INWRs8MHNoxnBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b065ada404a12cd7fb60cca7fd6c0932bf61093f1253b308ebc579879a06932","last_reissued_at":"2026-05-18T01:24:00.445979Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:00.445979Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.06480","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":"2026-05-18T01:24:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ejN6UNKiqgCP+umv/Vtor1CfLTgDr66jCpLHczipvU7pCsLmiYs7X6Opt+cprav9eInFZwbuFFJQdiVIxhnvAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T23:09:38.854718Z"},"content_sha256":"6435c5742ca6b9de6c3c33184c7f6b8d0b4ee1e6c4e8f2dcab3439fdb698b7e9","schema_version":"1.0","event_id":"sha256:6435c5742ca6b9de6c3c33184c7f6b8d0b4ee1e6c4e8f2dcab3439fdb698b7e9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:FMDFVWSAJIJM275WBTFH7VWASM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Characterizations of quadratic, cubic, and quartic residue matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"David S. Dummit, Evan P. Dummit, Hershy Kisilevsky","submitted_at":"2015-12-21T03:10:40Z","abstract_excerpt":"We construct a collection of matrices defined by quadratic residue symbols, termed \"quadratic residue matrices\", associated to the splitting behavior of prime ideals in a composite of quadratic extensions of $\\mathbb{Q}$, and prove a simple criterion characterizing such matrices. We also study the analogous classes of matrices constructed from the cubic and quartic residue symbols for a set of prime ideals of $\\mathbb{Q}(\\sqrt{-3})$ and $\\mathbb{Q}(i)$, respectively."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.06480","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":"2026-05-18T01:24:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vGi07PosxfuUYePXUID0yg0M2NTlDip1/LjWWiTtr66CxnseJt1fYRau14JjoW6/M1l2c2MGnIo3KTrg5xjZDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T23:09:38.855060Z"},"content_sha256":"b41e46716ab0635c1e2153c5c45f88b4f2c108307c14b1b8c802d65d772b3fc8","schema_version":"1.0","event_id":"sha256:b41e46716ab0635c1e2153c5c45f88b4f2c108307c14b1b8c802d65d772b3fc8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FMDFVWSAJIJM275WBTFH7VWASM/bundle.json","state_url":"https://pith.science/pith/FMDFVWSAJIJM275WBTFH7VWASM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FMDFVWSAJIJM275WBTFH7VWASM/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":"2026-06-08T23:09:38Z","links":{"resolver":"https://pith.science/pith/FMDFVWSAJIJM275WBTFH7VWASM","bundle":"https://pith.science/pith/FMDFVWSAJIJM275WBTFH7VWASM/bundle.json","state":"https://pith.science/pith/FMDFVWSAJIJM275WBTFH7VWASM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FMDFVWSAJIJM275WBTFH7VWASM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:FMDFVWSAJIJM275WBTFH7VWASM","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":"4a7a28def8b32379279e5668f260bb0f19cb4e866b9cba46750c40bf89bf9f1b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-12-21T03:10:40Z","title_canon_sha256":"36ecdf2db867674dfc4181ccadcbc07eb65dda3373120c2c371cd3e81e0eec02"},"schema_version":"1.0","source":{"id":"1512.06480","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.06480","created_at":"2026-05-18T01:24:00Z"},{"alias_kind":"arxiv_version","alias_value":"1512.06480v1","created_at":"2026-05-18T01:24:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.06480","created_at":"2026-05-18T01:24:00Z"},{"alias_kind":"pith_short_12","alias_value":"FMDFVWSAJIJM","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FMDFVWSAJIJM275W","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FMDFVWSA","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:b41e46716ab0635c1e2153c5c45f88b4f2c108307c14b1b8c802d65d772b3fc8","target":"graph","created_at":"2026-05-18T01:24:00Z","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 construct a collection of matrices defined by quadratic residue symbols, termed \"quadratic residue matrices\", associated to the splitting behavior of prime ideals in a composite of quadratic extensions of $\\mathbb{Q}$, and prove a simple criterion characterizing such matrices. We also study the analogous classes of matrices constructed from the cubic and quartic residue symbols for a set of prime ideals of $\\mathbb{Q}(\\sqrt{-3})$ and $\\mathbb{Q}(i)$, respectively.","authors_text":"David S. Dummit, Evan P. Dummit, Hershy Kisilevsky","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-12-21T03:10:40Z","title":"Characterizations of quadratic, cubic, and quartic residue matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.06480","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":"sha256:6435c5742ca6b9de6c3c33184c7f6b8d0b4ee1e6c4e8f2dcab3439fdb698b7e9","target":"record","created_at":"2026-05-18T01:24:00Z","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":"4a7a28def8b32379279e5668f260bb0f19cb4e866b9cba46750c40bf89bf9f1b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-12-21T03:10:40Z","title_canon_sha256":"36ecdf2db867674dfc4181ccadcbc07eb65dda3373120c2c371cd3e81e0eec02"},"schema_version":"1.0","source":{"id":"1512.06480","kind":"arxiv","version":1}},"canonical_sha256":"2b065ada404a12cd7fb60cca7fd6c0932bf61093f1253b308ebc579879a06932","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b065ada404a12cd7fb60cca7fd6c0932bf61093f1253b308ebc579879a06932","first_computed_at":"2026-05-18T01:24:00.445979Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:00.445979Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Jw+IFexyuWGMcNjVUoSG62+ZoHDBaGW5h/GEinwLBsIOsNxBXAudC8WjKT3Bl5Kfwj+/vth+INWRs8MHNoxnBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:00.446678Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.06480","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6435c5742ca6b9de6c3c33184c7f6b8d0b4ee1e6c4e8f2dcab3439fdb698b7e9","sha256:b41e46716ab0635c1e2153c5c45f88b4f2c108307c14b1b8c802d65d772b3fc8"],"state_sha256":"552809b59d8329772e498d3732249f564857c5bbbc188ddf41abfe1ece264af9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GpRRHZu5B0/iEilpGzJJOa0TqaqmMCwzQIZXfPaQtfQlXGX97f1hxfrTYcGDLomvUU/Fg7Vapcv2at2uWIYxBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T23:09:38.856959Z","bundle_sha256":"b8e72375ecab3938016076bebaf47648d4bb39f24d9c6557c6ff2095f7c7c519"}}