{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:44Y36ESOMRNNHPAVL3XNJ4VFNW","short_pith_number":"pith:44Y36ESO","canonical_record":{"source":{"id":"1608.06784","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-08-24T11:43:03Z","cross_cats_sorted":[],"title_canon_sha256":"ed0cb87742c48070f69f078265bc6bec2aba54934920c4ebe63b0f4bd491d3a4","abstract_canon_sha256":"a26395d03603472e56853c8d29908544294f206792f978e64cd848be4a94f5b4"},"schema_version":"1.0"},"canonical_sha256":"e731bf124e645ad3bc155eeed4f2a56d8f64ce99645e781eb542cf6a74535ea8","source":{"kind":"arxiv","id":"1608.06784","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.06784","created_at":"2026-05-18T00:39:29Z"},{"alias_kind":"arxiv_version","alias_value":"1608.06784v2","created_at":"2026-05-18T00:39:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.06784","created_at":"2026-05-18T00:39:29Z"},{"alias_kind":"pith_short_12","alias_value":"44Y36ESOMRNN","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"44Y36ESOMRNNHPAV","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"44Y36ESO","created_at":"2026-05-18T12:29:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:44Y36ESOMRNNHPAVL3XNJ4VFNW","target":"record","payload":{"canonical_record":{"source":{"id":"1608.06784","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-08-24T11:43:03Z","cross_cats_sorted":[],"title_canon_sha256":"ed0cb87742c48070f69f078265bc6bec2aba54934920c4ebe63b0f4bd491d3a4","abstract_canon_sha256":"a26395d03603472e56853c8d29908544294f206792f978e64cd848be4a94f5b4"},"schema_version":"1.0"},"canonical_sha256":"e731bf124e645ad3bc155eeed4f2a56d8f64ce99645e781eb542cf6a74535ea8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:29.030179Z","signature_b64":"LgQq/nD5n9vj9PONxnpABJDFYGnJ8CMEV9H79R06JjngVLfUqlnCo7zgVhfMyprlkisNCjdSyXZzt8nOCZMeCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e731bf124e645ad3bc155eeed4f2a56d8f64ce99645e781eb542cf6a74535ea8","last_reissued_at":"2026-05-18T00:39:29.029597Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:29.029597Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.06784","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":"2026-05-18T00:39:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gktUmd0DUq5yr8bZ65a9+y746py6jIfYfc6Twdy8KbzrTuQTCPjBuSvyKnpvyff9o1FyzQCc5oB6eRlArsj/Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T00:25:10.887756Z"},"content_sha256":"bbfff1a9c1d6e3c343392b4e6b4421bd42156f03d88c8fbd3cef333551ab8f89","schema_version":"1.0","event_id":"sha256:bbfff1a9c1d6e3c343392b4e6b4421bd42156f03d88c8fbd3cef333551ab8f89"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:44Y36ESOMRNNHPAVL3XNJ4VFNW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The twisting Sato-Tate group of the curve $y^2 = x^{8} - 14x^4 + 1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Aaron Landesman, Davide Lombardo, Jackson S. Morrow, Sonny Arora, Victoria Cantoral-Farf\\'an","submitted_at":"2016-08-24T11:43:03Z","abstract_excerpt":"We determine the twisting Sato-Tate group of the genus $3$ hyperelliptic curve $y^2 = x^{8} - 14x^4 + 1$ and show that all possible subgroups of the twisting Sato-Tate group arise as the Sato-Tate group of an explicit twist of $y^2 = x^{8} - 14x^4 + 1$. Furthermore, we prove the generalized Sato-Tate conjecture for the Jacobians of all $\\mathbb Q$-twists of the curve $y^2 = x^{8} - 14x^4 + 1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.06784","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":""},"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":"2026-05-18T00:39:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MsD7Wkrou6v7RQvNc9Z7mHANhvnP4ZaqpKpwqIYT8oo9jg5kdQSOHTyppqKHy0vw9J3uW7BFzm2VX3QGaW7fAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T00:25:10.888112Z"},"content_sha256":"b8b5778d8b66894799d138ed94858fab9c9f61e95d2e4505751084551a33dffb","schema_version":"1.0","event_id":"sha256:b8b5778d8b66894799d138ed94858fab9c9f61e95d2e4505751084551a33dffb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/44Y36ESOMRNNHPAVL3XNJ4VFNW/bundle.json","state_url":"https://pith.science/pith/44Y36ESOMRNNHPAVL3XNJ4VFNW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/44Y36ESOMRNNHPAVL3XNJ4VFNW/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":"2026-05-31T00:25:10Z","links":{"resolver":"https://pith.science/pith/44Y36ESOMRNNHPAVL3XNJ4VFNW","bundle":"https://pith.science/pith/44Y36ESOMRNNHPAVL3XNJ4VFNW/bundle.json","state":"https://pith.science/pith/44Y36ESOMRNNHPAVL3XNJ4VFNW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/44Y36ESOMRNNHPAVL3XNJ4VFNW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:44Y36ESOMRNNHPAVL3XNJ4VFNW","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":"a26395d03603472e56853c8d29908544294f206792f978e64cd848be4a94f5b4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-08-24T11:43:03Z","title_canon_sha256":"ed0cb87742c48070f69f078265bc6bec2aba54934920c4ebe63b0f4bd491d3a4"},"schema_version":"1.0","source":{"id":"1608.06784","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.06784","created_at":"2026-05-18T00:39:29Z"},{"alias_kind":"arxiv_version","alias_value":"1608.06784v2","created_at":"2026-05-18T00:39:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.06784","created_at":"2026-05-18T00:39:29Z"},{"alias_kind":"pith_short_12","alias_value":"44Y36ESOMRNN","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"44Y36ESOMRNNHPAV","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"44Y36ESO","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:b8b5778d8b66894799d138ed94858fab9c9f61e95d2e4505751084551a33dffb","target":"graph","created_at":"2026-05-18T00:39:29Z","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 determine the twisting Sato-Tate group of the genus $3$ hyperelliptic curve $y^2 = x^{8} - 14x^4 + 1$ and show that all possible subgroups of the twisting Sato-Tate group arise as the Sato-Tate group of an explicit twist of $y^2 = x^{8} - 14x^4 + 1$. Furthermore, we prove the generalized Sato-Tate conjecture for the Jacobians of all $\\mathbb Q$-twists of the curve $y^2 = x^{8} - 14x^4 + 1$.","authors_text":"Aaron Landesman, Davide Lombardo, Jackson S. Morrow, Sonny Arora, Victoria Cantoral-Farf\\'an","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-08-24T11:43:03Z","title":"The twisting Sato-Tate group of the curve $y^2 = x^{8} - 14x^4 + 1$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.06784","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:bbfff1a9c1d6e3c343392b4e6b4421bd42156f03d88c8fbd3cef333551ab8f89","target":"record","created_at":"2026-05-18T00:39:29Z","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":"a26395d03603472e56853c8d29908544294f206792f978e64cd848be4a94f5b4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-08-24T11:43:03Z","title_canon_sha256":"ed0cb87742c48070f69f078265bc6bec2aba54934920c4ebe63b0f4bd491d3a4"},"schema_version":"1.0","source":{"id":"1608.06784","kind":"arxiv","version":2}},"canonical_sha256":"e731bf124e645ad3bc155eeed4f2a56d8f64ce99645e781eb542cf6a74535ea8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e731bf124e645ad3bc155eeed4f2a56d8f64ce99645e781eb542cf6a74535ea8","first_computed_at":"2026-05-18T00:39:29.029597Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:29.029597Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LgQq/nD5n9vj9PONxnpABJDFYGnJ8CMEV9H79R06JjngVLfUqlnCo7zgVhfMyprlkisNCjdSyXZzt8nOCZMeCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:29.030179Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.06784","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bbfff1a9c1d6e3c343392b4e6b4421bd42156f03d88c8fbd3cef333551ab8f89","sha256:b8b5778d8b66894799d138ed94858fab9c9f61e95d2e4505751084551a33dffb"],"state_sha256":"966594fd4dc71aca6b228c4f1108946d420cd5fa977c680504496d8a0415173b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tLP3vhqY6bi6ZItQ7IfZ8XvHHLV32q/+qBNBzgWPwynE1wUE6kPQZn90U1+wiIc75KzJa7YVuQxbA36cWjmuAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T00:25:10.890431Z","bundle_sha256":"66e8c379fcdc1d819e3d620dfad2552ab827fcb858a1f91b5c649065a1560e38"}}