{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:KSHEYLT2G7EJ4CP6WL4GG7ZAL3","short_pith_number":"pith:KSHEYLT2","canonical_record":{"source":{"id":"1902.02914","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-02-08T01:39:38Z","cross_cats_sorted":[],"title_canon_sha256":"97b4a0a16b5464cda4f49c64c10c5689a4c997c516f7ace34277a5313b188f1f","abstract_canon_sha256":"ad7c2d36f393d7b7f1d1e9aa4f5523532dff31aee711ea4af2794190ba7e984c"},"schema_version":"1.0"},"canonical_sha256":"548e4c2e7a37c89e09feb2f8637f205ec4ab5c8b464e5886e37436f4a3369faf","source":{"kind":"arxiv","id":"1902.02914","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.02914","created_at":"2026-05-17T23:49:39Z"},{"alias_kind":"arxiv_version","alias_value":"1902.02914v2","created_at":"2026-05-17T23:49:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.02914","created_at":"2026-05-17T23:49:39Z"},{"alias_kind":"pith_short_12","alias_value":"KSHEYLT2G7EJ","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"KSHEYLT2G7EJ4CP6","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"KSHEYLT2","created_at":"2026-05-18T12:33:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:KSHEYLT2G7EJ4CP6WL4GG7ZAL3","target":"record","payload":{"canonical_record":{"source":{"id":"1902.02914","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-02-08T01:39:38Z","cross_cats_sorted":[],"title_canon_sha256":"97b4a0a16b5464cda4f49c64c10c5689a4c997c516f7ace34277a5313b188f1f","abstract_canon_sha256":"ad7c2d36f393d7b7f1d1e9aa4f5523532dff31aee711ea4af2794190ba7e984c"},"schema_version":"1.0"},"canonical_sha256":"548e4c2e7a37c89e09feb2f8637f205ec4ab5c8b464e5886e37436f4a3369faf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:39.249151Z","signature_b64":"xEWxyzYPPO0MywITlYlZh87/S76qhAZwvfnO0XbBd6x+qD1ENezRGPQSCb8Vgcu1TkbPB32SzrcpWxKAzHVNDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"548e4c2e7a37c89e09feb2f8637f205ec4ab5c8b464e5886e37436f4a3369faf","last_reissued_at":"2026-05-17T23:49:39.248490Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:39.248490Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.02914","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":"2026-05-17T23:49:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KrttNvWI1FqmaMzZhdy8aX3iSBevlkM5EnYikF32KxCSHObg2g/3PhTaaqTQ3kCry1OLLPuRiLYLqysxincKDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T19:55:53.205862Z"},"content_sha256":"a28a42ef78c75f10b13e177f3169b894ad3925f166c9b2b1447756491329f22e","schema_version":"1.0","event_id":"sha256:a28a42ef78c75f10b13e177f3169b894ad3925f166c9b2b1447756491329f22e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:KSHEYLT2G7EJ4CP6WL4GG7ZAL3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Invariants, Bitangents and Matrix Representations of Plane Quartics with 3-Cyclic Automorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Dun Liang","submitted_at":"2019-02-08T01:39:38Z","abstract_excerpt":"In this work we compute the Dixmier invariants and bitangents of the plane quartics with 3,6 or 9-cyclic automorphisms, we find that a quartic curve with 6-cyclic automorphism will have 3 horizontal bitangents which form an asysgetic triple. We also discuss the linear matrix representation problem of such curves, and find a degree 6 equation of 1 variable which solves the symbolic solution of the linear matrix representation problem for the curve with 6-cyclic automorphism."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.02914","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":"2026-05-17T23:49:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G7fLaz4YVZkPNHZ7MQNqeCcsfiRrOuL/aDQON2Tvuh5CiTgCRZD4oVoaJVYns55uTY/kK7GITiee3lEDAYc1Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T19:55:53.206609Z"},"content_sha256":"c32039a25504d37fa809562b3911d0830e016b21cbbbda99343309938265d34e","schema_version":"1.0","event_id":"sha256:c32039a25504d37fa809562b3911d0830e016b21cbbbda99343309938265d34e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KSHEYLT2G7EJ4CP6WL4GG7ZAL3/bundle.json","state_url":"https://pith.science/pith/KSHEYLT2G7EJ4CP6WL4GG7ZAL3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KSHEYLT2G7EJ4CP6WL4GG7ZAL3/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":"2026-06-06T19:55:53Z","links":{"resolver":"https://pith.science/pith/KSHEYLT2G7EJ4CP6WL4GG7ZAL3","bundle":"https://pith.science/pith/KSHEYLT2G7EJ4CP6WL4GG7ZAL3/bundle.json","state":"https://pith.science/pith/KSHEYLT2G7EJ4CP6WL4GG7ZAL3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KSHEYLT2G7EJ4CP6WL4GG7ZAL3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:KSHEYLT2G7EJ4CP6WL4GG7ZAL3","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":"ad7c2d36f393d7b7f1d1e9aa4f5523532dff31aee711ea4af2794190ba7e984c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-02-08T01:39:38Z","title_canon_sha256":"97b4a0a16b5464cda4f49c64c10c5689a4c997c516f7ace34277a5313b188f1f"},"schema_version":"1.0","source":{"id":"1902.02914","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.02914","created_at":"2026-05-17T23:49:39Z"},{"alias_kind":"arxiv_version","alias_value":"1902.02914v2","created_at":"2026-05-17T23:49:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.02914","created_at":"2026-05-17T23:49:39Z"},{"alias_kind":"pith_short_12","alias_value":"KSHEYLT2G7EJ","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"KSHEYLT2G7EJ4CP6","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"KSHEYLT2","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:c32039a25504d37fa809562b3911d0830e016b21cbbbda99343309938265d34e","target":"graph","created_at":"2026-05-17T23:49:39Z","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 work we compute the Dixmier invariants and bitangents of the plane quartics with 3,6 or 9-cyclic automorphisms, we find that a quartic curve with 6-cyclic automorphism will have 3 horizontal bitangents which form an asysgetic triple. We also discuss the linear matrix representation problem of such curves, and find a degree 6 equation of 1 variable which solves the symbolic solution of the linear matrix representation problem for the curve with 6-cyclic automorphism.","authors_text":"Dun Liang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-02-08T01:39:38Z","title":"Invariants, Bitangents and Matrix Representations of Plane Quartics with 3-Cyclic Automorphisms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.02914","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:a28a42ef78c75f10b13e177f3169b894ad3925f166c9b2b1447756491329f22e","target":"record","created_at":"2026-05-17T23:49:39Z","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":"ad7c2d36f393d7b7f1d1e9aa4f5523532dff31aee711ea4af2794190ba7e984c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-02-08T01:39:38Z","title_canon_sha256":"97b4a0a16b5464cda4f49c64c10c5689a4c997c516f7ace34277a5313b188f1f"},"schema_version":"1.0","source":{"id":"1902.02914","kind":"arxiv","version":2}},"canonical_sha256":"548e4c2e7a37c89e09feb2f8637f205ec4ab5c8b464e5886e37436f4a3369faf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"548e4c2e7a37c89e09feb2f8637f205ec4ab5c8b464e5886e37436f4a3369faf","first_computed_at":"2026-05-17T23:49:39.248490Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:39.248490Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xEWxyzYPPO0MywITlYlZh87/S76qhAZwvfnO0XbBd6x+qD1ENezRGPQSCb8Vgcu1TkbPB32SzrcpWxKAzHVNDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:39.249151Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.02914","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a28a42ef78c75f10b13e177f3169b894ad3925f166c9b2b1447756491329f22e","sha256:c32039a25504d37fa809562b3911d0830e016b21cbbbda99343309938265d34e"],"state_sha256":"5c556a5a7cfba5edffdd2f8f9842c27a21a117471d573a92c3ef840ffab5e24a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QFzMKVxa1qc23frW7zq7ZrhB1m4WDsfps+h516mprYzSBvA1O1BzPJWRh93aboEXuHtIhnzCQ/WFHIBaYU6iCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T19:55:53.210234Z","bundle_sha256":"659a2fb40658bfada554882a3cd396427711b101f9d6a584b27072c6f091f7e2"}}