{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:FPM26WJLS4HFLXMZYDTZJJV7VB","short_pith_number":"pith:FPM26WJL","canonical_record":{"source":{"id":"1807.02605","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-07-07T02:21:55Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"4e0d9da13005e099ec576e17a5c53ecca4dadf355751bf848d1295d924f6dd60","abstract_canon_sha256":"b285524a12b2b1c634f24052bf3ad4f938adcdf6a508a4288e6bdba2c42309da"},"schema_version":"1.0"},"canonical_sha256":"2bd9af592b970e55dd99c0e794a6bfa848cdba91778738e73b1273da983a022e","source":{"kind":"arxiv","id":"1807.02605","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.02605","created_at":"2026-05-17T23:43:33Z"},{"alias_kind":"arxiv_version","alias_value":"1807.02605v2","created_at":"2026-05-17T23:43:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.02605","created_at":"2026-05-17T23:43:33Z"},{"alias_kind":"pith_short_12","alias_value":"FPM26WJLS4HF","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"FPM26WJLS4HFLXMZ","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"FPM26WJL","created_at":"2026-05-18T12:32:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:FPM26WJLS4HFLXMZYDTZJJV7VB","target":"record","payload":{"canonical_record":{"source":{"id":"1807.02605","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-07-07T02:21:55Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"4e0d9da13005e099ec576e17a5c53ecca4dadf355751bf848d1295d924f6dd60","abstract_canon_sha256":"b285524a12b2b1c634f24052bf3ad4f938adcdf6a508a4288e6bdba2c42309da"},"schema_version":"1.0"},"canonical_sha256":"2bd9af592b970e55dd99c0e794a6bfa848cdba91778738e73b1273da983a022e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:33.271699Z","signature_b64":"ZojrHuyEDPxVntHguvQWyjnfnFJaBn/cCt1wJVM4wNV7jP+qhvxX+8hPU6bU7txyBt31j5od3ElBwqo1oQIhAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2bd9af592b970e55dd99c0e794a6bfa848cdba91778738e73b1273da983a022e","last_reissued_at":"2026-05-17T23:43:33.271220Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:33.271220Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.02605","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":"2026-05-17T23:43:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z26BeeG0Q5vWGts2RkDBz9/A/yPqzAARXubYwd96c1OcdjQAGEVWqIYRSCEhEJBc0EHCqsCs4Q+SPM7dg4LEDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T08:10:07.688044Z"},"content_sha256":"a78fdef4380fbc29b5cecbc3a7b42d7520834c56c537a62c9955cedc780fb406","schema_version":"1.0","event_id":"sha256:a78fdef4380fbc29b5cecbc3a7b42d7520834c56c537a62c9955cedc780fb406"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:FPM26WJLS4HFLXMZYDTZJJV7VB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Numerical computation of endomorphism rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Alexandre Zotine, Jeroen Sijsling, Nils Bruin","submitted_at":"2018-07-07T02:21:55Z","abstract_excerpt":"We give practical numerical methods to compute the period matrix of a plane algebraic curve (not necessarily smooth). We show how automorphisms and isomorphisms of such curves, as well as the decomposition of their Jacobians up to isogeny, can be calculated heuristically. Particular applications include the determination of (generically) non-Galois morphisms between curves and the identification of Prym varieties."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.02605","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":"2026-05-17T23:43:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mpspY1/sTpMhtR6hrwmSD5E9v8kXJ8PkRquX+KevKUEmvTXlkEFpcUuLyhJvYRxvJQCTNVRO2Uvlr2mzu6UVDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T08:10:07.688406Z"},"content_sha256":"7d1b0f7d3111d4eb69f88f5803064c8a43942e99c04ea8896dc25b4ed5f0fec2","schema_version":"1.0","event_id":"sha256:7d1b0f7d3111d4eb69f88f5803064c8a43942e99c04ea8896dc25b4ed5f0fec2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FPM26WJLS4HFLXMZYDTZJJV7VB/bundle.json","state_url":"https://pith.science/pith/FPM26WJLS4HFLXMZYDTZJJV7VB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FPM26WJLS4HFLXMZYDTZJJV7VB/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":"2026-05-28T08:10:07Z","links":{"resolver":"https://pith.science/pith/FPM26WJLS4HFLXMZYDTZJJV7VB","bundle":"https://pith.science/pith/FPM26WJLS4HFLXMZYDTZJJV7VB/bundle.json","state":"https://pith.science/pith/FPM26WJLS4HFLXMZYDTZJJV7VB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FPM26WJLS4HFLXMZYDTZJJV7VB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:FPM26WJLS4HFLXMZYDTZJJV7VB","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":"b285524a12b2b1c634f24052bf3ad4f938adcdf6a508a4288e6bdba2c42309da","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-07-07T02:21:55Z","title_canon_sha256":"4e0d9da13005e099ec576e17a5c53ecca4dadf355751bf848d1295d924f6dd60"},"schema_version":"1.0","source":{"id":"1807.02605","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.02605","created_at":"2026-05-17T23:43:33Z"},{"alias_kind":"arxiv_version","alias_value":"1807.02605v2","created_at":"2026-05-17T23:43:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.02605","created_at":"2026-05-17T23:43:33Z"},{"alias_kind":"pith_short_12","alias_value":"FPM26WJLS4HF","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"FPM26WJLS4HFLXMZ","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"FPM26WJL","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:7d1b0f7d3111d4eb69f88f5803064c8a43942e99c04ea8896dc25b4ed5f0fec2","target":"graph","created_at":"2026-05-17T23:43:33Z","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 give practical numerical methods to compute the period matrix of a plane algebraic curve (not necessarily smooth). We show how automorphisms and isomorphisms of such curves, as well as the decomposition of their Jacobians up to isogeny, can be calculated heuristically. Particular applications include the determination of (generically) non-Galois morphisms between curves and the identification of Prym varieties.","authors_text":"Alexandre Zotine, Jeroen Sijsling, Nils Bruin","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-07-07T02:21:55Z","title":"Numerical computation of endomorphism rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.02605","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:a78fdef4380fbc29b5cecbc3a7b42d7520834c56c537a62c9955cedc780fb406","target":"record","created_at":"2026-05-17T23:43:33Z","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":"b285524a12b2b1c634f24052bf3ad4f938adcdf6a508a4288e6bdba2c42309da","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-07-07T02:21:55Z","title_canon_sha256":"4e0d9da13005e099ec576e17a5c53ecca4dadf355751bf848d1295d924f6dd60"},"schema_version":"1.0","source":{"id":"1807.02605","kind":"arxiv","version":2}},"canonical_sha256":"2bd9af592b970e55dd99c0e794a6bfa848cdba91778738e73b1273da983a022e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2bd9af592b970e55dd99c0e794a6bfa848cdba91778738e73b1273da983a022e","first_computed_at":"2026-05-17T23:43:33.271220Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:33.271220Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZojrHuyEDPxVntHguvQWyjnfnFJaBn/cCt1wJVM4wNV7jP+qhvxX+8hPU6bU7txyBt31j5od3ElBwqo1oQIhAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:33.271699Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.02605","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a78fdef4380fbc29b5cecbc3a7b42d7520834c56c537a62c9955cedc780fb406","sha256:7d1b0f7d3111d4eb69f88f5803064c8a43942e99c04ea8896dc25b4ed5f0fec2"],"state_sha256":"085a305c5c2f1902bf3b70521abd545435d92525fafcf5fcbec7a3ce77e9e277"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1PwymznPrPdhgTj46k0++I1qcp6UvuhiY1S4yxnMXc6HEhohYxJLGLcYncRHxndo3KwhQtxzdShwl9LVg+bhAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T08:10:07.690375Z","bundle_sha256":"f18246d0f9706a8d7ffee801ffc78ba58f94055cba5c82ea323aa9dca7c4e59c"}}