{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:NMMHTBPSQ2IVAV2S6TIFKQJYAZ","short_pith_number":"pith:NMMHTBPS","canonical_record":{"source":{"id":"1708.03652","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-08-11T18:25:30Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"1ee87b84af8487932485c0c04f243a17d07aaa3d226e6013c705bbcec282e6fa","abstract_canon_sha256":"746856bc22f5590b452c13b7ffc0b4214a52c00d6348e4ff8e289e914f807206"},"schema_version":"1.0"},"canonical_sha256":"6b187985f28691505752f4d05541380669b33c5f622da1c5aa6a1062f45bcae9","source":{"kind":"arxiv","id":"1708.03652","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.03652","created_at":"2026-05-18T00:38:08Z"},{"alias_kind":"arxiv_version","alias_value":"1708.03652v1","created_at":"2026-05-18T00:38:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.03652","created_at":"2026-05-18T00:38:08Z"},{"alias_kind":"pith_short_12","alias_value":"NMMHTBPSQ2IV","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"NMMHTBPSQ2IVAV2S","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"NMMHTBPS","created_at":"2026-05-18T12:31:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:NMMHTBPSQ2IVAV2S6TIFKQJYAZ","target":"record","payload":{"canonical_record":{"source":{"id":"1708.03652","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-08-11T18:25:30Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"1ee87b84af8487932485c0c04f243a17d07aaa3d226e6013c705bbcec282e6fa","abstract_canon_sha256":"746856bc22f5590b452c13b7ffc0b4214a52c00d6348e4ff8e289e914f807206"},"schema_version":"1.0"},"canonical_sha256":"6b187985f28691505752f4d05541380669b33c5f622da1c5aa6a1062f45bcae9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:08.236818Z","signature_b64":"IxAwXdYvuXa8WMQ9Mg24dhrrQhD/q8cuJ3OFhDMxQGQDAnue6buYRMhW54ATJGi7aSe21zssBQQ33zLxm40HBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b187985f28691505752f4d05541380669b33c5f622da1c5aa6a1062f45bcae9","last_reissued_at":"2026-05-18T00:38:08.236305Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:08.236305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.03652","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":"2026-05-18T00:38:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jz8xLAShd7HMmaWZfvALyIS6ubaBbO8/Ng7hsCUNez+hS+7jb28mUQznjK9xCe/epyudlk24dQYJcrsoKzvtBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T12:42:14.194601Z"},"content_sha256":"1635bec3ba428aa62307f1db22f5f54a88a1eb1d3d9147bbb82a4b93de112f42","schema_version":"1.0","event_id":"sha256:1635bec3ba428aa62307f1db22f5f54a88a1eb1d3d9147bbb82a4b93de112f42"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:NMMHTBPSQ2IVAV2S6TIFKQJYAZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-ordinary curves with a Prym variety of low $p$-rank","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Burcin Gunes, Ekin Ozman, Lara Thomas, Rachel Newton, Rachel Pries, Turku Ozlum Celik, Yara Elias","submitted_at":"2017-08-11T18:25:30Z","abstract_excerpt":"If $\\pi: Y \\to X$ is an unramified double cover of a smooth curve of genus $g$, then the Prym variety $P_\\pi$ is a principally polarized abelian variety of dimension $g-1$. When $X$ is defined over an algebraically closed field $k$ of characteristic $p$, it is not known in general which $p$-ranks can occur for $P_\\pi$ under restrictions on the $p$-rank of $X$. In this paper, when $X$ is a non-hyperelliptic curve of genus $g=3$, we analyze the relationship between the Hasse-Witt matrices of $X$ and $P_\\pi$. As an application, when $p \\equiv 5 \\bmod 6$, we prove that there exists a curve $X$ of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.03652","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":"2026-05-18T00:38:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P7U8vhO8OeKJkK7MP151EUvvqm+QZR5N/w4LOjkSTTmqB0FKJmRLmPFeL62Ky3uIOEKQk9FhXMakigEEtpsDCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T12:42:14.194956Z"},"content_sha256":"63775170ad696fda039fcb5cd9a39322c065ec5d9ead327aa3beb8e6efb3cbab","schema_version":"1.0","event_id":"sha256:63775170ad696fda039fcb5cd9a39322c065ec5d9ead327aa3beb8e6efb3cbab"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NMMHTBPSQ2IVAV2S6TIFKQJYAZ/bundle.json","state_url":"https://pith.science/pith/NMMHTBPSQ2IVAV2S6TIFKQJYAZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NMMHTBPSQ2IVAV2S6TIFKQJYAZ/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":"2026-05-22T12:42:14Z","links":{"resolver":"https://pith.science/pith/NMMHTBPSQ2IVAV2S6TIFKQJYAZ","bundle":"https://pith.science/pith/NMMHTBPSQ2IVAV2S6TIFKQJYAZ/bundle.json","state":"https://pith.science/pith/NMMHTBPSQ2IVAV2S6TIFKQJYAZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NMMHTBPSQ2IVAV2S6TIFKQJYAZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:NMMHTBPSQ2IVAV2S6TIFKQJYAZ","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":"746856bc22f5590b452c13b7ffc0b4214a52c00d6348e4ff8e289e914f807206","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-08-11T18:25:30Z","title_canon_sha256":"1ee87b84af8487932485c0c04f243a17d07aaa3d226e6013c705bbcec282e6fa"},"schema_version":"1.0","source":{"id":"1708.03652","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.03652","created_at":"2026-05-18T00:38:08Z"},{"alias_kind":"arxiv_version","alias_value":"1708.03652v1","created_at":"2026-05-18T00:38:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.03652","created_at":"2026-05-18T00:38:08Z"},{"alias_kind":"pith_short_12","alias_value":"NMMHTBPSQ2IV","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"NMMHTBPSQ2IVAV2S","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"NMMHTBPS","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:63775170ad696fda039fcb5cd9a39322c065ec5d9ead327aa3beb8e6efb3cbab","target":"graph","created_at":"2026-05-18T00:38:08Z","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":"If $\\pi: Y \\to X$ is an unramified double cover of a smooth curve of genus $g$, then the Prym variety $P_\\pi$ is a principally polarized abelian variety of dimension $g-1$. When $X$ is defined over an algebraically closed field $k$ of characteristic $p$, it is not known in general which $p$-ranks can occur for $P_\\pi$ under restrictions on the $p$-rank of $X$. In this paper, when $X$ is a non-hyperelliptic curve of genus $g=3$, we analyze the relationship between the Hasse-Witt matrices of $X$ and $P_\\pi$. As an application, when $p \\equiv 5 \\bmod 6$, we prove that there exists a curve $X$ of ","authors_text":"Burcin Gunes, Ekin Ozman, Lara Thomas, Rachel Newton, Rachel Pries, Turku Ozlum Celik, Yara Elias","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-08-11T18:25:30Z","title":"Non-ordinary curves with a Prym variety of low $p$-rank"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.03652","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":"sha256:1635bec3ba428aa62307f1db22f5f54a88a1eb1d3d9147bbb82a4b93de112f42","target":"record","created_at":"2026-05-18T00:38:08Z","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":"746856bc22f5590b452c13b7ffc0b4214a52c00d6348e4ff8e289e914f807206","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-08-11T18:25:30Z","title_canon_sha256":"1ee87b84af8487932485c0c04f243a17d07aaa3d226e6013c705bbcec282e6fa"},"schema_version":"1.0","source":{"id":"1708.03652","kind":"arxiv","version":1}},"canonical_sha256":"6b187985f28691505752f4d05541380669b33c5f622da1c5aa6a1062f45bcae9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b187985f28691505752f4d05541380669b33c5f622da1c5aa6a1062f45bcae9","first_computed_at":"2026-05-18T00:38:08.236305Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:08.236305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IxAwXdYvuXa8WMQ9Mg24dhrrQhD/q8cuJ3OFhDMxQGQDAnue6buYRMhW54ATJGi7aSe21zssBQQ33zLxm40HBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:08.236818Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.03652","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1635bec3ba428aa62307f1db22f5f54a88a1eb1d3d9147bbb82a4b93de112f42","sha256:63775170ad696fda039fcb5cd9a39322c065ec5d9ead327aa3beb8e6efb3cbab"],"state_sha256":"8666609926220e3369ac9243943e18054f0a110518f897995d7488aa89135d25"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FosLu5Fx3/p9xpmdN+ddYHtR6O1ZXD40lXeYNM2gOuYXDLTJeN7JfUL45UbKN3La5FhntJamtln2f2mCukchBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T12:42:14.197764Z","bundle_sha256":"3ac5c0d463c1d74e724b87010d1763b11c04ab410341e29a3a93ea185b8239d5"}}