{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:Q6HIVT75V5COMGZFVPNPSRR7ET","short_pith_number":"pith:Q6HIVT75","schema_version":"1.0","canonical_sha256":"878e8acffdaf44e61b25abdaf9463f24ed566ca7af38c4e6e82f6a97cb3046da","source":{"kind":"arxiv","id":"2412.13022","version":1},"attestation_state":"computed","paper":{"title":"Relative $p$-class groups and $p$-Selmer groups","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Debajyoti De, Dipramit Majumdar, Sudipa Mondal","submitted_at":"2024-12-17T15:41:50Z","abstract_excerpt":"Let $E$ be an elliptic curve with $j$-invariant $0$ or $1728$ and let $\\widetilde{E}$ be a $k^{th}$ twist of $E$. We show that for any prime $p$ of good reduction of $\\widetilde{E}$, a degree $k$ relative $p$-class group and the root number of $\\widetilde{E}$ determines the dimension of the $p$-Selmer group of $\\widetilde{E}$. As a consequence, we construct families of large rank $p$-class group. We also relate congruent number and cube sum problem with relative $p$-class group."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2412.13022","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NT","submitted_at":"2024-12-17T15:41:50Z","cross_cats_sorted":[],"title_canon_sha256":"725653b0bc7e51b10232639699f4ffbf6aabbd516c1a281540b7f59856667aae","abstract_canon_sha256":"cee9d2f0dd30ab8a88621b0cfcd4ccaeea10933bd855616bcfdd89e5d5b71444"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:50:39.170580Z","signature_b64":"kgm42Ulgb/Y0qDAZzRieJCmm8olGj43VUKr8Fbqbk0gsgnEZvIVPK1hSM67Ik9vQyAOYJhAyDD9pzHlcKslNCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"878e8acffdaf44e61b25abdaf9463f24ed566ca7af38c4e6e82f6a97cb3046da","last_reissued_at":"2026-07-05T09:50:39.169992Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:50:39.169992Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Relative $p$-class groups and $p$-Selmer groups","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Debajyoti De, Dipramit Majumdar, Sudipa Mondal","submitted_at":"2024-12-17T15:41:50Z","abstract_excerpt":"Let $E$ be an elliptic curve with $j$-invariant $0$ or $1728$ and let $\\widetilde{E}$ be a $k^{th}$ twist of $E$. We show that for any prime $p$ of good reduction of $\\widetilde{E}$, a degree $k$ relative $p$-class group and the root number of $\\widetilde{E}$ determines the dimension of the $p$-Selmer group of $\\widetilde{E}$. As a consequence, we construct families of large rank $p$-class group. We also relate congruent number and cube sum problem with relative $p$-class group."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.13022","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.13022/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2412.13022","created_at":"2026-07-05T09:50:39.170067+00:00"},{"alias_kind":"arxiv_version","alias_value":"2412.13022v1","created_at":"2026-07-05T09:50:39.170067+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.13022","created_at":"2026-07-05T09:50:39.170067+00:00"},{"alias_kind":"pith_short_12","alias_value":"Q6HIVT75V5CO","created_at":"2026-07-05T09:50:39.170067+00:00"},{"alias_kind":"pith_short_16","alias_value":"Q6HIVT75V5COMGZF","created_at":"2026-07-05T09:50:39.170067+00:00"},{"alias_kind":"pith_short_8","alias_value":"Q6HIVT75","created_at":"2026-07-05T09:50:39.170067+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/Q6HIVT75V5COMGZFVPNPSRR7ET","json":"https://pith.science/pith/Q6HIVT75V5COMGZFVPNPSRR7ET.json","graph_json":"https://pith.science/api/pith-number/Q6HIVT75V5COMGZFVPNPSRR7ET/graph.json","events_json":"https://pith.science/api/pith-number/Q6HIVT75V5COMGZFVPNPSRR7ET/events.json","paper":"https://pith.science/paper/Q6HIVT75"},"agent_actions":{"view_html":"https://pith.science/pith/Q6HIVT75V5COMGZFVPNPSRR7ET","download_json":"https://pith.science/pith/Q6HIVT75V5COMGZFVPNPSRR7ET.json","view_paper":"https://pith.science/paper/Q6HIVT75","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2412.13022&json=true","fetch_graph":"https://pith.science/api/pith-number/Q6HIVT75V5COMGZFVPNPSRR7ET/graph.json","fetch_events":"https://pith.science/api/pith-number/Q6HIVT75V5COMGZFVPNPSRR7ET/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Q6HIVT75V5COMGZFVPNPSRR7ET/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Q6HIVT75V5COMGZFVPNPSRR7ET/action/storage_attestation","attest_author":"https://pith.science/pith/Q6HIVT75V5COMGZFVPNPSRR7ET/action/author_attestation","sign_citation":"https://pith.science/pith/Q6HIVT75V5COMGZFVPNPSRR7ET/action/citation_signature","submit_replication":"https://pith.science/pith/Q6HIVT75V5COMGZFVPNPSRR7ET/action/replication_record"}},"created_at":"2026-07-05T09:50:39.170067+00:00","updated_at":"2026-07-05T09:50:39.170067+00:00"}