{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:YOOHS4TQ4DHVANAFSTCSWD5CYI","short_pith_number":"pith:YOOHS4TQ","canonical_record":{"source":{"id":"2502.05705","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-02-08T21:57:41Z","cross_cats_sorted":[],"title_canon_sha256":"47b4cc4251594029656e4111342e74ed64bd17c4f0a49451882e8e6765da48e2","abstract_canon_sha256":"51d2e1ff215a4eca70fface589ac0cb2eb76c2b970fc163c5fb6a1466cc6a251"},"schema_version":"1.0"},"canonical_sha256":"c39c797270e0cf50340594c52b0fa2c23cb3e3e0a67935272f92518d617245c3","source":{"kind":"arxiv","id":"2502.05705","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.05705","created_at":"2026-07-05T10:11:42Z"},{"alias_kind":"arxiv_version","alias_value":"2502.05705v1","created_at":"2026-07-05T10:11:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.05705","created_at":"2026-07-05T10:11:42Z"},{"alias_kind":"pith_short_12","alias_value":"YOOHS4TQ4DHV","created_at":"2026-07-05T10:11:42Z"},{"alias_kind":"pith_short_16","alias_value":"YOOHS4TQ4DHVANAF","created_at":"2026-07-05T10:11:42Z"},{"alias_kind":"pith_short_8","alias_value":"YOOHS4TQ","created_at":"2026-07-05T10:11:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:YOOHS4TQ4DHVANAFSTCSWD5CYI","target":"record","payload":{"canonical_record":{"source":{"id":"2502.05705","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-02-08T21:57:41Z","cross_cats_sorted":[],"title_canon_sha256":"47b4cc4251594029656e4111342e74ed64bd17c4f0a49451882e8e6765da48e2","abstract_canon_sha256":"51d2e1ff215a4eca70fface589ac0cb2eb76c2b970fc163c5fb6a1466cc6a251"},"schema_version":"1.0"},"canonical_sha256":"c39c797270e0cf50340594c52b0fa2c23cb3e3e0a67935272f92518d617245c3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:11:42.291655Z","signature_b64":"QqE39TLuPTgWumPVCqKxSm1aBHREm5dpvj7aq10NyRAr18A1UROtQCYs0ZXdMur/T76HfeTCPoUaAP+4VKbcBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c39c797270e0cf50340594c52b0fa2c23cb3e3e0a67935272f92518d617245c3","last_reissued_at":"2026-07-05T10:11:42.291255Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:11:42.291255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2502.05705","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":"2026-07-05T10:11:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ivheCWpoKb9KikutcQgRu0eadU6PJQDAYCLs4QR73g76UXWMEODyyfjB09QbTx9/RW2jcmnL9pj9/e/G9dAzBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T14:19:13.156873Z"},"content_sha256":"edc50b99ccba696de22cd476ab7122f7833383f515f08536c55dce8f08dea762","schema_version":"1.0","event_id":"sha256:edc50b99ccba696de22cd476ab7122f7833383f515f08536c55dce8f08dea762"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:YOOHS4TQ4DHVANAFSTCSWD5CYI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rank growth of elliptic curves over S3 extensions with fixed quadratic resolvents","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Daniel Keliher, Sun Woo Park","submitted_at":"2025-02-08T21:57:41Z","abstract_excerpt":"We study the probability with which an elliptic curve $E/k$, subject to some technical conditions, gains rank upon base extension to an $S_3$-cubic extension $K/k$ with quadratic resolvent field $F/k$, all three fields of which are subject to some mild technical conditions. To do so, we determine the distribution (under a non-standard ordering) of Selmer ranks of an auxiliary abelian variety associated to $E$ and $S_3$-cubic extensions $K/k$ following ideas of Klagsbrun, Mazur, and Rubin. One corollary of this distribution is that $E$ gains rank by at most one upon base extension to $K$ with p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.05705","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/2502.05705/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:11:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"evQeohANUUttIEB40m30MnlKNNfrSETOKGTdeJwfaxbxcEG2Hu9MrK1O/xlDRa2B86YVYhumSHkMhcu1a5vFCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T14:19:13.157808Z"},"content_sha256":"c7123670182d29b6f1003104f4b462a567430cd8751e2fdd49ac3adb80f0a2ee","schema_version":"1.0","event_id":"sha256:c7123670182d29b6f1003104f4b462a567430cd8751e2fdd49ac3adb80f0a2ee"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YOOHS4TQ4DHVANAFSTCSWD5CYI/bundle.json","state_url":"https://pith.science/pith/YOOHS4TQ4DHVANAFSTCSWD5CYI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YOOHS4TQ4DHVANAFSTCSWD5CYI/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":"2026-08-18T14:19:13Z","links":{"resolver":"https://pith.science/pith/YOOHS4TQ4DHVANAFSTCSWD5CYI","bundle":"https://pith.science/pith/YOOHS4TQ4DHVANAFSTCSWD5CYI/bundle.json","state":"https://pith.science/pith/YOOHS4TQ4DHVANAFSTCSWD5CYI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YOOHS4TQ4DHVANAFSTCSWD5CYI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:YOOHS4TQ4DHVANAFSTCSWD5CYI","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":"51d2e1ff215a4eca70fface589ac0cb2eb76c2b970fc163c5fb6a1466cc6a251","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-02-08T21:57:41Z","title_canon_sha256":"47b4cc4251594029656e4111342e74ed64bd17c4f0a49451882e8e6765da48e2"},"schema_version":"1.0","source":{"id":"2502.05705","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.05705","created_at":"2026-07-05T10:11:42Z"},{"alias_kind":"arxiv_version","alias_value":"2502.05705v1","created_at":"2026-07-05T10:11:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.05705","created_at":"2026-07-05T10:11:42Z"},{"alias_kind":"pith_short_12","alias_value":"YOOHS4TQ4DHV","created_at":"2026-07-05T10:11:42Z"},{"alias_kind":"pith_short_16","alias_value":"YOOHS4TQ4DHVANAF","created_at":"2026-07-05T10:11:42Z"},{"alias_kind":"pith_short_8","alias_value":"YOOHS4TQ","created_at":"2026-07-05T10:11:42Z"}],"graph_snapshots":[{"event_id":"sha256:c7123670182d29b6f1003104f4b462a567430cd8751e2fdd49ac3adb80f0a2ee","target":"graph","created_at":"2026-07-05T10:11:42Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2502.05705/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the probability with which an elliptic curve $E/k$, subject to some technical conditions, gains rank upon base extension to an $S_3$-cubic extension $K/k$ with quadratic resolvent field $F/k$, all three fields of which are subject to some mild technical conditions. To do so, we determine the distribution (under a non-standard ordering) of Selmer ranks of an auxiliary abelian variety associated to $E$ and $S_3$-cubic extensions $K/k$ following ideas of Klagsbrun, Mazur, and Rubin. One corollary of this distribution is that $E$ gains rank by at most one upon base extension to $K$ with p","authors_text":"Daniel Keliher, Sun Woo Park","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-02-08T21:57:41Z","title":"Rank growth of elliptic curves over S3 extensions with fixed quadratic resolvents"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.05705","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:edc50b99ccba696de22cd476ab7122f7833383f515f08536c55dce8f08dea762","target":"record","created_at":"2026-07-05T10:11:42Z","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":"51d2e1ff215a4eca70fface589ac0cb2eb76c2b970fc163c5fb6a1466cc6a251","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-02-08T21:57:41Z","title_canon_sha256":"47b4cc4251594029656e4111342e74ed64bd17c4f0a49451882e8e6765da48e2"},"schema_version":"1.0","source":{"id":"2502.05705","kind":"arxiv","version":1}},"canonical_sha256":"c39c797270e0cf50340594c52b0fa2c23cb3e3e0a67935272f92518d617245c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c39c797270e0cf50340594c52b0fa2c23cb3e3e0a67935272f92518d617245c3","first_computed_at":"2026-07-05T10:11:42.291255Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:11:42.291255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QqE39TLuPTgWumPVCqKxSm1aBHREm5dpvj7aq10NyRAr18A1UROtQCYs0ZXdMur/T76HfeTCPoUaAP+4VKbcBw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:11:42.291655Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.05705","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:edc50b99ccba696de22cd476ab7122f7833383f515f08536c55dce8f08dea762","sha256:c7123670182d29b6f1003104f4b462a567430cd8751e2fdd49ac3adb80f0a2ee"],"state_sha256":"8fac718f285fa422750813ac186e086f8dffb26c70738716c3a4a2cb53d474a8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xHfiv1lDvDRguwEH+01qO00s2PPKIZtrHrPLvJMDHRDfceTvp47f+Kth1pATZlsFs1NRVTOVw4AYMb8kuMG/BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T14:19:13.197857Z","bundle_sha256":"8755482fe28df1b51b020a44314d737469a593da888bf359a79759360de16a73"}}