{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:XL2R2FUKSBYOE7K5DZ3TDHUMQL","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":"7867fbb69b14040ac47e490bf69a2fb9cc0e116246ea1af2d9a2107f278fdb22","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-10-19T10:08:00Z","title_canon_sha256":"e80c199b28b38a3768dfe0e8d13df09b58f83691f05bfb52849e0fae4b8b341b"},"schema_version":"1.0","source":{"id":"1110.4232","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.4232","created_at":"2026-05-18T02:58:00Z"},{"alias_kind":"arxiv_version","alias_value":"1110.4232v1","created_at":"2026-05-18T02:58:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.4232","created_at":"2026-05-18T02:58:00Z"},{"alias_kind":"pith_short_12","alias_value":"XL2R2FUKSBYO","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"XL2R2FUKSBYOE7K5","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"XL2R2FUK","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:f7bc2479c7b5a91c63799e6af99615fe7830a1bc06492289dd221d49f517eafa","target":"graph","created_at":"2026-05-18T02:58:00Z","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 explicit formulae for the logarithmic class group pairing on an elliptic curve defined over a number field. Then we relate it to the descent relative to a suitable cyclic isogeny. This allows us to connect the resulting Selmer group with the logarithmic class group of the base. These constructions are explicit and suitable for computer experimentation. From a conceptual point of view, the questions that arise here are analogues of \"visibility\" questions in the sense of Cremona and Mazur.","authors_text":"Christian Wuthrich, Jean Gillibert","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-10-19T10:08:00Z","title":"The class group pairing and $p$-descent on elliptic curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.4232","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":"sha256:1b01f7a7007bf9acc30189614a5964e775e53b17d55f5c9f6fa872f48c570634","target":"record","created_at":"2026-05-18T02:58:00Z","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":"7867fbb69b14040ac47e490bf69a2fb9cc0e116246ea1af2d9a2107f278fdb22","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-10-19T10:08:00Z","title_canon_sha256":"e80c199b28b38a3768dfe0e8d13df09b58f83691f05bfb52849e0fae4b8b341b"},"schema_version":"1.0","source":{"id":"1110.4232","kind":"arxiv","version":1}},"canonical_sha256":"baf51d168a9070e27d5d1e77319e8c82ee2ceea3c38145d7b7e0552dc3695f2a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"baf51d168a9070e27d5d1e77319e8c82ee2ceea3c38145d7b7e0552dc3695f2a","first_computed_at":"2026-05-18T02:58:00.319981Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:00.319981Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JmCUb13t6sRRPaDjyHNLotH7IsjzagXad6+0ot7L79/aFqU3yn4KNkT2sKSuumylwONfu7HWTlKVsRJV4RZ+Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:00.320627Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.4232","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1b01f7a7007bf9acc30189614a5964e775e53b17d55f5c9f6fa872f48c570634","sha256:f7bc2479c7b5a91c63799e6af99615fe7830a1bc06492289dd221d49f517eafa"],"state_sha256":"6fba16d8cb18ad94ec58a59143baa239598e4bbd42142721fb7f55c5fde779ac"}