{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:PCKWK2MFIVBYX3ZQU7B7PAK7SG","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":"361340429a9222dc35272dc61b141d7d0adf4be92c6abd7ca85834c09cfaacc5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-10-20T08:56:13Z","title_canon_sha256":"819c22d12a8328a76bc88a832ac01dcc27452c7013661d4ecf8bce32f41d5928"},"schema_version":"1.0","source":{"id":"1510.05795","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.05795","created_at":"2026-05-18T01:09:36Z"},{"alias_kind":"arxiv_version","alias_value":"1510.05795v2","created_at":"2026-05-18T01:09:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.05795","created_at":"2026-05-18T01:09:36Z"},{"alias_kind":"pith_short_12","alias_value":"PCKWK2MFIVBY","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PCKWK2MFIVBYX3ZQ","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PCKWK2MF","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:13558d7f498a8c3c0c378c0d0cb77d1613d65e9f2c26413e53a95cebf65beedf","target":"graph","created_at":"2026-05-18T01:09:36Z","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":"In [Pollack-Stevens 2011], efficient algorithms are given to compute with overconvergent modular symbols. These algorithms then allow for the fast computation of $p$-adic $L$-functions and have further been applied to compute rational points on elliptic curves (e.g. [Darmon-Pollack 2006, Trifkovi\\'c 2006]). In this paper, we generalize these algorithms to the case of families of overconvergent modular symbols. As a consequence, we can compute $p$-adic families of Hecke-eigenvalues, two-variable $p$-adic $L$-functions, $L$-invariants, as well as the shape and structure of ordinary Hida-Hecke al","authors_text":"Daniel Ross, Evan P. Dummit, Lalit Jain, M\\'arton Hablicsek, Robert Harron, Robert Pollack","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-10-20T08:56:13Z","title":"Explicit computations of Hida families via overconvergent modular symbols"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.05795","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":"sha256:8f9a79d7f57a9df88d9abdae61091e95d174af7f07e19d222cd4cd4acf57bba7","target":"record","created_at":"2026-05-18T01:09:36Z","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":"361340429a9222dc35272dc61b141d7d0adf4be92c6abd7ca85834c09cfaacc5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-10-20T08:56:13Z","title_canon_sha256":"819c22d12a8328a76bc88a832ac01dcc27452c7013661d4ecf8bce32f41d5928"},"schema_version":"1.0","source":{"id":"1510.05795","kind":"arxiv","version":2}},"canonical_sha256":"789565698545438bef30a7c3f7815f91b4601f884bf82858348678b74b9d630a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"789565698545438bef30a7c3f7815f91b4601f884bf82858348678b74b9d630a","first_computed_at":"2026-05-18T01:09:36.412268Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:36.412268Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8tJxZsFF/K8ynKl1hntdIDifMSlQDNTfIPkTsFifyOnQlad+86/O8+kookhG1UBusZYk3B4FPKKNj1WjOB1iCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:36.412721Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.05795","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8f9a79d7f57a9df88d9abdae61091e95d174af7f07e19d222cd4cd4acf57bba7","sha256:13558d7f498a8c3c0c378c0d0cb77d1613d65e9f2c26413e53a95cebf65beedf"],"state_sha256":"75b1aed23d6137bcd1caa71e1a256d43a756d1c975e3b35dbd6a5ec33a192ee4"}