{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:JW3UW6KY3EFT2MK4QUSBLXWSUT","short_pith_number":"pith:JW3UW6KY","canonical_record":{"source":{"id":"1407.1093","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-07-04T00:21:46Z","cross_cats_sorted":[],"title_canon_sha256":"91fee7d6d99da62351c41f2518e831e3394e016a0e4e7fc61ee85eb5ed3cdf33","abstract_canon_sha256":"b00e810c04cf5382213621613996ce92ca339a562dbc8cfab22ed6a0f8062807"},"schema_version":"1.0"},"canonical_sha256":"4db74b7958d90b3d315c852415ded2a4eb51f382dd579476b62f66d35880ecfc","source":{"kind":"arxiv","id":"1407.1093","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.1093","created_at":"2026-05-18T01:12:08Z"},{"alias_kind":"arxiv_version","alias_value":"1407.1093v1","created_at":"2026-05-18T01:12:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.1093","created_at":"2026-05-18T01:12:08Z"},{"alias_kind":"pith_short_12","alias_value":"JW3UW6KY3EFT","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"JW3UW6KY3EFT2MK4","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"JW3UW6KY","created_at":"2026-05-18T12:28:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:JW3UW6KY3EFT2MK4QUSBLXWSUT","target":"record","payload":{"canonical_record":{"source":{"id":"1407.1093","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-07-04T00:21:46Z","cross_cats_sorted":[],"title_canon_sha256":"91fee7d6d99da62351c41f2518e831e3394e016a0e4e7fc61ee85eb5ed3cdf33","abstract_canon_sha256":"b00e810c04cf5382213621613996ce92ca339a562dbc8cfab22ed6a0f8062807"},"schema_version":"1.0"},"canonical_sha256":"4db74b7958d90b3d315c852415ded2a4eb51f382dd579476b62f66d35880ecfc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:08.798553Z","signature_b64":"mzQPCRBqgysmSozPY1PRQswdhu+E1UEPKQvhYhX6JkdLA7wUfktExw91PLlM3gjtG+330DZyjvn3/3J66gNSBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4db74b7958d90b3d315c852415ded2a4eb51f382dd579476b62f66d35880ecfc","last_reissued_at":"2026-05-18T01:12:08.798083Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:08.798083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.1093","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":"2026-05-18T01:12:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3ft5CXBbnLwjGHh43AWk5RLSpD16aCWP8QC0hGTrBIaj9BvL5ngl3dhkaU7KEZr0Sh+7DFcBVw/mbigEHvJACA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T16:12:31.952991Z"},"content_sha256":"613bd5d490c082f8db8ff347398b62fcec34d1cc29310b88d28e926755bc3087","schema_version":"1.0","event_id":"sha256:613bd5d490c082f8db8ff347398b62fcec34d1cc29310b88d28e926755bc3087"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:JW3UW6KY3EFT2MK4QUSBLXWSUT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multiplicative reduction and the cyclotomic main conjecture for $\\mathrm{GL}_2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Christopher Skinner","submitted_at":"2014-07-04T00:21:46Z","abstract_excerpt":"We show that the cyclotomic Iwasawa--Greenberg Main Conjecture holds for a large class of modular forms with multiplicative reduction at $p$, extending previous results for the good ordinary case. In fact, the multiplicative case is deduced from the good case through the use of Hida families and a simple Fitting ideal argument."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.1093","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":"2026-05-18T01:12:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XVSYnDd20amKJ9VA61maYUVxGgFvj1C4tQyGiyjC9nHDbScj2A1bWwY5p16VKuh6S/UHD5YjeuSMBhpKDff4CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T16:12:31.953638Z"},"content_sha256":"01e7fb763725209e83fbf04974934242fb5bf4c55555a77ecd2d56a5f8434291","schema_version":"1.0","event_id":"sha256:01e7fb763725209e83fbf04974934242fb5bf4c55555a77ecd2d56a5f8434291"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JW3UW6KY3EFT2MK4QUSBLXWSUT/bundle.json","state_url":"https://pith.science/pith/JW3UW6KY3EFT2MK4QUSBLXWSUT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JW3UW6KY3EFT2MK4QUSBLXWSUT/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":"2026-05-29T16:12:31Z","links":{"resolver":"https://pith.science/pith/JW3UW6KY3EFT2MK4QUSBLXWSUT","bundle":"https://pith.science/pith/JW3UW6KY3EFT2MK4QUSBLXWSUT/bundle.json","state":"https://pith.science/pith/JW3UW6KY3EFT2MK4QUSBLXWSUT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JW3UW6KY3EFT2MK4QUSBLXWSUT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:JW3UW6KY3EFT2MK4QUSBLXWSUT","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":"b00e810c04cf5382213621613996ce92ca339a562dbc8cfab22ed6a0f8062807","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-07-04T00:21:46Z","title_canon_sha256":"91fee7d6d99da62351c41f2518e831e3394e016a0e4e7fc61ee85eb5ed3cdf33"},"schema_version":"1.0","source":{"id":"1407.1093","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.1093","created_at":"2026-05-18T01:12:08Z"},{"alias_kind":"arxiv_version","alias_value":"1407.1093v1","created_at":"2026-05-18T01:12:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.1093","created_at":"2026-05-18T01:12:08Z"},{"alias_kind":"pith_short_12","alias_value":"JW3UW6KY3EFT","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"JW3UW6KY3EFT2MK4","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"JW3UW6KY","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:01e7fb763725209e83fbf04974934242fb5bf4c55555a77ecd2d56a5f8434291","target":"graph","created_at":"2026-05-18T01:12:08Z","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":"We show that the cyclotomic Iwasawa--Greenberg Main Conjecture holds for a large class of modular forms with multiplicative reduction at $p$, extending previous results for the good ordinary case. In fact, the multiplicative case is deduced from the good case through the use of Hida families and a simple Fitting ideal argument.","authors_text":"Christopher Skinner","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-07-04T00:21:46Z","title":"Multiplicative reduction and the cyclotomic main conjecture for $\\mathrm{GL}_2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.1093","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":"sha256:613bd5d490c082f8db8ff347398b62fcec34d1cc29310b88d28e926755bc3087","target":"record","created_at":"2026-05-18T01:12:08Z","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":"b00e810c04cf5382213621613996ce92ca339a562dbc8cfab22ed6a0f8062807","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-07-04T00:21:46Z","title_canon_sha256":"91fee7d6d99da62351c41f2518e831e3394e016a0e4e7fc61ee85eb5ed3cdf33"},"schema_version":"1.0","source":{"id":"1407.1093","kind":"arxiv","version":1}},"canonical_sha256":"4db74b7958d90b3d315c852415ded2a4eb51f382dd579476b62f66d35880ecfc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4db74b7958d90b3d315c852415ded2a4eb51f382dd579476b62f66d35880ecfc","first_computed_at":"2026-05-18T01:12:08.798083Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:08.798083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mzQPCRBqgysmSozPY1PRQswdhu+E1UEPKQvhYhX6JkdLA7wUfktExw91PLlM3gjtG+330DZyjvn3/3J66gNSBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:08.798553Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.1093","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:613bd5d490c082f8db8ff347398b62fcec34d1cc29310b88d28e926755bc3087","sha256:01e7fb763725209e83fbf04974934242fb5bf4c55555a77ecd2d56a5f8434291"],"state_sha256":"680edce2a9ebfe46004adeb969b0e6a863e042d301a70c6422e2c775dbdce5b8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M1m+PWSPuJmWXxRzWAVLUV2BUHPAPpeyQcPzyhCoqQFLZTyKoeWR1TxQ83FIYZRnYnuHvCWwMwaCh4drKLO/Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T16:12:31.956385Z","bundle_sha256":"3c37af5e31fa61e9cadc435aa7ce3522ec5b74ba04826c486b31e4b1e17f10a1"}}