{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:WNUVY4APR5KE55SSSNDPJOMKZX","short_pith_number":"pith:WNUVY4AP","canonical_record":{"source":{"id":"2312.04666","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-12-07T19:57:58Z","cross_cats_sorted":[],"title_canon_sha256":"3c3d7cce571fd96e285980a7eab7690fcefcc11f8ff38b7de68c3e5688753c1d","abstract_canon_sha256":"fa3cec1cbc9a7b5260a1985ff2ff57bec52a619838f55ab0aa162cabd3771e7d"},"schema_version":"1.0"},"canonical_sha256":"b3695c700f8f544ef6529346f4b98acdd7dc91d171b99be2fc45b2391fbde4aa","source":{"kind":"arxiv","id":"2312.04666","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.04666","created_at":"2026-06-23T01:12:43Z"},{"alias_kind":"arxiv_version","alias_value":"2312.04666v3","created_at":"2026-06-23T01:12:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.04666","created_at":"2026-06-23T01:12:43Z"},{"alias_kind":"pith_short_12","alias_value":"WNUVY4APR5KE","created_at":"2026-06-23T01:12:43Z"},{"alias_kind":"pith_short_16","alias_value":"WNUVY4APR5KE55SS","created_at":"2026-06-23T01:12:43Z"},{"alias_kind":"pith_short_8","alias_value":"WNUVY4AP","created_at":"2026-06-23T01:12:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:WNUVY4APR5KE55SSSNDPJOMKZX","target":"record","payload":{"canonical_record":{"source":{"id":"2312.04666","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-12-07T19:57:58Z","cross_cats_sorted":[],"title_canon_sha256":"3c3d7cce571fd96e285980a7eab7690fcefcc11f8ff38b7de68c3e5688753c1d","abstract_canon_sha256":"fa3cec1cbc9a7b5260a1985ff2ff57bec52a619838f55ab0aa162cabd3771e7d"},"schema_version":"1.0"},"canonical_sha256":"b3695c700f8f544ef6529346f4b98acdd7dc91d171b99be2fc45b2391fbde4aa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T01:12:43.893356Z","signature_b64":"iHuJGmSUzzNdWIdl5Y1PdMpaimsIV2V2sNeRFo1GN6OjP8EPCAPPQgg/9YDT7xah1wtFqoSBoCVHZRWQZn65Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b3695c700f8f544ef6529346f4b98acdd7dc91d171b99be2fc45b2391fbde4aa","last_reissued_at":"2026-06-23T01:12:43.892932Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T01:12:43.892932Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2312.04666","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-23T01:12:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BZG8NDkZwOfedmlnSqWn7RxxjPwOzcndRN8ZbpdoWrb/PUkfhTn/eBF43jJS685lGhYQ9H7df9d1HBi1jfkvBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T11:10:17.165577Z"},"content_sha256":"a32d8155bfbdcf25a67f489c086c06be560aab0e89700d56c9f37cd6dafd3663","schema_version":"1.0","event_id":"sha256:a32d8155bfbdcf25a67f489c086c06be560aab0e89700d56c9f37cd6dafd3663"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:WNUVY4APR5KE55SSSNDPJOMKZX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The algebra $\\mathbb{Z}_\\ell[[\\mathbb{Z}_p^d]]$ and applications to Iwasawa theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Andrea Bandini, Ignazio Longhi","submitted_at":"2023-12-07T19:57:58Z","abstract_excerpt":"Let $\\ell$ and $p$ be distinct primes, and let $\\G$ be an abelian pro-$p$-group. We study the structure of the algebra $\\L:=\\Z_\\ell[[\\G]]$ and of $\\L$-modules. The algebra $\\L$ turns out to be a direct product of copies of ring of integers of cyclotomic extensions of $\\Q_\\ell$ and this induces a similar decomposition for a family of $\\L$-modules. Inside this family we define Sinnott modules and provide characteristic ideals and formulas \\`a la Iwasawa for orders and ranks of their quotients. When $\\G\\simeq \\Z_p^d$\\, is the Galois group of an extension of global fields, $\\ell$-class groups and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.04666","kind":"arxiv","version":3},"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/2312.04666/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":"2026-06-23T01:12:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FofvXWPDiw2CHyFnoU8Qs/oLnmevyJ4BpS2PA1540zX2IbsoZAHShJJjXHCEbOYRWE8t1EYuczJT/iC8K0GKDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T11:10:17.165974Z"},"content_sha256":"160d8d4fdd6652f99fbcc9a40ebaf39469afd16368211d601fab9ee2910d1c2b","schema_version":"1.0","event_id":"sha256:160d8d4fdd6652f99fbcc9a40ebaf39469afd16368211d601fab9ee2910d1c2b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WNUVY4APR5KE55SSSNDPJOMKZX/bundle.json","state_url":"https://pith.science/pith/WNUVY4APR5KE55SSSNDPJOMKZX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WNUVY4APR5KE55SSSNDPJOMKZX/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":"2026-06-24T11:10:17Z","links":{"resolver":"https://pith.science/pith/WNUVY4APR5KE55SSSNDPJOMKZX","bundle":"https://pith.science/pith/WNUVY4APR5KE55SSSNDPJOMKZX/bundle.json","state":"https://pith.science/pith/WNUVY4APR5KE55SSSNDPJOMKZX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WNUVY4APR5KE55SSSNDPJOMKZX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:WNUVY4APR5KE55SSSNDPJOMKZX","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":"fa3cec1cbc9a7b5260a1985ff2ff57bec52a619838f55ab0aa162cabd3771e7d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-12-07T19:57:58Z","title_canon_sha256":"3c3d7cce571fd96e285980a7eab7690fcefcc11f8ff38b7de68c3e5688753c1d"},"schema_version":"1.0","source":{"id":"2312.04666","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.04666","created_at":"2026-06-23T01:12:43Z"},{"alias_kind":"arxiv_version","alias_value":"2312.04666v3","created_at":"2026-06-23T01:12:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.04666","created_at":"2026-06-23T01:12:43Z"},{"alias_kind":"pith_short_12","alias_value":"WNUVY4APR5KE","created_at":"2026-06-23T01:12:43Z"},{"alias_kind":"pith_short_16","alias_value":"WNUVY4APR5KE55SS","created_at":"2026-06-23T01:12:43Z"},{"alias_kind":"pith_short_8","alias_value":"WNUVY4AP","created_at":"2026-06-23T01:12:43Z"}],"graph_snapshots":[{"event_id":"sha256:160d8d4fdd6652f99fbcc9a40ebaf39469afd16368211d601fab9ee2910d1c2b","target":"graph","created_at":"2026-06-23T01:12:43Z","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/2312.04666/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $\\ell$ and $p$ be distinct primes, and let $\\G$ be an abelian pro-$p$-group. We study the structure of the algebra $\\L:=\\Z_\\ell[[\\G]]$ and of $\\L$-modules. The algebra $\\L$ turns out to be a direct product of copies of ring of integers of cyclotomic extensions of $\\Q_\\ell$ and this induces a similar decomposition for a family of $\\L$-modules. Inside this family we define Sinnott modules and provide characteristic ideals and formulas \\`a la Iwasawa for orders and ranks of their quotients. When $\\G\\simeq \\Z_p^d$\\, is the Galois group of an extension of global fields, $\\ell$-class groups and ","authors_text":"Andrea Bandini, Ignazio Longhi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-12-07T19:57:58Z","title":"The algebra $\\mathbb{Z}_\\ell[[\\mathbb{Z}_p^d]]$ and applications to Iwasawa theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.04666","kind":"arxiv","version":3},"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:a32d8155bfbdcf25a67f489c086c06be560aab0e89700d56c9f37cd6dafd3663","target":"record","created_at":"2026-06-23T01:12:43Z","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":"fa3cec1cbc9a7b5260a1985ff2ff57bec52a619838f55ab0aa162cabd3771e7d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-12-07T19:57:58Z","title_canon_sha256":"3c3d7cce571fd96e285980a7eab7690fcefcc11f8ff38b7de68c3e5688753c1d"},"schema_version":"1.0","source":{"id":"2312.04666","kind":"arxiv","version":3}},"canonical_sha256":"b3695c700f8f544ef6529346f4b98acdd7dc91d171b99be2fc45b2391fbde4aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b3695c700f8f544ef6529346f4b98acdd7dc91d171b99be2fc45b2391fbde4aa","first_computed_at":"2026-06-23T01:12:43.892932Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T01:12:43.892932Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iHuJGmSUzzNdWIdl5Y1PdMpaimsIV2V2sNeRFo1GN6OjP8EPCAPPQgg/9YDT7xah1wtFqoSBoCVHZRWQZn65Bg==","signature_status":"signed_v1","signed_at":"2026-06-23T01:12:43.893356Z","signed_message":"canonical_sha256_bytes"},"source_id":"2312.04666","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a32d8155bfbdcf25a67f489c086c06be560aab0e89700d56c9f37cd6dafd3663","sha256:160d8d4fdd6652f99fbcc9a40ebaf39469afd16368211d601fab9ee2910d1c2b"],"state_sha256":"d51e97eeffac85ade78e0d9ba53bd7367703e489348995e5bbb277aeaa5a3856"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dzsi6mRlFGcnVbRrPDtq6tpDWwvYrJm6CsWfcZN9hiSUhQvakvAPabO9AitkbYugmbFGJtmjgANHL6veOWdsBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T11:10:17.168143Z","bundle_sha256":"92f849c5d8db9211c3ea1d2ce1927ea9d14337005b9f80b404bbd5a6bfd0a849"}}