{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:GTOWKRQ7XW73TJRZTUAOM5CW4G","short_pith_number":"pith:GTOWKRQ7","canonical_record":{"source":{"id":"1811.06611","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-11-15T22:12:57Z","cross_cats_sorted":[],"title_canon_sha256":"ed0cb72ac212aa170f35e09d086b01b6b3027369fae5b4f8a039fb7dd321c573","abstract_canon_sha256":"10cebbbcc319733d1b98550a17a8ea7ec7a9e529de8597c610d9e201597b4c20"},"schema_version":"1.0"},"canonical_sha256":"34dd65461fbdbfb9a6399d00e67456e1b3ad88286c79cf90f4fe8eef59db36e3","source":{"kind":"arxiv","id":"1811.06611","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.06611","created_at":"2026-05-18T00:00:34Z"},{"alias_kind":"arxiv_version","alias_value":"1811.06611v1","created_at":"2026-05-18T00:00:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.06611","created_at":"2026-05-18T00:00:34Z"},{"alias_kind":"pith_short_12","alias_value":"GTOWKRQ7XW73","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"GTOWKRQ7XW73TJRZ","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"GTOWKRQ7","created_at":"2026-05-18T12:32:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:GTOWKRQ7XW73TJRZTUAOM5CW4G","target":"record","payload":{"canonical_record":{"source":{"id":"1811.06611","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-11-15T22:12:57Z","cross_cats_sorted":[],"title_canon_sha256":"ed0cb72ac212aa170f35e09d086b01b6b3027369fae5b4f8a039fb7dd321c573","abstract_canon_sha256":"10cebbbcc319733d1b98550a17a8ea7ec7a9e529de8597c610d9e201597b4c20"},"schema_version":"1.0"},"canonical_sha256":"34dd65461fbdbfb9a6399d00e67456e1b3ad88286c79cf90f4fe8eef59db36e3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:34.371375Z","signature_b64":"5bDBrpb9SM/XTja1Vun8ZQOJaACEEp7RcAOQEMxlytWSiA1yXt7Bk/AGJoaILIcb4OdkMXShulBU3Z/lNRkqCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"34dd65461fbdbfb9a6399d00e67456e1b3ad88286c79cf90f4fe8eef59db36e3","last_reissued_at":"2026-05-18T00:00:34.370867Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:34.370867Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.06611","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":"2026-05-18T00:00:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+E7UyXZD1i5t6eHnYT/Ahu0SPdkfzUeBgt8fqQe+ld1QbWoRvskncTLHlk+WLaGPjjs5d+AbE/WPTPqJviHKAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T14:47:37.876045Z"},"content_sha256":"01d92dbf0d1c1f5082433191042c3fc9e0e4e78813654a31502f30c38bbf6404","schema_version":"1.0","event_id":"sha256:01d92dbf0d1c1f5082433191042c3fc9e0e4e78813654a31502f30c38bbf6404"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:GTOWKRQ7XW73TJRZTUAOM5CW4G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fitting ideals of Class groups in Carlitz-Hayes cyclotomic extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Andrea Bandini, Edoardo Coscelli, Francesc Bars","submitted_at":"2018-11-15T22:12:57Z","abstract_excerpt":"We generalize some results of Greither and Popescu to a geometric Galois cover $X\\rightarrow Y$ which appears naturally for example in extensions generated by $\\mathfrak{p}^n$-torsion points of a rank 1 normalized Drinfeld module (i.e. in subextensions of Carlitz-Hayes cyclotomic extensions of global fields of positive characteristic). We obtain a description of the Fitting ideal of class groups (or of their dual) via a formula involving Stickelberger elements and providing a link (similar to the one in \\cite{ABBL}) with Goss $\\zeta$-function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.06611","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":"2026-05-18T00:00:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YZltk9p/zN6JJr/Lm1ZLmy1DdaNcXIeumG7dgQgcI9DAGPy9K/CHUbvD9N6cAw7gc5Vy4qmVkax5h7wmUSPRDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T14:47:37.876395Z"},"content_sha256":"0413f99ba74b973f81ee7fdd7cd51c32df9e704fbbba78b7fedfbd318caa085b","schema_version":"1.0","event_id":"sha256:0413f99ba74b973f81ee7fdd7cd51c32df9e704fbbba78b7fedfbd318caa085b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GTOWKRQ7XW73TJRZTUAOM5CW4G/bundle.json","state_url":"https://pith.science/pith/GTOWKRQ7XW73TJRZTUAOM5CW4G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GTOWKRQ7XW73TJRZTUAOM5CW4G/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":"2026-06-24T14:47:37Z","links":{"resolver":"https://pith.science/pith/GTOWKRQ7XW73TJRZTUAOM5CW4G","bundle":"https://pith.science/pith/GTOWKRQ7XW73TJRZTUAOM5CW4G/bundle.json","state":"https://pith.science/pith/GTOWKRQ7XW73TJRZTUAOM5CW4G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GTOWKRQ7XW73TJRZTUAOM5CW4G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:GTOWKRQ7XW73TJRZTUAOM5CW4G","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":"10cebbbcc319733d1b98550a17a8ea7ec7a9e529de8597c610d9e201597b4c20","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-11-15T22:12:57Z","title_canon_sha256":"ed0cb72ac212aa170f35e09d086b01b6b3027369fae5b4f8a039fb7dd321c573"},"schema_version":"1.0","source":{"id":"1811.06611","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.06611","created_at":"2026-05-18T00:00:34Z"},{"alias_kind":"arxiv_version","alias_value":"1811.06611v1","created_at":"2026-05-18T00:00:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.06611","created_at":"2026-05-18T00:00:34Z"},{"alias_kind":"pith_short_12","alias_value":"GTOWKRQ7XW73","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"GTOWKRQ7XW73TJRZ","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"GTOWKRQ7","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:0413f99ba74b973f81ee7fdd7cd51c32df9e704fbbba78b7fedfbd318caa085b","target":"graph","created_at":"2026-05-18T00:00:34Z","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 generalize some results of Greither and Popescu to a geometric Galois cover $X\\rightarrow Y$ which appears naturally for example in extensions generated by $\\mathfrak{p}^n$-torsion points of a rank 1 normalized Drinfeld module (i.e. in subextensions of Carlitz-Hayes cyclotomic extensions of global fields of positive characteristic). We obtain a description of the Fitting ideal of class groups (or of their dual) via a formula involving Stickelberger elements and providing a link (similar to the one in \\cite{ABBL}) with Goss $\\zeta$-function.","authors_text":"Andrea Bandini, Edoardo Coscelli, Francesc Bars","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-11-15T22:12:57Z","title":"Fitting ideals of Class groups in Carlitz-Hayes cyclotomic extensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.06611","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":"sha256:01d92dbf0d1c1f5082433191042c3fc9e0e4e78813654a31502f30c38bbf6404","target":"record","created_at":"2026-05-18T00:00:34Z","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":"10cebbbcc319733d1b98550a17a8ea7ec7a9e529de8597c610d9e201597b4c20","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-11-15T22:12:57Z","title_canon_sha256":"ed0cb72ac212aa170f35e09d086b01b6b3027369fae5b4f8a039fb7dd321c573"},"schema_version":"1.0","source":{"id":"1811.06611","kind":"arxiv","version":1}},"canonical_sha256":"34dd65461fbdbfb9a6399d00e67456e1b3ad88286c79cf90f4fe8eef59db36e3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"34dd65461fbdbfb9a6399d00e67456e1b3ad88286c79cf90f4fe8eef59db36e3","first_computed_at":"2026-05-18T00:00:34.370867Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:34.370867Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5bDBrpb9SM/XTja1Vun8ZQOJaACEEp7RcAOQEMxlytWSiA1yXt7Bk/AGJoaILIcb4OdkMXShulBU3Z/lNRkqCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:34.371375Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.06611","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:01d92dbf0d1c1f5082433191042c3fc9e0e4e78813654a31502f30c38bbf6404","sha256:0413f99ba74b973f81ee7fdd7cd51c32df9e704fbbba78b7fedfbd318caa085b"],"state_sha256":"d5b798b63c5a3be6cd3ffff46d715e4a841a3f6d2d59578d4938c2ecd8dbdda4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tLpLiHpviG0usdXPbd7e5mdOFQYGkl5TysxH4eqSdaYXv1ppkD8BRJOcdLebzhyur5zpzzKW2kOHTcgjTcbQBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T14:47:37.878174Z","bundle_sha256":"a2e3bdf23fdbc2bbae5482dfd615560d1b62c566811698adb4bf3385b7d8d86f"}}