{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:K2BIRVYPRLIJAGINQ23OMZLE5P","short_pith_number":"pith:K2BIRVYP","canonical_record":{"source":{"id":"1109.4071","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-09-19T16:01:28Z","cross_cats_sorted":[],"title_canon_sha256":"1bd2a18a48f9402fcbb1fadc725fe907826820cead0c95f81e1ba9fc78789255","abstract_canon_sha256":"10c7d2db86dae516ca29f23e98580eb6978f1edb3d379b9d3c130f1a9276b252"},"schema_version":"1.0"},"canonical_sha256":"568288d70f8ad090190d86b6e66564ebd7d1dad72dd86f15e150ce25c40c32c2","source":{"kind":"arxiv","id":"1109.4071","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.4071","created_at":"2026-05-18T02:55:27Z"},{"alias_kind":"arxiv_version","alias_value":"1109.4071v3","created_at":"2026-05-18T02:55:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.4071","created_at":"2026-05-18T02:55:27Z"},{"alias_kind":"pith_short_12","alias_value":"K2BIRVYPRLIJ","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"K2BIRVYPRLIJAGIN","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"K2BIRVYP","created_at":"2026-05-18T12:26:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:K2BIRVYPRLIJAGINQ23OMZLE5P","target":"record","payload":{"canonical_record":{"source":{"id":"1109.4071","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-09-19T16:01:28Z","cross_cats_sorted":[],"title_canon_sha256":"1bd2a18a48f9402fcbb1fadc725fe907826820cead0c95f81e1ba9fc78789255","abstract_canon_sha256":"10c7d2db86dae516ca29f23e98580eb6978f1edb3d379b9d3c130f1a9276b252"},"schema_version":"1.0"},"canonical_sha256":"568288d70f8ad090190d86b6e66564ebd7d1dad72dd86f15e150ce25c40c32c2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:55:27.929325Z","signature_b64":"FVkGfmHbFkn8JBbN8819lhxu97uC46bM9FnkaIb0+4g0OZq8HkN2wMFprq5hcT06xV2Tt0ofnL2uclARMJdmCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"568288d70f8ad090190d86b6e66564ebd7d1dad72dd86f15e150ce25c40c32c2","last_reissued_at":"2026-05-18T02:55:27.928660Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:55:27.928660Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.4071","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":"2026-05-18T02:55:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BJHoiWc82SDzr41ue7sytOwflGZV+A8RAhsraaGD5tt25ndf7Ct4FpLeRR3H6p3R93XEk/eKGRqqithrt3JgCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T19:18:42.982690Z"},"content_sha256":"106180e01ecb614cfd32d64e8178e864de9fd468333e1ec1c5637f227bd28cb6","schema_version":"1.0","event_id":"sha256:106180e01ecb614cfd32d64e8178e864de9fd468333e1ec1c5637f227bd28cb6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:K2BIRVYPRLIJAGINQ23OMZLE5P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Parameterizing solutions to any Galois embedding problem over Z/p^nZ with elementary p-abelian kernel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Andrew Schultz","submitted_at":"2011-09-19T16:01:28Z","abstract_excerpt":"In this paper we use the Galois module structure for the classical parameterizing spaces for elementary p-abelian extensions of a field K to give necessary and sufficient conditions for the solvability of any embedding problem which is an extension of Z/p^nZ with elementary p-abelian kernel. This allows us to count the total number of solutions to a given embedding problem when the appropriate modules are finite, and leads to some nontrivial automatic realization and realization multiplicity results for Galois groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.4071","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":""},"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":"2026-05-18T02:55:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OfJmDs6FBqRMp7vdjQYp18/jSUP1347wNDCPXY9hNnh77ol59qdlUKowZeTRw1YMPSQLlfg9/OuTk5665I5CAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T19:18:42.983057Z"},"content_sha256":"7250d44d7d2c4682722194af30e379f4747f8b47d69a34610fa6dce81875117b","schema_version":"1.0","event_id":"sha256:7250d44d7d2c4682722194af30e379f4747f8b47d69a34610fa6dce81875117b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K2BIRVYPRLIJAGINQ23OMZLE5P/bundle.json","state_url":"https://pith.science/pith/K2BIRVYPRLIJAGINQ23OMZLE5P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K2BIRVYPRLIJAGINQ23OMZLE5P/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":"2026-06-05T19:18:42Z","links":{"resolver":"https://pith.science/pith/K2BIRVYPRLIJAGINQ23OMZLE5P","bundle":"https://pith.science/pith/K2BIRVYPRLIJAGINQ23OMZLE5P/bundle.json","state":"https://pith.science/pith/K2BIRVYPRLIJAGINQ23OMZLE5P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K2BIRVYPRLIJAGINQ23OMZLE5P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:K2BIRVYPRLIJAGINQ23OMZLE5P","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":"10c7d2db86dae516ca29f23e98580eb6978f1edb3d379b9d3c130f1a9276b252","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-09-19T16:01:28Z","title_canon_sha256":"1bd2a18a48f9402fcbb1fadc725fe907826820cead0c95f81e1ba9fc78789255"},"schema_version":"1.0","source":{"id":"1109.4071","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.4071","created_at":"2026-05-18T02:55:27Z"},{"alias_kind":"arxiv_version","alias_value":"1109.4071v3","created_at":"2026-05-18T02:55:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.4071","created_at":"2026-05-18T02:55:27Z"},{"alias_kind":"pith_short_12","alias_value":"K2BIRVYPRLIJ","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"K2BIRVYPRLIJAGIN","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"K2BIRVYP","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:7250d44d7d2c4682722194af30e379f4747f8b47d69a34610fa6dce81875117b","target":"graph","created_at":"2026-05-18T02:55:27Z","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 this paper we use the Galois module structure for the classical parameterizing spaces for elementary p-abelian extensions of a field K to give necessary and sufficient conditions for the solvability of any embedding problem which is an extension of Z/p^nZ with elementary p-abelian kernel. This allows us to count the total number of solutions to a given embedding problem when the appropriate modules are finite, and leads to some nontrivial automatic realization and realization multiplicity results for Galois groups.","authors_text":"Andrew Schultz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-09-19T16:01:28Z","title":"Parameterizing solutions to any Galois embedding problem over Z/p^nZ with elementary p-abelian kernel"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.4071","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":"sha256:106180e01ecb614cfd32d64e8178e864de9fd468333e1ec1c5637f227bd28cb6","target":"record","created_at":"2026-05-18T02:55:27Z","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":"10c7d2db86dae516ca29f23e98580eb6978f1edb3d379b9d3c130f1a9276b252","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-09-19T16:01:28Z","title_canon_sha256":"1bd2a18a48f9402fcbb1fadc725fe907826820cead0c95f81e1ba9fc78789255"},"schema_version":"1.0","source":{"id":"1109.4071","kind":"arxiv","version":3}},"canonical_sha256":"568288d70f8ad090190d86b6e66564ebd7d1dad72dd86f15e150ce25c40c32c2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"568288d70f8ad090190d86b6e66564ebd7d1dad72dd86f15e150ce25c40c32c2","first_computed_at":"2026-05-18T02:55:27.928660Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:55:27.928660Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FVkGfmHbFkn8JBbN8819lhxu97uC46bM9FnkaIb0+4g0OZq8HkN2wMFprq5hcT06xV2Tt0ofnL2uclARMJdmCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:55:27.929325Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.4071","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:106180e01ecb614cfd32d64e8178e864de9fd468333e1ec1c5637f227bd28cb6","sha256:7250d44d7d2c4682722194af30e379f4747f8b47d69a34610fa6dce81875117b"],"state_sha256":"1ad6bb976e1832126727743335e20c23f290cd47a222224e75eaaa80bf6a3b39"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lkeXBjiB9IoeXKPw7+V4LJsHDPmfCHh5RLlTnWLf+Y6+1nm+NkgCU9E0GlGVRX2x1HPamqwO5M7mz6PKMy6dBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T19:18:42.985279Z","bundle_sha256":"fd70f58b43e82d79838673c36b1e4f6351403fc0b11400ab4c1318d92e020ccd"}}