{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:5HH64KG2Y5Y5HMU4AWWJN2GE7S","short_pith_number":"pith:5HH64KG2","canonical_record":{"source":{"id":"1601.03424","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-01-13T22:03:01Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"fee4e75d76f067c4044887ab75e0719ae9a767dab65b8a7d60312f2221387ffc","abstract_canon_sha256":"71994e9450d5d91d68f65cca58fae569ea2018015bdb45d17333554cf3f7b5c5"},"schema_version":"1.0"},"canonical_sha256":"e9cfee28dac771d3b29c05ac96e8c4fcaf17a08a51741ed85f8c6d0202174ba5","source":{"kind":"arxiv","id":"1601.03424","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.03424","created_at":"2026-05-18T01:22:53Z"},{"alias_kind":"arxiv_version","alias_value":"1601.03424v1","created_at":"2026-05-18T01:22:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.03424","created_at":"2026-05-18T01:22:53Z"},{"alias_kind":"pith_short_12","alias_value":"5HH64KG2Y5Y5","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5HH64KG2Y5Y5HMU4","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5HH64KG2","created_at":"2026-05-18T12:30:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:5HH64KG2Y5Y5HMU4AWWJN2GE7S","target":"record","payload":{"canonical_record":{"source":{"id":"1601.03424","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-01-13T22:03:01Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"fee4e75d76f067c4044887ab75e0719ae9a767dab65b8a7d60312f2221387ffc","abstract_canon_sha256":"71994e9450d5d91d68f65cca58fae569ea2018015bdb45d17333554cf3f7b5c5"},"schema_version":"1.0"},"canonical_sha256":"e9cfee28dac771d3b29c05ac96e8c4fcaf17a08a51741ed85f8c6d0202174ba5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:53.557260Z","signature_b64":"9WMTiSY4z/bpf+VRLbaOlOGDu9uQ7nKRmoyzjPL+Z3u4YyVffOJQnUl8qtypzTrvznD3iaEu8ZVGH4CmEYI9Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e9cfee28dac771d3b29c05ac96e8c4fcaf17a08a51741ed85f8c6d0202174ba5","last_reissued_at":"2026-05-18T01:22:53.556594Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:53.556594Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.03424","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":"2026-05-18T01:22:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x9Px9SNIFJMWwY21p4k6LuRZ4E7ianWIICQRF8oXVMgwijJPcf4SVF7ioh4n27p+bxAEb4ZGYnxEm6UTQaX1Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T23:29:01.587309Z"},"content_sha256":"d6642a8989e7ea05a3fe075f9f8ca5314c932ecb1e62d5bc5f1edfc4e3fae7c8","schema_version":"1.0","event_id":"sha256:d6642a8989e7ea05a3fe075f9f8ca5314c932ecb1e62d5bc5f1edfc4e3fae7c8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:5HH64KG2Y5Y5HMU4AWWJN2GE7S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multiplicative groups of fields and hereditarily irreducible polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.RA","authors_text":"Alice Medvedev, Ramin Takloo-Bighash","submitted_at":"2016-01-13T22:03:01Z","abstract_excerpt":"In this paper we explore the concept of {\\em good heredity} for fields from a group theoretic perspective. Extending results from \\cite{alice}, we show that several natural families of fields are of good heredity, and some others are not. We also construct several examples to show that various wishful thinking expectations are not true."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.03424","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":"2026-05-18T01:22:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/SB8WrlpK1zSMseuXLYtFGHYo1xyAxDsrpfatA/mmrzcV4TP0p91thTBIYfXFJaouvJ17eWzxXU6ruX1P7rhCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T23:29:01.587980Z"},"content_sha256":"aca60fd469f8342413d84064251c3d2f03babbe1a5b35b0be7e69b47b7a05d59","schema_version":"1.0","event_id":"sha256:aca60fd469f8342413d84064251c3d2f03babbe1a5b35b0be7e69b47b7a05d59"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5HH64KG2Y5Y5HMU4AWWJN2GE7S/bundle.json","state_url":"https://pith.science/pith/5HH64KG2Y5Y5HMU4AWWJN2GE7S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5HH64KG2Y5Y5HMU4AWWJN2GE7S/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":"2026-05-27T23:29:01Z","links":{"resolver":"https://pith.science/pith/5HH64KG2Y5Y5HMU4AWWJN2GE7S","bundle":"https://pith.science/pith/5HH64KG2Y5Y5HMU4AWWJN2GE7S/bundle.json","state":"https://pith.science/pith/5HH64KG2Y5Y5HMU4AWWJN2GE7S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5HH64KG2Y5Y5HMU4AWWJN2GE7S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:5HH64KG2Y5Y5HMU4AWWJN2GE7S","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":"71994e9450d5d91d68f65cca58fae569ea2018015bdb45d17333554cf3f7b5c5","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-01-13T22:03:01Z","title_canon_sha256":"fee4e75d76f067c4044887ab75e0719ae9a767dab65b8a7d60312f2221387ffc"},"schema_version":"1.0","source":{"id":"1601.03424","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.03424","created_at":"2026-05-18T01:22:53Z"},{"alias_kind":"arxiv_version","alias_value":"1601.03424v1","created_at":"2026-05-18T01:22:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.03424","created_at":"2026-05-18T01:22:53Z"},{"alias_kind":"pith_short_12","alias_value":"5HH64KG2Y5Y5","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5HH64KG2Y5Y5HMU4","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5HH64KG2","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:aca60fd469f8342413d84064251c3d2f03babbe1a5b35b0be7e69b47b7a05d59","target":"graph","created_at":"2026-05-18T01:22:53Z","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 explore the concept of {\\em good heredity} for fields from a group theoretic perspective. Extending results from \\cite{alice}, we show that several natural families of fields are of good heredity, and some others are not. We also construct several examples to show that various wishful thinking expectations are not true.","authors_text":"Alice Medvedev, Ramin Takloo-Bighash","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-01-13T22:03:01Z","title":"Multiplicative groups of fields and hereditarily irreducible polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.03424","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:d6642a8989e7ea05a3fe075f9f8ca5314c932ecb1e62d5bc5f1edfc4e3fae7c8","target":"record","created_at":"2026-05-18T01:22:53Z","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":"71994e9450d5d91d68f65cca58fae569ea2018015bdb45d17333554cf3f7b5c5","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-01-13T22:03:01Z","title_canon_sha256":"fee4e75d76f067c4044887ab75e0719ae9a767dab65b8a7d60312f2221387ffc"},"schema_version":"1.0","source":{"id":"1601.03424","kind":"arxiv","version":1}},"canonical_sha256":"e9cfee28dac771d3b29c05ac96e8c4fcaf17a08a51741ed85f8c6d0202174ba5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e9cfee28dac771d3b29c05ac96e8c4fcaf17a08a51741ed85f8c6d0202174ba5","first_computed_at":"2026-05-18T01:22:53.556594Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:53.556594Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9WMTiSY4z/bpf+VRLbaOlOGDu9uQ7nKRmoyzjPL+Z3u4YyVffOJQnUl8qtypzTrvznD3iaEu8ZVGH4CmEYI9Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:53.557260Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.03424","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d6642a8989e7ea05a3fe075f9f8ca5314c932ecb1e62d5bc5f1edfc4e3fae7c8","sha256:aca60fd469f8342413d84064251c3d2f03babbe1a5b35b0be7e69b47b7a05d59"],"state_sha256":"51dc67cf9158a545fdd2b410c07d292ef823f06c9374df89bff2e54ea72a546d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F55MlfUuWKQiBDRRt8yI8lFT911EFTkoXESHpWo8jeRzN7qiXovcFH7Bgn64OLTtC/EUujxnNI6+5/IPIYCDAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T23:29:01.591531Z","bundle_sha256":"d427a9e262c15f2707d8cba90bc381ba81ff4c174ece07d4c01fffa7df553728"}}