{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:3Z4CETDAK2UTPSQYS243XMI33G","short_pith_number":"pith:3Z4CETDA","canonical_record":{"source":{"id":"1709.03094","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-09-10T12:35:55Z","cross_cats_sorted":[],"title_canon_sha256":"ff8e7b9f3f100b1340399f566e3256ceebbc4d2ac9d7416ad00c1ba5f9bf91d9","abstract_canon_sha256":"f4b80b7a7413c4a1a0af5e6d51dabfc9c444d07dc463db35d6e36bf18359de3b"},"schema_version":"1.0"},"canonical_sha256":"de78224c6056a937ca1896b9bbb11bd9a90a3e73bd3a03ab6774680133fb0aec","source":{"kind":"arxiv","id":"1709.03094","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.03094","created_at":"2026-05-18T00:26:43Z"},{"alias_kind":"arxiv_version","alias_value":"1709.03094v2","created_at":"2026-05-18T00:26:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.03094","created_at":"2026-05-18T00:26:43Z"},{"alias_kind":"pith_short_12","alias_value":"3Z4CETDAK2UT","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3Z4CETDAK2UTPSQY","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3Z4CETDA","created_at":"2026-05-18T12:30:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:3Z4CETDAK2UTPSQYS243XMI33G","target":"record","payload":{"canonical_record":{"source":{"id":"1709.03094","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-09-10T12:35:55Z","cross_cats_sorted":[],"title_canon_sha256":"ff8e7b9f3f100b1340399f566e3256ceebbc4d2ac9d7416ad00c1ba5f9bf91d9","abstract_canon_sha256":"f4b80b7a7413c4a1a0af5e6d51dabfc9c444d07dc463db35d6e36bf18359de3b"},"schema_version":"1.0"},"canonical_sha256":"de78224c6056a937ca1896b9bbb11bd9a90a3e73bd3a03ab6774680133fb0aec","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:43.626496Z","signature_b64":"dcj2CCVz2fvNZKPmedP++VHac8JDCbMD5Lb9GWAYFjs9zvbsv2/lyrzIGWzeE3RxrDZtaF4vkiqZD46nD9cLDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"de78224c6056a937ca1896b9bbb11bd9a90a3e73bd3a03ab6774680133fb0aec","last_reissued_at":"2026-05-18T00:26:43.625846Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:43.625846Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.03094","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:26:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ujW8jamwhWNR1BsengHOZvyMNVfdtU+7KG/vIFTXTbP0ddig0UdlyjZf1GOcV7r+cryj3CdVMjco1Sfy2LNtDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T00:46:16.704456Z"},"content_sha256":"97705cb85514519de2857b2dfeb0b91acf552e43ac3c4069e1a63557c73e39c4","schema_version":"1.0","event_id":"sha256:97705cb85514519de2857b2dfeb0b91acf552e43ac3c4069e1a63557c73e39c4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:3Z4CETDAK2UTPSQYS243XMI33G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the local behaviour of specializations of function field extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Danny Neftin, Fran\\c{c}ois Legrand, Joachim K\\\"onig","submitted_at":"2017-09-10T12:35:55Z","abstract_excerpt":"Given a field $k$ of characteristic zero and an indeterminate $T$ over $k$, we investigate the local behaviour at primes of $k$ of finite Galois extensions of $k$ arising as specializations of finite Galois extensions $E/k(T)$ (with $E/k$ regular) at points $t_0 \\in \\mathbb{P}^1(k)$. We provide a general result about decomposition groups at primes of $k$ in specializations, extending a fundamental result of Beckmann concerning inertia groups. We then apply our result to study crossed products, the Hilbert--Grunwald property, and finite parametric sets."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.03094","kind":"arxiv","version":2},"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":"2026-05-18T00:26:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LkdStPjU07vlWNWG4rXkfS1CSyyUZCG8oZablDkjprvBi9m69p7kQDsSMPTk2VFdRFE39EOAvjyMnx9qmlgyDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T00:46:16.704942Z"},"content_sha256":"ae11527a5a1e5e84a1afa53839acb7fe58b14e812045532fa7292c9db7b9d5dd","schema_version":"1.0","event_id":"sha256:ae11527a5a1e5e84a1afa53839acb7fe58b14e812045532fa7292c9db7b9d5dd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3Z4CETDAK2UTPSQYS243XMI33G/bundle.json","state_url":"https://pith.science/pith/3Z4CETDAK2UTPSQYS243XMI33G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3Z4CETDAK2UTPSQYS243XMI33G/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":"2026-06-26T00:46:16Z","links":{"resolver":"https://pith.science/pith/3Z4CETDAK2UTPSQYS243XMI33G","bundle":"https://pith.science/pith/3Z4CETDAK2UTPSQYS243XMI33G/bundle.json","state":"https://pith.science/pith/3Z4CETDAK2UTPSQYS243XMI33G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3Z4CETDAK2UTPSQYS243XMI33G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:3Z4CETDAK2UTPSQYS243XMI33G","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":"f4b80b7a7413c4a1a0af5e6d51dabfc9c444d07dc463db35d6e36bf18359de3b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-09-10T12:35:55Z","title_canon_sha256":"ff8e7b9f3f100b1340399f566e3256ceebbc4d2ac9d7416ad00c1ba5f9bf91d9"},"schema_version":"1.0","source":{"id":"1709.03094","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.03094","created_at":"2026-05-18T00:26:43Z"},{"alias_kind":"arxiv_version","alias_value":"1709.03094v2","created_at":"2026-05-18T00:26:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.03094","created_at":"2026-05-18T00:26:43Z"},{"alias_kind":"pith_short_12","alias_value":"3Z4CETDAK2UT","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3Z4CETDAK2UTPSQY","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3Z4CETDA","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:ae11527a5a1e5e84a1afa53839acb7fe58b14e812045532fa7292c9db7b9d5dd","target":"graph","created_at":"2026-05-18T00:26:43Z","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"},"paper":{"abstract_excerpt":"Given a field $k$ of characteristic zero and an indeterminate $T$ over $k$, we investigate the local behaviour at primes of $k$ of finite Galois extensions of $k$ arising as specializations of finite Galois extensions $E/k(T)$ (with $E/k$ regular) at points $t_0 \\in \\mathbb{P}^1(k)$. We provide a general result about decomposition groups at primes of $k$ in specializations, extending a fundamental result of Beckmann concerning inertia groups. We then apply our result to study crossed products, the Hilbert--Grunwald property, and finite parametric sets.","authors_text":"Danny Neftin, Fran\\c{c}ois Legrand, Joachim K\\\"onig","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-09-10T12:35:55Z","title":"On the local behaviour of specializations of function field extensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.03094","kind":"arxiv","version":2},"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":"sha256:97705cb85514519de2857b2dfeb0b91acf552e43ac3c4069e1a63557c73e39c4","target":"record","created_at":"2026-05-18T00:26:43Z","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":"f4b80b7a7413c4a1a0af5e6d51dabfc9c444d07dc463db35d6e36bf18359de3b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-09-10T12:35:55Z","title_canon_sha256":"ff8e7b9f3f100b1340399f566e3256ceebbc4d2ac9d7416ad00c1ba5f9bf91d9"},"schema_version":"1.0","source":{"id":"1709.03094","kind":"arxiv","version":2}},"canonical_sha256":"de78224c6056a937ca1896b9bbb11bd9a90a3e73bd3a03ab6774680133fb0aec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"de78224c6056a937ca1896b9bbb11bd9a90a3e73bd3a03ab6774680133fb0aec","first_computed_at":"2026-05-18T00:26:43.625846Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:43.625846Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dcj2CCVz2fvNZKPmedP++VHac8JDCbMD5Lb9GWAYFjs9zvbsv2/lyrzIGWzeE3RxrDZtaF4vkiqZD46nD9cLDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:43.626496Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.03094","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:97705cb85514519de2857b2dfeb0b91acf552e43ac3c4069e1a63557c73e39c4","sha256:ae11527a5a1e5e84a1afa53839acb7fe58b14e812045532fa7292c9db7b9d5dd"],"state_sha256":"71c92f1f7d8ce6e2042098fdf222a6188718fc735295069b29705ada2483e8b7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ys+I8bR96yUdcIrIdMoSaoJtjTl/8pXemAff90XWdtmjiv8P6ZXQQA8O/ca4IU3Wce7Z8n9YXRqvEFjhvrwqDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T00:46:16.707761Z","bundle_sha256":"d1c0f0db17d8d45d79a90937f7a0ee69faa215e3711af2eaa6bae40a5c781cc4"}}