{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:EO6MM2YG54GRJLSVOVPVR4V6A2","short_pith_number":"pith:EO6MM2YG","canonical_record":{"source":{"id":"1504.06671","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-04-24T23:53:57Z","cross_cats_sorted":[],"title_canon_sha256":"c19da2c2c3436823e165a0b9a9104a9635d8b0d676be3386503aaea5b32bac09","abstract_canon_sha256":"dbe1f0c21d4c26e62ae2dfbef8a73e3fd00d9040e3f879b7487c1e5a85897b79"},"schema_version":"1.0"},"canonical_sha256":"23bcc66b06ef0d14ae55755f58f2be069cf5f8659e6fa91d15ab32041ceb1748","source":{"kind":"arxiv","id":"1504.06671","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.06671","created_at":"2026-05-18T00:48:20Z"},{"alias_kind":"arxiv_version","alias_value":"1504.06671v1","created_at":"2026-05-18T00:48:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.06671","created_at":"2026-05-18T00:48:20Z"},{"alias_kind":"pith_short_12","alias_value":"EO6MM2YG54GR","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"EO6MM2YG54GRJLSV","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"EO6MM2YG","created_at":"2026-05-18T12:29:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:EO6MM2YG54GRJLSVOVPVR4V6A2","target":"record","payload":{"canonical_record":{"source":{"id":"1504.06671","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-04-24T23:53:57Z","cross_cats_sorted":[],"title_canon_sha256":"c19da2c2c3436823e165a0b9a9104a9635d8b0d676be3386503aaea5b32bac09","abstract_canon_sha256":"dbe1f0c21d4c26e62ae2dfbef8a73e3fd00d9040e3f879b7487c1e5a85897b79"},"schema_version":"1.0"},"canonical_sha256":"23bcc66b06ef0d14ae55755f58f2be069cf5f8659e6fa91d15ab32041ceb1748","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:20.729044Z","signature_b64":"HtfrppfIxdc3yWhsAdFNy1KB6Z8Q7xwkHO7BXJNqqo4sIvBdyuqg9UZu9VZpqfqogVfv3z3jZUvQYEgjNpITCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"23bcc66b06ef0d14ae55755f58f2be069cf5f8659e6fa91d15ab32041ceb1748","last_reissued_at":"2026-05-18T00:48:20.728312Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:20.728312Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.06671","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":"2026-05-18T00:48:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/Al8zG0H9D9pHEuxbzgS1AOnxa67BgleduqZMACVMY2DmXV98xmnBLSYF0B+qqo5wO/IQAcM3Ay0JgLhVPk0Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T12:51:31.820034Z"},"content_sha256":"90b48735adc475a4aab29ecddf79b3b9d2ee80089b12ed5f1af8c5d2ddd784d3","schema_version":"1.0","event_id":"sha256:90b48735adc475a4aab29ecddf79b3b9d2ee80089b12ed5f1af8c5d2ddd784d3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:EO6MM2YG54GRJLSVOVPVR4V6A2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Enumerating Extensions of $(\\pi)$-Adic Fields with Given Invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Brian Sinclair, Sebastian Pauli","submitted_at":"2015-04-24T23:53:57Z","abstract_excerpt":"We give an algorithm that constructs a minimal set of polynomials defining all extension of a $(\\pi)$-adic field with given, inertia degree, ramification index, discriminant, ramification polygon, and residual polynomials of the segments of the ramification polygon."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06671","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":"2026-05-18T00:48:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NA2e/2mDw65RI2DC7/luBUc0WRC4z3nmpQRg1NqiGLDZbmTu6/W1SQxi0ug5G1RfYQTE27bmhnwuYEKJhz8uCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T12:51:31.820384Z"},"content_sha256":"13df97ecefc04ca84b0678add618fe84435f4c48e73388a1189a7dff200f8c1f","schema_version":"1.0","event_id":"sha256:13df97ecefc04ca84b0678add618fe84435f4c48e73388a1189a7dff200f8c1f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EO6MM2YG54GRJLSVOVPVR4V6A2/bundle.json","state_url":"https://pith.science/pith/EO6MM2YG54GRJLSVOVPVR4V6A2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EO6MM2YG54GRJLSVOVPVR4V6A2/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":"2026-06-25T12:51:31Z","links":{"resolver":"https://pith.science/pith/EO6MM2YG54GRJLSVOVPVR4V6A2","bundle":"https://pith.science/pith/EO6MM2YG54GRJLSVOVPVR4V6A2/bundle.json","state":"https://pith.science/pith/EO6MM2YG54GRJLSVOVPVR4V6A2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EO6MM2YG54GRJLSVOVPVR4V6A2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:EO6MM2YG54GRJLSVOVPVR4V6A2","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":"dbe1f0c21d4c26e62ae2dfbef8a73e3fd00d9040e3f879b7487c1e5a85897b79","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-04-24T23:53:57Z","title_canon_sha256":"c19da2c2c3436823e165a0b9a9104a9635d8b0d676be3386503aaea5b32bac09"},"schema_version":"1.0","source":{"id":"1504.06671","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.06671","created_at":"2026-05-18T00:48:20Z"},{"alias_kind":"arxiv_version","alias_value":"1504.06671v1","created_at":"2026-05-18T00:48:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.06671","created_at":"2026-05-18T00:48:20Z"},{"alias_kind":"pith_short_12","alias_value":"EO6MM2YG54GR","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"EO6MM2YG54GRJLSV","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"EO6MM2YG","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:13df97ecefc04ca84b0678add618fe84435f4c48e73388a1189a7dff200f8c1f","target":"graph","created_at":"2026-05-18T00:48:20Z","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 give an algorithm that constructs a minimal set of polynomials defining all extension of a $(\\pi)$-adic field with given, inertia degree, ramification index, discriminant, ramification polygon, and residual polynomials of the segments of the ramification polygon.","authors_text":"Brian Sinclair, Sebastian Pauli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-04-24T23:53:57Z","title":"Enumerating Extensions of $(\\pi)$-Adic Fields with Given Invariants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06671","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":"sha256:90b48735adc475a4aab29ecddf79b3b9d2ee80089b12ed5f1af8c5d2ddd784d3","target":"record","created_at":"2026-05-18T00:48:20Z","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":"dbe1f0c21d4c26e62ae2dfbef8a73e3fd00d9040e3f879b7487c1e5a85897b79","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-04-24T23:53:57Z","title_canon_sha256":"c19da2c2c3436823e165a0b9a9104a9635d8b0d676be3386503aaea5b32bac09"},"schema_version":"1.0","source":{"id":"1504.06671","kind":"arxiv","version":1}},"canonical_sha256":"23bcc66b06ef0d14ae55755f58f2be069cf5f8659e6fa91d15ab32041ceb1748","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"23bcc66b06ef0d14ae55755f58f2be069cf5f8659e6fa91d15ab32041ceb1748","first_computed_at":"2026-05-18T00:48:20.728312Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:20.728312Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HtfrppfIxdc3yWhsAdFNy1KB6Z8Q7xwkHO7BXJNqqo4sIvBdyuqg9UZu9VZpqfqogVfv3z3jZUvQYEgjNpITCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:20.729044Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.06671","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:90b48735adc475a4aab29ecddf79b3b9d2ee80089b12ed5f1af8c5d2ddd784d3","sha256:13df97ecefc04ca84b0678add618fe84435f4c48e73388a1189a7dff200f8c1f"],"state_sha256":"6c4dfadd6a6faba74ef7d393ef1a0b7a3d0b65a2ab9823b919e41636198794a2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"umsVlVwHhqTVYtMBlxCeikAKPin0DlAdt1E1FhAlh01RovqH4gmWzuVjEataySH6b3o63zYt+sp0yWFzMQjeBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T12:51:31.822249Z","bundle_sha256":"3632339ce6cfaf0af2913a4fad695b89f1a6d4632a4e658bb4f26e59956edb94"}}