{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:UAW3UDCSBMVNELGRLV74T3AJM7","short_pith_number":"pith:UAW3UDCS","canonical_record":{"source":{"id":"1507.02753","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-07-10T00:31:42Z","cross_cats_sorted":[],"title_canon_sha256":"26f404d5a0a9bc94512279067de8bb00901e0d9e0dab96b5a801a9903c52cab1","abstract_canon_sha256":"8039c7cb830629b2d89715742ca545dc937ec55068f02b21c591168eaa51e7c5"},"schema_version":"1.0"},"canonical_sha256":"a02dba0c520b2ad22cd15d7fc9ec0967f9b5a46aec970a9a128bd252b1ef415d","source":{"kind":"arxiv","id":"1507.02753","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.02753","created_at":"2026-05-17T23:54:17Z"},{"alias_kind":"arxiv_version","alias_value":"1507.02753v1","created_at":"2026-05-17T23:54:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.02753","created_at":"2026-05-17T23:54:17Z"},{"alias_kind":"pith_short_12","alias_value":"UAW3UDCSBMVN","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UAW3UDCSBMVNELGR","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UAW3UDCS","created_at":"2026-05-18T12:29:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:UAW3UDCSBMVNELGRLV74T3AJM7","target":"record","payload":{"canonical_record":{"source":{"id":"1507.02753","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-07-10T00:31:42Z","cross_cats_sorted":[],"title_canon_sha256":"26f404d5a0a9bc94512279067de8bb00901e0d9e0dab96b5a801a9903c52cab1","abstract_canon_sha256":"8039c7cb830629b2d89715742ca545dc937ec55068f02b21c591168eaa51e7c5"},"schema_version":"1.0"},"canonical_sha256":"a02dba0c520b2ad22cd15d7fc9ec0967f9b5a46aec970a9a128bd252b1ef415d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:17.116997Z","signature_b64":"ACTyE9U1zXsTyduwUWW8hf/uCgOMWKxNxww0vFwttuV39I1kmlSsEtRmRpfixcdkJt36bOUjvnY7bfuAFJ/UAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a02dba0c520b2ad22cd15d7fc9ec0967f9b5a46aec970a9a128bd252b1ef415d","last_reissued_at":"2026-05-17T23:54:17.116360Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:17.116360Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.02753","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":"2026-05-17T23:54:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9UAnFRDTEDmQm4Jsm7RpSDrM7fJmRBjRHqvmZHJTKxtuUsqRi0lc8wT/W1Pv6ch9dLXI82evBQnxg0Yo/qtXDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T18:10:51.799138Z"},"content_sha256":"f1c374e87c7ccadab0ad307eee738c8577587f6aa3b3e41b55a9937c0a85974f","schema_version":"1.0","event_id":"sha256:f1c374e87c7ccadab0ad307eee738c8577587f6aa3b3e41b55a9937c0a85974f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:UAW3UDCSBMVNELGRLV74T3AJM7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Density of Shifted and Affine Eisenstein Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Giacomo Micheli, Reto Schnyder","submitted_at":"2015-07-10T00:31:42Z","abstract_excerpt":"In this paper we provide a complete answer to a question by Heyman and Shparlinski concerning the natural density of polynomials which are irreducible by Eisenstein's criterion after applying some shift. The main tool we use is a local to global principle for density computations over a free $\\mathbb Z$-module of finite rank."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02753","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":"2026-05-17T23:54:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UJ+lHwscBbeATAuyvRCoLCSKIdHDdA4la5XeGKR1kwKn3eW1aw4inzKdgKo2PByImDhMVLaB+/HHjZ6/yQvpAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T18:10:51.799493Z"},"content_sha256":"7696c16944ebe5fdaedbbe3386fde08835b6ea7a0d5a35b819fe78c4169efa9e","schema_version":"1.0","event_id":"sha256:7696c16944ebe5fdaedbbe3386fde08835b6ea7a0d5a35b819fe78c4169efa9e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UAW3UDCSBMVNELGRLV74T3AJM7/bundle.json","state_url":"https://pith.science/pith/UAW3UDCSBMVNELGRLV74T3AJM7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UAW3UDCSBMVNELGRLV74T3AJM7/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":"2026-06-23T18:10:51Z","links":{"resolver":"https://pith.science/pith/UAW3UDCSBMVNELGRLV74T3AJM7","bundle":"https://pith.science/pith/UAW3UDCSBMVNELGRLV74T3AJM7/bundle.json","state":"https://pith.science/pith/UAW3UDCSBMVNELGRLV74T3AJM7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UAW3UDCSBMVNELGRLV74T3AJM7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:UAW3UDCSBMVNELGRLV74T3AJM7","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":"8039c7cb830629b2d89715742ca545dc937ec55068f02b21c591168eaa51e7c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-07-10T00:31:42Z","title_canon_sha256":"26f404d5a0a9bc94512279067de8bb00901e0d9e0dab96b5a801a9903c52cab1"},"schema_version":"1.0","source":{"id":"1507.02753","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.02753","created_at":"2026-05-17T23:54:17Z"},{"alias_kind":"arxiv_version","alias_value":"1507.02753v1","created_at":"2026-05-17T23:54:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.02753","created_at":"2026-05-17T23:54:17Z"},{"alias_kind":"pith_short_12","alias_value":"UAW3UDCSBMVN","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UAW3UDCSBMVNELGR","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UAW3UDCS","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:7696c16944ebe5fdaedbbe3386fde08835b6ea7a0d5a35b819fe78c4169efa9e","target":"graph","created_at":"2026-05-17T23:54:17Z","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 provide a complete answer to a question by Heyman and Shparlinski concerning the natural density of polynomials which are irreducible by Eisenstein's criterion after applying some shift. The main tool we use is a local to global principle for density computations over a free $\\mathbb Z$-module of finite rank.","authors_text":"Giacomo Micheli, Reto Schnyder","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-07-10T00:31:42Z","title":"The Density of Shifted and Affine Eisenstein Polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02753","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:f1c374e87c7ccadab0ad307eee738c8577587f6aa3b3e41b55a9937c0a85974f","target":"record","created_at":"2026-05-17T23:54:17Z","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":"8039c7cb830629b2d89715742ca545dc937ec55068f02b21c591168eaa51e7c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-07-10T00:31:42Z","title_canon_sha256":"26f404d5a0a9bc94512279067de8bb00901e0d9e0dab96b5a801a9903c52cab1"},"schema_version":"1.0","source":{"id":"1507.02753","kind":"arxiv","version":1}},"canonical_sha256":"a02dba0c520b2ad22cd15d7fc9ec0967f9b5a46aec970a9a128bd252b1ef415d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a02dba0c520b2ad22cd15d7fc9ec0967f9b5a46aec970a9a128bd252b1ef415d","first_computed_at":"2026-05-17T23:54:17.116360Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:17.116360Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ACTyE9U1zXsTyduwUWW8hf/uCgOMWKxNxww0vFwttuV39I1kmlSsEtRmRpfixcdkJt36bOUjvnY7bfuAFJ/UAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:17.116997Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.02753","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f1c374e87c7ccadab0ad307eee738c8577587f6aa3b3e41b55a9937c0a85974f","sha256:7696c16944ebe5fdaedbbe3386fde08835b6ea7a0d5a35b819fe78c4169efa9e"],"state_sha256":"0cfd40f72df3b37280f50fb571e794777fbdfc9bfb78f3fa8568849591ea2dc5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wNMTw6nACjhNbegKNf4rinqyb5BXn+BM5cjiDXEQ9CCMMwsOrl3ikvKZXG+K4dmX5bkrfmHPEk2eBeWMyCBhBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T18:10:51.801338Z","bundle_sha256":"4c856abd85e8ec3e6a4cb01b921018903f9330f9ab060bbae103436dc1c48828"}}