{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:TW6ZRGRMBG7ZC2GWPWYZTYWAKA","short_pith_number":"pith:TW6ZRGRM","canonical_record":{"source":{"id":"1112.2290","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-12-10T17:11:49Z","cross_cats_sorted":[],"title_canon_sha256":"4343f5b1476b6ba5b30b7660ea4da127379d4c2c12a6cd6a0fba6f13bb5f909e","abstract_canon_sha256":"163b7e54b57b6fa542495e8e6af7c1c7814d2d4ca14883df3ae5ef772684c148"},"schema_version":"1.0"},"canonical_sha256":"9dbd989a2c09bf9168d67db199e2c0503bd0ff569bc6eb833e98a25eff70af5d","source":{"kind":"arxiv","id":"1112.2290","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.2290","created_at":"2026-05-18T04:05:57Z"},{"alias_kind":"arxiv_version","alias_value":"1112.2290v2","created_at":"2026-05-18T04:05:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.2290","created_at":"2026-05-18T04:05:57Z"},{"alias_kind":"pith_short_12","alias_value":"TW6ZRGRMBG7Z","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TW6ZRGRMBG7ZC2GW","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TW6ZRGRM","created_at":"2026-05-18T12:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:TW6ZRGRMBG7ZC2GWPWYZTYWAKA","target":"record","payload":{"canonical_record":{"source":{"id":"1112.2290","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-12-10T17:11:49Z","cross_cats_sorted":[],"title_canon_sha256":"4343f5b1476b6ba5b30b7660ea4da127379d4c2c12a6cd6a0fba6f13bb5f909e","abstract_canon_sha256":"163b7e54b57b6fa542495e8e6af7c1c7814d2d4ca14883df3ae5ef772684c148"},"schema_version":"1.0"},"canonical_sha256":"9dbd989a2c09bf9168d67db199e2c0503bd0ff569bc6eb833e98a25eff70af5d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:05:57.228587Z","signature_b64":"tfwlmEw4uHvjY3b/Z5BLHYSItZ3Mm1q2Rrbru1JrZGbd+hAW7IVp1+FUQAa/NawY67sHZmuhhC1LQUuMdSzXAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9dbd989a2c09bf9168d67db199e2c0503bd0ff569bc6eb833e98a25eff70af5d","last_reissued_at":"2026-05-18T04:05:57.227824Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:05:57.227824Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.2290","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":"2026-05-18T04:05:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v4HBXtyPVYsHh8/J8guFJP2Fsci2q0NHlKXBL6nSULMxFCFuhiDtukp68Q49dMJJWYazJPM+NeiK1j81kII1Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T01:13:53.932218Z"},"content_sha256":"71a6fbcc431bea8458453003d251cee923cae817aa74f9a32c4b189b0798642b","schema_version":"1.0","event_id":"sha256:71a6fbcc431bea8458453003d251cee923cae817aa74f9a32c4b189b0798642b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:TW6ZRGRMBG7ZC2GWPWYZTYWAKA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Remarks on Eisenstein","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alexander Borichev, Yuri Bilu","submitted_at":"2011-12-10T17:11:49Z","abstract_excerpt":"We obtain a fully explicit quantitative version of the Eisenstein theorem on algebraic power series which is more suitable for certain applications than the existing version due to Dwork, Robba, Schmidt and van der Poorten. We also treat ramified series and Laurent series, and we demonstrate some applications; for instance, we estimate the discriminant of the number field generated by the coefficients."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.2290","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":"2026-05-18T04:05:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JeJyMcVLb5SdF0KE3wE528TGQzB10ZgL0+DZk5QKJnApDWV3vzGGEsA9vpanCy+fUq3qnVG0YSEcAMlOY3JVAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T01:13:53.932913Z"},"content_sha256":"de6db7efccf9111bc470d58b97ae4cca623ff200508659df6d88c61c1cd67ca9","schema_version":"1.0","event_id":"sha256:de6db7efccf9111bc470d58b97ae4cca623ff200508659df6d88c61c1cd67ca9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TW6ZRGRMBG7ZC2GWPWYZTYWAKA/bundle.json","state_url":"https://pith.science/pith/TW6ZRGRMBG7ZC2GWPWYZTYWAKA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TW6ZRGRMBG7ZC2GWPWYZTYWAKA/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":"2026-05-26T01:13:53Z","links":{"resolver":"https://pith.science/pith/TW6ZRGRMBG7ZC2GWPWYZTYWAKA","bundle":"https://pith.science/pith/TW6ZRGRMBG7ZC2GWPWYZTYWAKA/bundle.json","state":"https://pith.science/pith/TW6ZRGRMBG7ZC2GWPWYZTYWAKA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TW6ZRGRMBG7ZC2GWPWYZTYWAKA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:TW6ZRGRMBG7ZC2GWPWYZTYWAKA","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":"163b7e54b57b6fa542495e8e6af7c1c7814d2d4ca14883df3ae5ef772684c148","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-12-10T17:11:49Z","title_canon_sha256":"4343f5b1476b6ba5b30b7660ea4da127379d4c2c12a6cd6a0fba6f13bb5f909e"},"schema_version":"1.0","source":{"id":"1112.2290","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.2290","created_at":"2026-05-18T04:05:57Z"},{"alias_kind":"arxiv_version","alias_value":"1112.2290v2","created_at":"2026-05-18T04:05:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.2290","created_at":"2026-05-18T04:05:57Z"},{"alias_kind":"pith_short_12","alias_value":"TW6ZRGRMBG7Z","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TW6ZRGRMBG7ZC2GW","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TW6ZRGRM","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:de6db7efccf9111bc470d58b97ae4cca623ff200508659df6d88c61c1cd67ca9","target":"graph","created_at":"2026-05-18T04:05:57Z","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 obtain a fully explicit quantitative version of the Eisenstein theorem on algebraic power series which is more suitable for certain applications than the existing version due to Dwork, Robba, Schmidt and van der Poorten. We also treat ramified series and Laurent series, and we demonstrate some applications; for instance, we estimate the discriminant of the number field generated by the coefficients.","authors_text":"Alexander Borichev, Yuri Bilu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-12-10T17:11:49Z","title":"Remarks on Eisenstein"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.2290","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":"sha256:71a6fbcc431bea8458453003d251cee923cae817aa74f9a32c4b189b0798642b","target":"record","created_at":"2026-05-18T04:05:57Z","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":"163b7e54b57b6fa542495e8e6af7c1c7814d2d4ca14883df3ae5ef772684c148","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-12-10T17:11:49Z","title_canon_sha256":"4343f5b1476b6ba5b30b7660ea4da127379d4c2c12a6cd6a0fba6f13bb5f909e"},"schema_version":"1.0","source":{"id":"1112.2290","kind":"arxiv","version":2}},"canonical_sha256":"9dbd989a2c09bf9168d67db199e2c0503bd0ff569bc6eb833e98a25eff70af5d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9dbd989a2c09bf9168d67db199e2c0503bd0ff569bc6eb833e98a25eff70af5d","first_computed_at":"2026-05-18T04:05:57.227824Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:05:57.227824Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tfwlmEw4uHvjY3b/Z5BLHYSItZ3Mm1q2Rrbru1JrZGbd+hAW7IVp1+FUQAa/NawY67sHZmuhhC1LQUuMdSzXAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:05:57.228587Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.2290","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:71a6fbcc431bea8458453003d251cee923cae817aa74f9a32c4b189b0798642b","sha256:de6db7efccf9111bc470d58b97ae4cca623ff200508659df6d88c61c1cd67ca9"],"state_sha256":"5a964ac98d88a6bd944a29c4f54a2e0e0f7467d78d1450d136d94bb483a0f4d8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fhZooX15lCNJ0B3KrkibWnbq1gjEyP0fB2AOMMMac2gVtiZcDl2U0KLHujLe1ZVUpLLZX/+6xvA/TX4qn80RAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T01:13:53.936134Z","bundle_sha256":"dfba9b79dd8387e083eef6a1d52a795aa0d0c1b718933c90dc3cff874c74492d"}}