{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:D33XICVALXAS3BTPU74IV52LLI","short_pith_number":"pith:D33XICVA","canonical_record":{"source":{"id":"1204.4671","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-04-20T16:37:13Z","cross_cats_sorted":[],"title_canon_sha256":"b01d0796d51adf61df6c274fed7e0b22f6b7815f2282d22449956432a08943cf","abstract_canon_sha256":"46d30e9583633979312bd46c7bb280bbf97c2a79f226beb58806dbf8bef4c813"},"schema_version":"1.0"},"canonical_sha256":"1ef7740aa05dc12d866fa7f88af74b5a17b4ba585d9c6e7bbe3ba447bbaac49f","source":{"kind":"arxiv","id":"1204.4671","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.4671","created_at":"2026-05-18T03:57:25Z"},{"alias_kind":"arxiv_version","alias_value":"1204.4671v1","created_at":"2026-05-18T03:57:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.4671","created_at":"2026-05-18T03:57:25Z"},{"alias_kind":"pith_short_12","alias_value":"D33XICVALXAS","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"D33XICVALXAS3BTP","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"D33XICVA","created_at":"2026-05-18T12:27:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:D33XICVALXAS3BTPU74IV52LLI","target":"record","payload":{"canonical_record":{"source":{"id":"1204.4671","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-04-20T16:37:13Z","cross_cats_sorted":[],"title_canon_sha256":"b01d0796d51adf61df6c274fed7e0b22f6b7815f2282d22449956432a08943cf","abstract_canon_sha256":"46d30e9583633979312bd46c7bb280bbf97c2a79f226beb58806dbf8bef4c813"},"schema_version":"1.0"},"canonical_sha256":"1ef7740aa05dc12d866fa7f88af74b5a17b4ba585d9c6e7bbe3ba447bbaac49f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:57:25.745912Z","signature_b64":"NSDXWwEzXP371+z3nsHUtSu5KheQtaqnjLPNjgENUSEJXZWJ6Y3H6KxG3fK3DJ60bq9Zsf5Yy2pQGfsYPOWnAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1ef7740aa05dc12d866fa7f88af74b5a17b4ba585d9c6e7bbe3ba447bbaac49f","last_reissued_at":"2026-05-18T03:57:25.745098Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:57:25.745098Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.4671","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":"2026-05-18T03:57:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jO3nhGz+w04f2SbDVxqKVFRWQBzp/3pJlRICpKXRvGNPFws8edvOmD4rXAg0JTbNV1shE5ob+Mtm5M9t0qKoAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T13:03:55.494671Z"},"content_sha256":"94f3b4213420901e5872327fe51dd9752b91946233be6cfdb8d2c0241ea7dd8b","schema_version":"1.0","event_id":"sha256:94f3b4213420901e5872327fe51dd9752b91946233be6cfdb8d2c0241ea7dd8b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:D33XICVALXAS3BTPU74IV52LLI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Complexity of OM factorizations of polynomials over local fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Enric Nart, Hayden D. Stainsby, Jens-Dietrich Bauch","submitted_at":"2012-04-20T16:37:13Z","abstract_excerpt":"Let $k$ be a locally compact complete field with respect to a discrete valuation $v$. Let $\\oo$ be the valuation ring, $\\m$ the maximal ideal and $F(x)\\in\\oo[x]$ a monic separable polynomial of degree $n$. Let $\\delta=v(\\dsc(F))$. The Montes algorithm computes an OM factorization of $F$. The single-factor lifting algorithm derives from this data a factorization of $F \\md{\\m^\\nu}$, for a prescribed precision $\\nu$. In this paper we find a new estimate for the complexity of the Montes algorithm, leading to an estimation of $O(n^{2+\\epsilon}+n^{1+\\epsilon}\\delta^{2+\\epsilon}+n^2\\nu^{1+\\epsilon})$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.4671","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":"2026-05-18T03:57:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9KmmkA/N47XJSnXX6f5xbf4nzTT47NcYHMinOlhRs2gttdJNOIrMpj9QToFe2JDvSpckXLBHh7g/H4rQbGYTDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T13:03:55.495021Z"},"content_sha256":"58152e77317ae7121ea6d40d51dc59252a965944154afa604ae167e77caff5d4","schema_version":"1.0","event_id":"sha256:58152e77317ae7121ea6d40d51dc59252a965944154afa604ae167e77caff5d4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D33XICVALXAS3BTPU74IV52LLI/bundle.json","state_url":"https://pith.science/pith/D33XICVALXAS3BTPU74IV52LLI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D33XICVALXAS3BTPU74IV52LLI/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":"2026-06-02T13:03:55Z","links":{"resolver":"https://pith.science/pith/D33XICVALXAS3BTPU74IV52LLI","bundle":"https://pith.science/pith/D33XICVALXAS3BTPU74IV52LLI/bundle.json","state":"https://pith.science/pith/D33XICVALXAS3BTPU74IV52LLI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D33XICVALXAS3BTPU74IV52LLI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:D33XICVALXAS3BTPU74IV52LLI","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":"46d30e9583633979312bd46c7bb280bbf97c2a79f226beb58806dbf8bef4c813","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-04-20T16:37:13Z","title_canon_sha256":"b01d0796d51adf61df6c274fed7e0b22f6b7815f2282d22449956432a08943cf"},"schema_version":"1.0","source":{"id":"1204.4671","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.4671","created_at":"2026-05-18T03:57:25Z"},{"alias_kind":"arxiv_version","alias_value":"1204.4671v1","created_at":"2026-05-18T03:57:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.4671","created_at":"2026-05-18T03:57:25Z"},{"alias_kind":"pith_short_12","alias_value":"D33XICVALXAS","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"D33XICVALXAS3BTP","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"D33XICVA","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:58152e77317ae7121ea6d40d51dc59252a965944154afa604ae167e77caff5d4","target":"graph","created_at":"2026-05-18T03:57:25Z","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":"Let $k$ be a locally compact complete field with respect to a discrete valuation $v$. Let $\\oo$ be the valuation ring, $\\m$ the maximal ideal and $F(x)\\in\\oo[x]$ a monic separable polynomial of degree $n$. Let $\\delta=v(\\dsc(F))$. The Montes algorithm computes an OM factorization of $F$. The single-factor lifting algorithm derives from this data a factorization of $F \\md{\\m^\\nu}$, for a prescribed precision $\\nu$. In this paper we find a new estimate for the complexity of the Montes algorithm, leading to an estimation of $O(n^{2+\\epsilon}+n^{1+\\epsilon}\\delta^{2+\\epsilon}+n^2\\nu^{1+\\epsilon})$","authors_text":"Enric Nart, Hayden D. Stainsby, Jens-Dietrich Bauch","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-04-20T16:37:13Z","title":"Complexity of OM factorizations of polynomials over local fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.4671","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":"sha256:94f3b4213420901e5872327fe51dd9752b91946233be6cfdb8d2c0241ea7dd8b","target":"record","created_at":"2026-05-18T03:57:25Z","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":"46d30e9583633979312bd46c7bb280bbf97c2a79f226beb58806dbf8bef4c813","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-04-20T16:37:13Z","title_canon_sha256":"b01d0796d51adf61df6c274fed7e0b22f6b7815f2282d22449956432a08943cf"},"schema_version":"1.0","source":{"id":"1204.4671","kind":"arxiv","version":1}},"canonical_sha256":"1ef7740aa05dc12d866fa7f88af74b5a17b4ba585d9c6e7bbe3ba447bbaac49f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ef7740aa05dc12d866fa7f88af74b5a17b4ba585d9c6e7bbe3ba447bbaac49f","first_computed_at":"2026-05-18T03:57:25.745098Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:57:25.745098Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NSDXWwEzXP371+z3nsHUtSu5KheQtaqnjLPNjgENUSEJXZWJ6Y3H6KxG3fK3DJ60bq9Zsf5Yy2pQGfsYPOWnAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:57:25.745912Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.4671","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:94f3b4213420901e5872327fe51dd9752b91946233be6cfdb8d2c0241ea7dd8b","sha256:58152e77317ae7121ea6d40d51dc59252a965944154afa604ae167e77caff5d4"],"state_sha256":"cb5493179d0dc66db22977d45b5409c5f92ded6a0de64bbd75ea31f44b3b35e0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W2wdqrOatQdX704O/qMP/BZAgYEKXAHfPHglCp/ZH9Mq5VdWi/Xy0e1CMtSXQNplm3nSK+ZqV6UcUP4tdsDIAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T13:03:55.496988Z","bundle_sha256":"1efa75b0d641b4e686aac6fc4a38cf2025df23a74afe0c88844219e51c612012"}}