{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:6FPTYG3PDLC4UE6W7G7ZKM3DKW","short_pith_number":"pith:6FPTYG3P","canonical_record":{"source":{"id":"1412.3570","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2014-12-11T08:41:03Z","cross_cats_sorted":["cs.CC","cs.DS"],"title_canon_sha256":"05104aeca1277e4bfdf0cb68aa10bad7877939d9e6d0be01a12cd3f865a524bb","abstract_canon_sha256":"9cdb2ef4c584d3d31202e6162118939a630d97d0d4bccdef2170016b159d84d9"},"schema_version":"1.0"},"canonical_sha256":"f15f3c1b6f1ac5ca13d6f9bf9533635583d045cfa087536ff4875794fc3ffa51","source":{"kind":"arxiv","id":"1412.3570","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.3570","created_at":"2026-05-18T01:21:41Z"},{"alias_kind":"arxiv_version","alias_value":"1412.3570v2","created_at":"2026-05-18T01:21:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.3570","created_at":"2026-05-18T01:21:41Z"},{"alias_kind":"pith_short_12","alias_value":"6FPTYG3PDLC4","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6FPTYG3PDLC4UE6W","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6FPTYG3P","created_at":"2026-05-18T12:28:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:6FPTYG3PDLC4UE6W7G7ZKM3DKW","target":"record","payload":{"canonical_record":{"source":{"id":"1412.3570","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2014-12-11T08:41:03Z","cross_cats_sorted":["cs.CC","cs.DS"],"title_canon_sha256":"05104aeca1277e4bfdf0cb68aa10bad7877939d9e6d0be01a12cd3f865a524bb","abstract_canon_sha256":"9cdb2ef4c584d3d31202e6162118939a630d97d0d4bccdef2170016b159d84d9"},"schema_version":"1.0"},"canonical_sha256":"f15f3c1b6f1ac5ca13d6f9bf9533635583d045cfa087536ff4875794fc3ffa51","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:41.892270Z","signature_b64":"WiN2OkA3SkWtLQZOMUv9R5Z9/izwZ5hHM4zLf0jzVmNT/IgYAtUA1PDnJ99DW9I6O2h4PYoc5XgzvS8hqW7xDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f15f3c1b6f1ac5ca13d6f9bf9533635583d045cfa087536ff4875794fc3ffa51","last_reissued_at":"2026-05-18T01:21:41.891648Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:41.891648Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.3570","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":"2026-05-18T01:21:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K8eqj35puR79Z3AU+ujvVkVeMybUMhQeZD6oj+5GalNhT4Q5huBauVnMn1phDfaM39rnIYwgWhkjbueJJi3xAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T23:40:38.163976Z"},"content_sha256":"d3fb8f16f3d91ce0961f4efb7e86c26f5e35218ba6e9dba9cfb45d6f6fa6219d","schema_version":"1.0","event_id":"sha256:d3fb8f16f3d91ce0961f4efb7e86c26f5e35218ba6e9dba9cfb45d6f6fa6219d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:6FPTYG3PDLC4UE6W7G7ZKM3DKW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bounded-degree factors of lacunary multivariate polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DS"],"primary_cat":"cs.SC","authors_text":"Bruno Grenet","submitted_at":"2014-12-11T08:41:03Z","abstract_excerpt":"In this paper, we present a new method for computing bounded-degree factors of lacunary multivariate polynomials. In particular for polynomials over number fields, we give a new algorithm that takes as input a multivariate polynomial f in lacunary representation and a degree bound d and computes the irreducible factors of degree at most d of f in time polynomial in the lacunary size of f and in d. Our algorithm, which is valid for any field of zero characteristic, is based on a new gap theorem that enables reducing the problem to several instances of (a) the univariate case and (b) low-degree "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3570","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":"2026-05-18T01:21:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GYFS88//s8RZa+knGJDSryN4NNv4zr+yodNYEDyawXn5x2GHfgD0f7QeMY9ey09TJ5uygG3us8YsEKvnyzGTBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T23:40:38.164346Z"},"content_sha256":"e6a64a4b294dcc61b6d45137ba76c24a211acdb787944796eb95985bb3bb6297","schema_version":"1.0","event_id":"sha256:e6a64a4b294dcc61b6d45137ba76c24a211acdb787944796eb95985bb3bb6297"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6FPTYG3PDLC4UE6W7G7ZKM3DKW/bundle.json","state_url":"https://pith.science/pith/6FPTYG3PDLC4UE6W7G7ZKM3DKW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6FPTYG3PDLC4UE6W7G7ZKM3DKW/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":"2026-06-22T23:40:38Z","links":{"resolver":"https://pith.science/pith/6FPTYG3PDLC4UE6W7G7ZKM3DKW","bundle":"https://pith.science/pith/6FPTYG3PDLC4UE6W7G7ZKM3DKW/bundle.json","state":"https://pith.science/pith/6FPTYG3PDLC4UE6W7G7ZKM3DKW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6FPTYG3PDLC4UE6W7G7ZKM3DKW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:6FPTYG3PDLC4UE6W7G7ZKM3DKW","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":"9cdb2ef4c584d3d31202e6162118939a630d97d0d4bccdef2170016b159d84d9","cross_cats_sorted":["cs.CC","cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2014-12-11T08:41:03Z","title_canon_sha256":"05104aeca1277e4bfdf0cb68aa10bad7877939d9e6d0be01a12cd3f865a524bb"},"schema_version":"1.0","source":{"id":"1412.3570","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.3570","created_at":"2026-05-18T01:21:41Z"},{"alias_kind":"arxiv_version","alias_value":"1412.3570v2","created_at":"2026-05-18T01:21:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.3570","created_at":"2026-05-18T01:21:41Z"},{"alias_kind":"pith_short_12","alias_value":"6FPTYG3PDLC4","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6FPTYG3PDLC4UE6W","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6FPTYG3P","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:e6a64a4b294dcc61b6d45137ba76c24a211acdb787944796eb95985bb3bb6297","target":"graph","created_at":"2026-05-18T01:21:41Z","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 present a new method for computing bounded-degree factors of lacunary multivariate polynomials. In particular for polynomials over number fields, we give a new algorithm that takes as input a multivariate polynomial f in lacunary representation and a degree bound d and computes the irreducible factors of degree at most d of f in time polynomial in the lacunary size of f and in d. Our algorithm, which is valid for any field of zero characteristic, is based on a new gap theorem that enables reducing the problem to several instances of (a) the univariate case and (b) low-degree ","authors_text":"Bruno Grenet","cross_cats":["cs.CC","cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2014-12-11T08:41:03Z","title":"Bounded-degree factors of lacunary multivariate polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3570","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:d3fb8f16f3d91ce0961f4efb7e86c26f5e35218ba6e9dba9cfb45d6f6fa6219d","target":"record","created_at":"2026-05-18T01:21:41Z","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":"9cdb2ef4c584d3d31202e6162118939a630d97d0d4bccdef2170016b159d84d9","cross_cats_sorted":["cs.CC","cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2014-12-11T08:41:03Z","title_canon_sha256":"05104aeca1277e4bfdf0cb68aa10bad7877939d9e6d0be01a12cd3f865a524bb"},"schema_version":"1.0","source":{"id":"1412.3570","kind":"arxiv","version":2}},"canonical_sha256":"f15f3c1b6f1ac5ca13d6f9bf9533635583d045cfa087536ff4875794fc3ffa51","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f15f3c1b6f1ac5ca13d6f9bf9533635583d045cfa087536ff4875794fc3ffa51","first_computed_at":"2026-05-18T01:21:41.891648Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:41.891648Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WiN2OkA3SkWtLQZOMUv9R5Z9/izwZ5hHM4zLf0jzVmNT/IgYAtUA1PDnJ99DW9I6O2h4PYoc5XgzvS8hqW7xDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:41.892270Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.3570","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d3fb8f16f3d91ce0961f4efb7e86c26f5e35218ba6e9dba9cfb45d6f6fa6219d","sha256:e6a64a4b294dcc61b6d45137ba76c24a211acdb787944796eb95985bb3bb6297"],"state_sha256":"42de288cb942428243c0c4d425ff9f40b24a470eae0b06ccc81a75869e4efd05"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ilU++z8OURXjnEZdn0O6fcdtBWSxXT1/weZcC/9iPznsETEEeIC4ZX4oaky7UNZ7bdnaEpo3b5vCM6m898UADw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T23:40:38.166300Z","bundle_sha256":"7100ef66ec83046c718186dfbe60bf8e04efc82fb7c64b9672a93c468d41ff78"}}