{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:WKCXVI7TTZOVATO66EZBSP5LU3","short_pith_number":"pith:WKCXVI7T","canonical_record":{"source":{"id":"2411.18366","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2024-11-27T14:13:30Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"44731abd756aed55daea18d45ef4bc0f9367ab9e2d573d04fee2da972917c6ff","abstract_canon_sha256":"dec0cc07827c93210cfdc379f43cb4bf9bae5bed52299a3b948e84316bb96bde"},"schema_version":"1.0"},"canonical_sha256":"b2857aa3f39e5d504ddef132193faba6ff8be9d6b5243474af12eab6bf9775fa","source":{"kind":"arxiv","id":"2411.18366","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.18366","created_at":"2026-05-20T00:02:47Z"},{"alias_kind":"arxiv_version","alias_value":"2411.18366v1","created_at":"2026-05-20T00:02:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.18366","created_at":"2026-05-20T00:02:47Z"},{"alias_kind":"pith_short_12","alias_value":"WKCXVI7TTZOV","created_at":"2026-05-20T00:02:47Z"},{"alias_kind":"pith_short_16","alias_value":"WKCXVI7TTZOVATO6","created_at":"2026-05-20T00:02:47Z"},{"alias_kind":"pith_short_8","alias_value":"WKCXVI7T","created_at":"2026-05-20T00:02:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:WKCXVI7TTZOVATO66EZBSP5LU3","target":"record","payload":{"canonical_record":{"source":{"id":"2411.18366","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2024-11-27T14:13:30Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"44731abd756aed55daea18d45ef4bc0f9367ab9e2d573d04fee2da972917c6ff","abstract_canon_sha256":"dec0cc07827c93210cfdc379f43cb4bf9bae5bed52299a3b948e84316bb96bde"},"schema_version":"1.0"},"canonical_sha256":"b2857aa3f39e5d504ddef132193faba6ff8be9d6b5243474af12eab6bf9775fa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:02:47.511130Z","signature_b64":"I50M53FqXpl4qZ0DZ72Jzv5bDENT19p2y1CXrbWw3B1r5bBMkvnaIuOi6AEXQBE7D2xVRJrbjrPzAebz4vbCCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b2857aa3f39e5d504ddef132193faba6ff8be9d6b5243474af12eab6bf9775fa","last_reissued_at":"2026-05-20T00:02:47.510385Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:02:47.510385Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.18366","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":"2026-05-20T00:02:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3Uf83RpdI+HqBpwPAggq9iQYpr7eG67op5CaO49AGRwoM4PKaSZ+SGxjp3HanA4J0JH/xEBf9bi7OcIO2OxBBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T00:18:58.764709Z"},"content_sha256":"cfe4f2f6e4b79ae9cd58e93996e67deed3d3086e7471034c68af7dcc4a353446","schema_version":"1.0","event_id":"sha256:cfe4f2f6e4b79ae9cd58e93996e67deed3d3086e7471034c68af7dcc4a353446"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:WKCXVI7TTZOVATO66EZBSP5LU3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Prime numbers and factorization of polynomials","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Jitender Singh","submitted_at":"2024-11-27T14:13:30Z","abstract_excerpt":"In this article, we obtain upper bounds on the number of irreducible factors of some classes of polynomials having integer coefficients, which in particular yield some of the well known irreducibility criteria. For devising our results, we use the information about prime factorization of the values taken by such polynomials at sufficiently large integer arguments along with the information about their root location in the complex plane. Further, these techniques are extended to bivariate polynomials over arbitrary fields using non-Archimedean absolute values, yielding extensions of the irreduc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.18366","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.18366/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-05-20T00:02:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MSTzWITXn/RVAP3u+4IVh/8RYe1NqyA1jvK7eBWDbOkscPjVJiASCIF4aRRMuiVbAhlSIN9Y5vEvsJ5KFtAcCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T00:18:58.765088Z"},"content_sha256":"9341be53d173ae104ae9b6e3a6f08afa85ad57582fbffa8911c1ff5072145b0a","schema_version":"1.0","event_id":"sha256:9341be53d173ae104ae9b6e3a6f08afa85ad57582fbffa8911c1ff5072145b0a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WKCXVI7TTZOVATO66EZBSP5LU3/bundle.json","state_url":"https://pith.science/pith/WKCXVI7TTZOVATO66EZBSP5LU3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WKCXVI7TTZOVATO66EZBSP5LU3/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":"2026-06-02T00:18:58Z","links":{"resolver":"https://pith.science/pith/WKCXVI7TTZOVATO66EZBSP5LU3","bundle":"https://pith.science/pith/WKCXVI7TTZOVATO66EZBSP5LU3/bundle.json","state":"https://pith.science/pith/WKCXVI7TTZOVATO66EZBSP5LU3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WKCXVI7TTZOVATO66EZBSP5LU3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:WKCXVI7TTZOVATO66EZBSP5LU3","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":"dec0cc07827c93210cfdc379f43cb4bf9bae5bed52299a3b948e84316bb96bde","cross_cats_sorted":["math.AG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2024-11-27T14:13:30Z","title_canon_sha256":"44731abd756aed55daea18d45ef4bc0f9367ab9e2d573d04fee2da972917c6ff"},"schema_version":"1.0","source":{"id":"2411.18366","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.18366","created_at":"2026-05-20T00:02:47Z"},{"alias_kind":"arxiv_version","alias_value":"2411.18366v1","created_at":"2026-05-20T00:02:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.18366","created_at":"2026-05-20T00:02:47Z"},{"alias_kind":"pith_short_12","alias_value":"WKCXVI7TTZOV","created_at":"2026-05-20T00:02:47Z"},{"alias_kind":"pith_short_16","alias_value":"WKCXVI7TTZOVATO6","created_at":"2026-05-20T00:02:47Z"},{"alias_kind":"pith_short_8","alias_value":"WKCXVI7T","created_at":"2026-05-20T00:02:47Z"}],"graph_snapshots":[{"event_id":"sha256:9341be53d173ae104ae9b6e3a6f08afa85ad57582fbffa8911c1ff5072145b0a","target":"graph","created_at":"2026-05-20T00:02:47Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2411.18366/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this article, we obtain upper bounds on the number of irreducible factors of some classes of polynomials having integer coefficients, which in particular yield some of the well known irreducibility criteria. For devising our results, we use the information about prime factorization of the values taken by such polynomials at sufficiently large integer arguments along with the information about their root location in the complex plane. Further, these techniques are extended to bivariate polynomials over arbitrary fields using non-Archimedean absolute values, yielding extensions of the irreduc","authors_text":"Jitender Singh","cross_cats":["math.AG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2024-11-27T14:13:30Z","title":"Prime numbers and factorization of polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.18366","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:cfe4f2f6e4b79ae9cd58e93996e67deed3d3086e7471034c68af7dcc4a353446","target":"record","created_at":"2026-05-20T00:02:47Z","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":"dec0cc07827c93210cfdc379f43cb4bf9bae5bed52299a3b948e84316bb96bde","cross_cats_sorted":["math.AG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2024-11-27T14:13:30Z","title_canon_sha256":"44731abd756aed55daea18d45ef4bc0f9367ab9e2d573d04fee2da972917c6ff"},"schema_version":"1.0","source":{"id":"2411.18366","kind":"arxiv","version":1}},"canonical_sha256":"b2857aa3f39e5d504ddef132193faba6ff8be9d6b5243474af12eab6bf9775fa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b2857aa3f39e5d504ddef132193faba6ff8be9d6b5243474af12eab6bf9775fa","first_computed_at":"2026-05-20T00:02:47.510385Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:02:47.510385Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"I50M53FqXpl4qZ0DZ72Jzv5bDENT19p2y1CXrbWw3B1r5bBMkvnaIuOi6AEXQBE7D2xVRJrbjrPzAebz4vbCCg==","signature_status":"signed_v1","signed_at":"2026-05-20T00:02:47.511130Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.18366","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cfe4f2f6e4b79ae9cd58e93996e67deed3d3086e7471034c68af7dcc4a353446","sha256:9341be53d173ae104ae9b6e3a6f08afa85ad57582fbffa8911c1ff5072145b0a"],"state_sha256":"8820c70187077f0ef3af0b5c77babcdc2b48539165dc5c0d51865ff996aa2502"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d4IsUEjmgTTZkEqB4ugG+TDsPJBK1nboJxwYDKxJlNarVc+sE6mr2QxUL9HAfYP6pN0nBF2mo2oK/AuoX/5rDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T00:18:58.767121Z","bundle_sha256":"c879ade6882aedb7fe8fc0a0254de76aa368703903316309eba88921eb630ab1"}}