{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:ZSPZ6XIGPRETUJYN2R6U6IBWDT","short_pith_number":"pith:ZSPZ6XIG","canonical_record":{"source":{"id":"2504.10722","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2025-04-14T21:28:35Z","cross_cats_sorted":[],"title_canon_sha256":"8019a8790db9fff6b08cf31bb4c77d2242b1613b46884a6b7553505a28977291","abstract_canon_sha256":"3bee02d9e63e7edbfe1986aaef3be54ec11c6016ec9c0c078c0310890773e6ff"},"schema_version":"1.0"},"canonical_sha256":"cc9f9f5d067c493a270dd47d4f20361cee29e13c9a38da601218acf5431c7495","source":{"kind":"arxiv","id":"2504.10722","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.10722","created_at":"2026-07-05T10:51:37Z"},{"alias_kind":"arxiv_version","alias_value":"2504.10722v2","created_at":"2026-07-05T10:51:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.10722","created_at":"2026-07-05T10:51:37Z"},{"alias_kind":"pith_short_12","alias_value":"ZSPZ6XIGPRET","created_at":"2026-07-05T10:51:37Z"},{"alias_kind":"pith_short_16","alias_value":"ZSPZ6XIGPRETUJYN","created_at":"2026-07-05T10:51:37Z"},{"alias_kind":"pith_short_8","alias_value":"ZSPZ6XIG","created_at":"2026-07-05T10:51:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:ZSPZ6XIGPRETUJYN2R6U6IBWDT","target":"record","payload":{"canonical_record":{"source":{"id":"2504.10722","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2025-04-14T21:28:35Z","cross_cats_sorted":[],"title_canon_sha256":"8019a8790db9fff6b08cf31bb4c77d2242b1613b46884a6b7553505a28977291","abstract_canon_sha256":"3bee02d9e63e7edbfe1986aaef3be54ec11c6016ec9c0c078c0310890773e6ff"},"schema_version":"1.0"},"canonical_sha256":"cc9f9f5d067c493a270dd47d4f20361cee29e13c9a38da601218acf5431c7495","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:51:37.002509Z","signature_b64":"WsA62hI71gIUw6nBRxZCpr/gfOSiAxtdupurzg0RQQIl1Y9x5OwzmjdJxlRJEkLDqij50fnxbTukGgceod1vAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cc9f9f5d067c493a270dd47d4f20361cee29e13c9a38da601218acf5431c7495","last_reissued_at":"2026-07-05T10:51:37.001978Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:51:37.001978Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2504.10722","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":"2026-07-05T10:51:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ngzSduySof/SC+CFBKwbIS5sQEngDHr5K3GWgRjuDv7FUtxKUP66jaYGVlwt7ynb/9syZJFBlWowTHX3SGyPDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T00:08:59.487246Z"},"content_sha256":"461759e23ef7542e939765878407555a453d9b7c7b7563dc8beb4389dc83d2df","schema_version":"1.0","event_id":"sha256:461759e23ef7542e939765878407555a453d9b7c7b7563dc8beb4389dc83d2df"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:ZSPZ6XIGPRETUJYN2R6U6IBWDT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On GL-domains and the ascent of the IDF property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Ishan Panpaliya, Victor Gonzalez","submitted_at":"2025-04-14T21:28:35Z","abstract_excerpt":"Following the terminology introduced by Arnold and Sheldon back in 1975, we say that an integral domain $D$ is a GL-domain if the product of any two primitive polynomials over $D$ is again a primitive polynomial. In this paper, we study the class of GL-domains. First, we propose a characterization of GL-domain in terms of certain elements we call prime-like. Then we identify a new class of GL-domains. An integral domain $D$ is also said to have the IDF property provided that each nonzero element of $D$ is divisible by only finitely many non-associate irreducible divisors. It was proved by Malc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.10722","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2504.10722/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":"2026-07-05T10:51:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CKlUoc+ftofBT8OwAQQ3oMEajCZzdCYlzOfFD2Nq3t1DimTDDcYShhjtZavPqxyLQHMpHEfwbQxIwI4TN9KvDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T00:08:59.487618Z"},"content_sha256":"70b24603ea6c51b407ce66caae9c26200425ec16f4853f75d60b8ba52f013e37","schema_version":"1.0","event_id":"sha256:70b24603ea6c51b407ce66caae9c26200425ec16f4853f75d60b8ba52f013e37"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZSPZ6XIGPRETUJYN2R6U6IBWDT/bundle.json","state_url":"https://pith.science/pith/ZSPZ6XIGPRETUJYN2R6U6IBWDT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZSPZ6XIGPRETUJYN2R6U6IBWDT/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":"2026-08-14T00:08:59Z","links":{"resolver":"https://pith.science/pith/ZSPZ6XIGPRETUJYN2R6U6IBWDT","bundle":"https://pith.science/pith/ZSPZ6XIGPRETUJYN2R6U6IBWDT/bundle.json","state":"https://pith.science/pith/ZSPZ6XIGPRETUJYN2R6U6IBWDT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZSPZ6XIGPRETUJYN2R6U6IBWDT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:ZSPZ6XIGPRETUJYN2R6U6IBWDT","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":"3bee02d9e63e7edbfe1986aaef3be54ec11c6016ec9c0c078c0310890773e6ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2025-04-14T21:28:35Z","title_canon_sha256":"8019a8790db9fff6b08cf31bb4c77d2242b1613b46884a6b7553505a28977291"},"schema_version":"1.0","source":{"id":"2504.10722","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.10722","created_at":"2026-07-05T10:51:37Z"},{"alias_kind":"arxiv_version","alias_value":"2504.10722v2","created_at":"2026-07-05T10:51:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.10722","created_at":"2026-07-05T10:51:37Z"},{"alias_kind":"pith_short_12","alias_value":"ZSPZ6XIGPRET","created_at":"2026-07-05T10:51:37Z"},{"alias_kind":"pith_short_16","alias_value":"ZSPZ6XIGPRETUJYN","created_at":"2026-07-05T10:51:37Z"},{"alias_kind":"pith_short_8","alias_value":"ZSPZ6XIG","created_at":"2026-07-05T10:51:37Z"}],"graph_snapshots":[{"event_id":"sha256:70b24603ea6c51b407ce66caae9c26200425ec16f4853f75d60b8ba52f013e37","target":"graph","created_at":"2026-07-05T10:51:37Z","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/2504.10722/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Following the terminology introduced by Arnold and Sheldon back in 1975, we say that an integral domain $D$ is a GL-domain if the product of any two primitive polynomials over $D$ is again a primitive polynomial. In this paper, we study the class of GL-domains. First, we propose a characterization of GL-domain in terms of certain elements we call prime-like. Then we identify a new class of GL-domains. An integral domain $D$ is also said to have the IDF property provided that each nonzero element of $D$ is divisible by only finitely many non-associate irreducible divisors. It was proved by Malc","authors_text":"Ishan Panpaliya, Victor Gonzalez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2025-04-14T21:28:35Z","title":"On GL-domains and the ascent of the IDF property"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.10722","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":"sha256:461759e23ef7542e939765878407555a453d9b7c7b7563dc8beb4389dc83d2df","target":"record","created_at":"2026-07-05T10:51:37Z","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":"3bee02d9e63e7edbfe1986aaef3be54ec11c6016ec9c0c078c0310890773e6ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2025-04-14T21:28:35Z","title_canon_sha256":"8019a8790db9fff6b08cf31bb4c77d2242b1613b46884a6b7553505a28977291"},"schema_version":"1.0","source":{"id":"2504.10722","kind":"arxiv","version":2}},"canonical_sha256":"cc9f9f5d067c493a270dd47d4f20361cee29e13c9a38da601218acf5431c7495","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cc9f9f5d067c493a270dd47d4f20361cee29e13c9a38da601218acf5431c7495","first_computed_at":"2026-07-05T10:51:37.001978Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:51:37.001978Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WsA62hI71gIUw6nBRxZCpr/gfOSiAxtdupurzg0RQQIl1Y9x5OwzmjdJxlRJEkLDqij50fnxbTukGgceod1vAA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:51:37.002509Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.10722","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:461759e23ef7542e939765878407555a453d9b7c7b7563dc8beb4389dc83d2df","sha256:70b24603ea6c51b407ce66caae9c26200425ec16f4853f75d60b8ba52f013e37"],"state_sha256":"03d3be0fbb5c1b7730493aa02824fd8b50095322778e768d2fe6871ea97be43d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GbpkI0n2ZPlDIMplsndqvLiyby/1XyGk5mxnfGtaOmuTAma+bmOK//unspGOxTE9+HpbH9K/OnvkK1h3CmzQDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T00:08:59.489941Z","bundle_sha256":"abea50edf2ec08796a23f43339e0cffac3788eee4ef6aa680770e420852d6322"}}