{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:W54MLGUQXVSD5DS4FGGV5ETNDK","short_pith_number":"pith:W54MLGUQ","canonical_record":{"source":{"id":"2411.16151","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AC","submitted_at":"2024-11-25T07:21:46Z","cross_cats_sorted":[],"title_canon_sha256":"60fa273a379bdbce5821bda13bb40387e0304ce2dd847191ac83e646bf7bccaf","abstract_canon_sha256":"a3b3b009e9c91361e4062fdbbb1aa7e674cee4024d2ab3c7ef1cc95d4ebcfe60"},"schema_version":"1.0"},"canonical_sha256":"b778c59a90bd643e8e5c298d5e926d1aa1aab3348b60accad12832e0bf8ca4d5","source":{"kind":"arxiv","id":"2411.16151","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.16151","created_at":"2026-07-05T09:40:05Z"},{"alias_kind":"arxiv_version","alias_value":"2411.16151v1","created_at":"2026-07-05T09:40:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.16151","created_at":"2026-07-05T09:40:05Z"},{"alias_kind":"pith_short_12","alias_value":"W54MLGUQXVSD","created_at":"2026-07-05T09:40:05Z"},{"alias_kind":"pith_short_16","alias_value":"W54MLGUQXVSD5DS4","created_at":"2026-07-05T09:40:05Z"},{"alias_kind":"pith_short_8","alias_value":"W54MLGUQ","created_at":"2026-07-05T09:40:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:W54MLGUQXVSD5DS4FGGV5ETNDK","target":"record","payload":{"canonical_record":{"source":{"id":"2411.16151","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AC","submitted_at":"2024-11-25T07:21:46Z","cross_cats_sorted":[],"title_canon_sha256":"60fa273a379bdbce5821bda13bb40387e0304ce2dd847191ac83e646bf7bccaf","abstract_canon_sha256":"a3b3b009e9c91361e4062fdbbb1aa7e674cee4024d2ab3c7ef1cc95d4ebcfe60"},"schema_version":"1.0"},"canonical_sha256":"b778c59a90bd643e8e5c298d5e926d1aa1aab3348b60accad12832e0bf8ca4d5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:40:05.253365Z","signature_b64":"yIg2bs3yZI4EUlPmStRU3u3iqGk9Z68CdcvnA1bKD47XuAaCNT+cKufTw4RIRxyC3soDWGdV6iI7MhHUbr2/Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b778c59a90bd643e8e5c298d5e926d1aa1aab3348b60accad12832e0bf8ca4d5","last_reissued_at":"2026-07-05T09:40:05.252899Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:40:05.252899Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.16151","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":"2026-07-05T09:40:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c0XTEkkmdrzxzRgegP/B7h51TUlN9/FNq05wdj5bX+mlsBJN9RuhCXJezDzvvLjv68oNtncLfra/06V2DCUhCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T22:35:46.312328Z"},"content_sha256":"1a3e9a5591dade274aef8b978fea02d133cc59e0d88b4004ad0930f0eb7d9e11","schema_version":"1.0","event_id":"sha256:1a3e9a5591dade274aef8b978fea02d133cc59e0d88b4004ad0930f0eb7d9e11"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:W54MLGUQXVSD5DS4FGGV5ETNDK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the atomicity of one-dimensional monoid algebras","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Ishan Panpaliya","submitted_at":"2024-11-25T07:21:46Z","abstract_excerpt":"The ascending chain condition on principal ideals (ACCP) is almost always complementary to atomicity within integral domains: in fact, Cohn initially stated that these two conditions were equivalent. This assertion has been shown to be false, however most counterexamples require technical algebraic constructions. In 2017, Gotti conjectured that for every $q$ in the set $S := ((0, 1) \\cap \\mathbb{Q}) \\setminus {\\mathbb{N}}^{-1}_{> 1}$, atomicity ascends from the exponentially cyclic Puiseux monoid $M_q$ to its monoid algebra over the field of rationals. If this conjecture were true, it would pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.16151","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/2411.16151/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":"2026-07-05T09:40:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"upbomIZx6WKrlHSWgjj5MlPVTFsFhcDO2Z8D1+6P6iNX8+xZpbMfKDnLzNDX4/KMEno8MImp4acjQtZ/JC+0CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T22:35:46.312943Z"},"content_sha256":"abb8fa02cece811ff673541f070286e7aa8c2cf1fe9a6db00c0950dc17e24ca2","schema_version":"1.0","event_id":"sha256:abb8fa02cece811ff673541f070286e7aa8c2cf1fe9a6db00c0950dc17e24ca2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W54MLGUQXVSD5DS4FGGV5ETNDK/bundle.json","state_url":"https://pith.science/pith/W54MLGUQXVSD5DS4FGGV5ETNDK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W54MLGUQXVSD5DS4FGGV5ETNDK/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":"2026-08-12T22:35:46Z","links":{"resolver":"https://pith.science/pith/W54MLGUQXVSD5DS4FGGV5ETNDK","bundle":"https://pith.science/pith/W54MLGUQXVSD5DS4FGGV5ETNDK/bundle.json","state":"https://pith.science/pith/W54MLGUQXVSD5DS4FGGV5ETNDK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W54MLGUQXVSD5DS4FGGV5ETNDK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:W54MLGUQXVSD5DS4FGGV5ETNDK","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":"a3b3b009e9c91361e4062fdbbb1aa7e674cee4024d2ab3c7ef1cc95d4ebcfe60","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AC","submitted_at":"2024-11-25T07:21:46Z","title_canon_sha256":"60fa273a379bdbce5821bda13bb40387e0304ce2dd847191ac83e646bf7bccaf"},"schema_version":"1.0","source":{"id":"2411.16151","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.16151","created_at":"2026-07-05T09:40:05Z"},{"alias_kind":"arxiv_version","alias_value":"2411.16151v1","created_at":"2026-07-05T09:40:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.16151","created_at":"2026-07-05T09:40:05Z"},{"alias_kind":"pith_short_12","alias_value":"W54MLGUQXVSD","created_at":"2026-07-05T09:40:05Z"},{"alias_kind":"pith_short_16","alias_value":"W54MLGUQXVSD5DS4","created_at":"2026-07-05T09:40:05Z"},{"alias_kind":"pith_short_8","alias_value":"W54MLGUQ","created_at":"2026-07-05T09:40:05Z"}],"graph_snapshots":[{"event_id":"sha256:abb8fa02cece811ff673541f070286e7aa8c2cf1fe9a6db00c0950dc17e24ca2","target":"graph","created_at":"2026-07-05T09:40:05Z","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/2411.16151/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The ascending chain condition on principal ideals (ACCP) is almost always complementary to atomicity within integral domains: in fact, Cohn initially stated that these two conditions were equivalent. This assertion has been shown to be false, however most counterexamples require technical algebraic constructions. In 2017, Gotti conjectured that for every $q$ in the set $S := ((0, 1) \\cap \\mathbb{Q}) \\setminus {\\mathbb{N}}^{-1}_{> 1}$, atomicity ascends from the exponentially cyclic Puiseux monoid $M_q$ to its monoid algebra over the field of rationals. If this conjecture were true, it would pr","authors_text":"Ishan Panpaliya","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AC","submitted_at":"2024-11-25T07:21:46Z","title":"On the atomicity of one-dimensional monoid algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.16151","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":"sha256:1a3e9a5591dade274aef8b978fea02d133cc59e0d88b4004ad0930f0eb7d9e11","target":"record","created_at":"2026-07-05T09:40:05Z","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":"a3b3b009e9c91361e4062fdbbb1aa7e674cee4024d2ab3c7ef1cc95d4ebcfe60","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AC","submitted_at":"2024-11-25T07:21:46Z","title_canon_sha256":"60fa273a379bdbce5821bda13bb40387e0304ce2dd847191ac83e646bf7bccaf"},"schema_version":"1.0","source":{"id":"2411.16151","kind":"arxiv","version":1}},"canonical_sha256":"b778c59a90bd643e8e5c298d5e926d1aa1aab3348b60accad12832e0bf8ca4d5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b778c59a90bd643e8e5c298d5e926d1aa1aab3348b60accad12832e0bf8ca4d5","first_computed_at":"2026-07-05T09:40:05.252899Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:40:05.252899Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yIg2bs3yZI4EUlPmStRU3u3iqGk9Z68CdcvnA1bKD47XuAaCNT+cKufTw4RIRxyC3soDWGdV6iI7MhHUbr2/Dg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:40:05.253365Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.16151","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a3e9a5591dade274aef8b978fea02d133cc59e0d88b4004ad0930f0eb7d9e11","sha256:abb8fa02cece811ff673541f070286e7aa8c2cf1fe9a6db00c0950dc17e24ca2"],"state_sha256":"9e8a95eb9958a3d12bc9fd492171858a9d7e77f9ccbfce10106014599ba49e58"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lti19sMBH9oO2A9c/0ty5LwDqxCYnxeGn6bQ5zSLWaJoeejKPLCKF2Mv69rbQ9NfAMZCCyDHoWJaxJ5SoX+vBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T22:35:46.318573Z","bundle_sha256":"c80e1a9e2a6847cfb91f615dea09e0388e7a3ccf3ae0be56c8c8c50378896b58"}}