{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:MMMQ3LDNDPSHCKTAPD56F22LBY","short_pith_number":"pith:MMMQ3LDN","canonical_record":{"source":{"id":"2401.12444","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2024-01-23T02:24:15Z","cross_cats_sorted":[],"title_canon_sha256":"f67196a94f15990b1fa9c9c1233c4ff26304b93fc09a8d5822661fde153aa4b8","abstract_canon_sha256":"4f5a9712c1546c7b8a27a4a0ff83f3e819acc6a6a0820d3cdc0d83e0a4f9a9fa"},"schema_version":"1.0"},"canonical_sha256":"63190dac6d1be4712a6078fbe2eb4b0e3b9f0e39da5a4a374f0aa92e41411647","source":{"kind":"arxiv","id":"2401.12444","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.12444","created_at":"2026-07-05T07:36:30Z"},{"alias_kind":"arxiv_version","alias_value":"2401.12444v1","created_at":"2026-07-05T07:36:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.12444","created_at":"2026-07-05T07:36:30Z"},{"alias_kind":"pith_short_12","alias_value":"MMMQ3LDNDPSH","created_at":"2026-07-05T07:36:30Z"},{"alias_kind":"pith_short_16","alias_value":"MMMQ3LDNDPSHCKTA","created_at":"2026-07-05T07:36:30Z"},{"alias_kind":"pith_short_8","alias_value":"MMMQ3LDN","created_at":"2026-07-05T07:36:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:MMMQ3LDNDPSHCKTAPD56F22LBY","target":"record","payload":{"canonical_record":{"source":{"id":"2401.12444","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2024-01-23T02:24:15Z","cross_cats_sorted":[],"title_canon_sha256":"f67196a94f15990b1fa9c9c1233c4ff26304b93fc09a8d5822661fde153aa4b8","abstract_canon_sha256":"4f5a9712c1546c7b8a27a4a0ff83f3e819acc6a6a0820d3cdc0d83e0a4f9a9fa"},"schema_version":"1.0"},"canonical_sha256":"63190dac6d1be4712a6078fbe2eb4b0e3b9f0e39da5a4a374f0aa92e41411647","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:36:30.935756Z","signature_b64":"uQ6BVWJNU9InumE3i3oFwohUraqtDAAZYoNeqaxGBW4Iep42Q3Bbz2yGQI0O7p9NyShHBLpg9nO7E6EhtF36Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"63190dac6d1be4712a6078fbe2eb4b0e3b9f0e39da5a4a374f0aa92e41411647","last_reissued_at":"2026-07-05T07:36:30.935419Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:36:30.935419Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2401.12444","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":"2026-07-05T07:36:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H/fBguvVwVI5/LsI2vIylW7cVdG9RxAMwOjHGM/BTemlGe9n64NBEA3PlnUsPRF5/PTnmKrKYZHfunFwogDsAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T17:13:54.798321Z"},"content_sha256":"7e26428e6a5d9236f2208a82098ce86578da11200ef13c1d9441349431cebd17","schema_version":"1.0","event_id":"sha256:7e26428e6a5d9236f2208a82098ce86578da11200ef13c1d9441349431cebd17"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:MMMQ3LDNDPSHCKTAPD56F22LBY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the atomicity of power monoids of Puiseux monoids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Eddy Li, Henrick Rabinovitz, Marcos Tirador, Pedro Rodriguez, Victor Gonzalez","submitted_at":"2024-01-23T02:24:15Z","abstract_excerpt":"A submonoid of the additive group $\\mathbb{Q}$ is called a Puiseux monoid if it consists of nonnegative rationals. Given a monoid $M$, the set consisting of all nonempty finite subsets of $M$ is also a monoid under the Minkowski sum, and it is called the (finitary) power monoid of $M$. In this paper we study atomicity and factorization properties in power monoids of Puiseux monoids. We specially focus on the ascent of the property of being atomic and both the bounded and the finite factorization properties (the ascending chain on principal ideals and the length-finite factorization properties "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.12444","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/2401.12444/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":"2026-07-05T07:36:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+Acich9C06ed/MMiv3LTqxdNhAHDhrRUX1nASem9ppod4MgHdA9ADXMd8SV9Yl56yIHYrgIFx0rbUj7JQKxBCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T17:13:54.798854Z"},"content_sha256":"ce44d8dbc098277f82198a2e0a12d7504104acd894f0d0d484c7d95d4fb14f18","schema_version":"1.0","event_id":"sha256:ce44d8dbc098277f82198a2e0a12d7504104acd894f0d0d484c7d95d4fb14f18"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MMMQ3LDNDPSHCKTAPD56F22LBY/bundle.json","state_url":"https://pith.science/pith/MMMQ3LDNDPSHCKTAPD56F22LBY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MMMQ3LDNDPSHCKTAPD56F22LBY/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":"2026-08-13T17:13:54Z","links":{"resolver":"https://pith.science/pith/MMMQ3LDNDPSHCKTAPD56F22LBY","bundle":"https://pith.science/pith/MMMQ3LDNDPSHCKTAPD56F22LBY/bundle.json","state":"https://pith.science/pith/MMMQ3LDNDPSHCKTAPD56F22LBY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MMMQ3LDNDPSHCKTAPD56F22LBY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:MMMQ3LDNDPSHCKTAPD56F22LBY","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":"4f5a9712c1546c7b8a27a4a0ff83f3e819acc6a6a0820d3cdc0d83e0a4f9a9fa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2024-01-23T02:24:15Z","title_canon_sha256":"f67196a94f15990b1fa9c9c1233c4ff26304b93fc09a8d5822661fde153aa4b8"},"schema_version":"1.0","source":{"id":"2401.12444","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.12444","created_at":"2026-07-05T07:36:30Z"},{"alias_kind":"arxiv_version","alias_value":"2401.12444v1","created_at":"2026-07-05T07:36:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.12444","created_at":"2026-07-05T07:36:30Z"},{"alias_kind":"pith_short_12","alias_value":"MMMQ3LDNDPSH","created_at":"2026-07-05T07:36:30Z"},{"alias_kind":"pith_short_16","alias_value":"MMMQ3LDNDPSHCKTA","created_at":"2026-07-05T07:36:30Z"},{"alias_kind":"pith_short_8","alias_value":"MMMQ3LDN","created_at":"2026-07-05T07:36:30Z"}],"graph_snapshots":[{"event_id":"sha256:ce44d8dbc098277f82198a2e0a12d7504104acd894f0d0d484c7d95d4fb14f18","target":"graph","created_at":"2026-07-05T07:36:30Z","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/2401.12444/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A submonoid of the additive group $\\mathbb{Q}$ is called a Puiseux monoid if it consists of nonnegative rationals. Given a monoid $M$, the set consisting of all nonempty finite subsets of $M$ is also a monoid under the Minkowski sum, and it is called the (finitary) power monoid of $M$. In this paper we study atomicity and factorization properties in power monoids of Puiseux monoids. We specially focus on the ascent of the property of being atomic and both the bounded and the finite factorization properties (the ascending chain on principal ideals and the length-finite factorization properties ","authors_text":"Eddy Li, Henrick Rabinovitz, Marcos Tirador, Pedro Rodriguez, Victor Gonzalez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2024-01-23T02:24:15Z","title":"On the atomicity of power monoids of Puiseux monoids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.12444","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":"sha256:7e26428e6a5d9236f2208a82098ce86578da11200ef13c1d9441349431cebd17","target":"record","created_at":"2026-07-05T07:36:30Z","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":"4f5a9712c1546c7b8a27a4a0ff83f3e819acc6a6a0820d3cdc0d83e0a4f9a9fa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2024-01-23T02:24:15Z","title_canon_sha256":"f67196a94f15990b1fa9c9c1233c4ff26304b93fc09a8d5822661fde153aa4b8"},"schema_version":"1.0","source":{"id":"2401.12444","kind":"arxiv","version":1}},"canonical_sha256":"63190dac6d1be4712a6078fbe2eb4b0e3b9f0e39da5a4a374f0aa92e41411647","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"63190dac6d1be4712a6078fbe2eb4b0e3b9f0e39da5a4a374f0aa92e41411647","first_computed_at":"2026-07-05T07:36:30.935419Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:36:30.935419Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uQ6BVWJNU9InumE3i3oFwohUraqtDAAZYoNeqaxGBW4Iep42Q3Bbz2yGQI0O7p9NyShHBLpg9nO7E6EhtF36Cg==","signature_status":"signed_v1","signed_at":"2026-07-05T07:36:30.935756Z","signed_message":"canonical_sha256_bytes"},"source_id":"2401.12444","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7e26428e6a5d9236f2208a82098ce86578da11200ef13c1d9441349431cebd17","sha256:ce44d8dbc098277f82198a2e0a12d7504104acd894f0d0d484c7d95d4fb14f18"],"state_sha256":"e38b9568f4dbb49460a176e61a5ad8eaa1470dbd11d13cb8ea80bff8a6f60673"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"574plx9dVvnMo0jHnyy9hp5JUwa4uasRcPAUtC1P0VBU8fAht8GHW4wlQKeAUcNK4JIyFV3u+CHqE5gLgMGxBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T17:13:54.837128Z","bundle_sha256":"4feea70e27dd20dd53a556f1491554883702375a2b3f59a0869890db8449c3b5"}}