{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:FQHUYH37RKKZ6IIVJLKNGOCJJU","short_pith_number":"pith:FQHUYH37","canonical_record":{"source":{"id":"2507.04537","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2025-07-06T21:06:59Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"81602986cbe8f173d77c6eaab611c4078a1108bcf75a2db59bd4fa0f00de106b","abstract_canon_sha256":"bf2ff70936b973e1a2fc7062c5eba4c17ccf18728c94905678f6cb541c1844f5"},"schema_version":"1.0"},"canonical_sha256":"2c0f4c1f7f8a959f21154ad4d338494d14bb106a7a8bd0eae5fdf24d63202830","source":{"kind":"arxiv","id":"2507.04537","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.04537","created_at":"2026-07-05T11:32:49Z"},{"alias_kind":"arxiv_version","alias_value":"2507.04537v1","created_at":"2026-07-05T11:32:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.04537","created_at":"2026-07-05T11:32:49Z"},{"alias_kind":"pith_short_12","alias_value":"FQHUYH37RKKZ","created_at":"2026-07-05T11:32:49Z"},{"alias_kind":"pith_short_16","alias_value":"FQHUYH37RKKZ6IIV","created_at":"2026-07-05T11:32:49Z"},{"alias_kind":"pith_short_8","alias_value":"FQHUYH37","created_at":"2026-07-05T11:32:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:FQHUYH37RKKZ6IIVJLKNGOCJJU","target":"record","payload":{"canonical_record":{"source":{"id":"2507.04537","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2025-07-06T21:06:59Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"81602986cbe8f173d77c6eaab611c4078a1108bcf75a2db59bd4fa0f00de106b","abstract_canon_sha256":"bf2ff70936b973e1a2fc7062c5eba4c17ccf18728c94905678f6cb541c1844f5"},"schema_version":"1.0"},"canonical_sha256":"2c0f4c1f7f8a959f21154ad4d338494d14bb106a7a8bd0eae5fdf24d63202830","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:32:49.562530Z","signature_b64":"bDsLJfIFJlyEwN4qUElVwBx3A3zrS/ewbN5uo9LxJS22KmTj+g2MXQwL6ulSCLwUayGBwPYBobpzxrnJPd3lCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2c0f4c1f7f8a959f21154ad4d338494d14bb106a7a8bd0eae5fdf24d63202830","last_reissued_at":"2026-07-05T11:32:49.562053Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:32:49.562053Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.04537","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":"2026-07-05T11:32:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WirQP7kespeqoK9Nj6ruwOO+DiGCCDdu9re0sC6sI+E//JipEVrd1319bu1IkmQPt+yB+2sSP2HdyYiLBvUNAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-24T01:30:46.669566Z"},"content_sha256":"5154eb264bf49d0ad7c330796b02ec685d58b4a80a638d37a74f3b7264d4779b","schema_version":"1.0","event_id":"sha256:5154eb264bf49d0ad7c330796b02ec685d58b4a80a638d37a74f3b7264d4779b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:FQHUYH37RKKZ6IIVJLKNGOCJJU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Fair Periodic Assignment Problem","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.DS","authors_text":"Bart van Rossum, Rolf van Lieshout","submitted_at":"2025-07-06T21:06:59Z","abstract_excerpt":"We study the periodic assignment problem, in which a set of periodically repeating tasks must be assigned to workers within a repeating schedule. The classical efficiency objective is to minimize the number of workers required to operate the schedule. We propose a O(n log n) algorithm to solve this problem. Next, we formalize a notion of fairness among workers, and impose that each worker performs the same work over time. We analyze the resulting trade-off between efficiency and fairness, showing that the price of fairness is at most one extra worker, and that such a fair solution can always b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.04537","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/2507.04537/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":"2026-07-05T11:32:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LMC2NE2b4N82inhaKPXOZBGoFZkI5FwuTEyNEZXvHHIf9CwsfuDVmpRIQJXOR2dVtx5XDgIqoyhuSH9xLXs3BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-24T01:30:46.670098Z"},"content_sha256":"fc1f62868b770fa334d834279326128fc794e9156238306cea40e9b1adbb934e","schema_version":"1.0","event_id":"sha256:fc1f62868b770fa334d834279326128fc794e9156238306cea40e9b1adbb934e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FQHUYH37RKKZ6IIVJLKNGOCJJU/bundle.json","state_url":"https://pith.science/pith/FQHUYH37RKKZ6IIVJLKNGOCJJU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FQHUYH37RKKZ6IIVJLKNGOCJJU/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":"2026-08-24T01:30:46Z","links":{"resolver":"https://pith.science/pith/FQHUYH37RKKZ6IIVJLKNGOCJJU","bundle":"https://pith.science/pith/FQHUYH37RKKZ6IIVJLKNGOCJJU/bundle.json","state":"https://pith.science/pith/FQHUYH37RKKZ6IIVJLKNGOCJJU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FQHUYH37RKKZ6IIVJLKNGOCJJU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:FQHUYH37RKKZ6IIVJLKNGOCJJU","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":"bf2ff70936b973e1a2fc7062c5eba4c17ccf18728c94905678f6cb541c1844f5","cross_cats_sorted":["math.OC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2025-07-06T21:06:59Z","title_canon_sha256":"81602986cbe8f173d77c6eaab611c4078a1108bcf75a2db59bd4fa0f00de106b"},"schema_version":"1.0","source":{"id":"2507.04537","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.04537","created_at":"2026-07-05T11:32:49Z"},{"alias_kind":"arxiv_version","alias_value":"2507.04537v1","created_at":"2026-07-05T11:32:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.04537","created_at":"2026-07-05T11:32:49Z"},{"alias_kind":"pith_short_12","alias_value":"FQHUYH37RKKZ","created_at":"2026-07-05T11:32:49Z"},{"alias_kind":"pith_short_16","alias_value":"FQHUYH37RKKZ6IIV","created_at":"2026-07-05T11:32:49Z"},{"alias_kind":"pith_short_8","alias_value":"FQHUYH37","created_at":"2026-07-05T11:32:49Z"}],"graph_snapshots":[{"event_id":"sha256:fc1f62868b770fa334d834279326128fc794e9156238306cea40e9b1adbb934e","target":"graph","created_at":"2026-07-05T11:32:49Z","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/2507.04537/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the periodic assignment problem, in which a set of periodically repeating tasks must be assigned to workers within a repeating schedule. The classical efficiency objective is to minimize the number of workers required to operate the schedule. We propose a O(n log n) algorithm to solve this problem. Next, we formalize a notion of fairness among workers, and impose that each worker performs the same work over time. We analyze the resulting trade-off between efficiency and fairness, showing that the price of fairness is at most one extra worker, and that such a fair solution can always b","authors_text":"Bart van Rossum, Rolf van Lieshout","cross_cats":["math.OC"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2025-07-06T21:06:59Z","title":"The Fair Periodic Assignment Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.04537","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":"sha256:5154eb264bf49d0ad7c330796b02ec685d58b4a80a638d37a74f3b7264d4779b","target":"record","created_at":"2026-07-05T11:32:49Z","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":"bf2ff70936b973e1a2fc7062c5eba4c17ccf18728c94905678f6cb541c1844f5","cross_cats_sorted":["math.OC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2025-07-06T21:06:59Z","title_canon_sha256":"81602986cbe8f173d77c6eaab611c4078a1108bcf75a2db59bd4fa0f00de106b"},"schema_version":"1.0","source":{"id":"2507.04537","kind":"arxiv","version":1}},"canonical_sha256":"2c0f4c1f7f8a959f21154ad4d338494d14bb106a7a8bd0eae5fdf24d63202830","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2c0f4c1f7f8a959f21154ad4d338494d14bb106a7a8bd0eae5fdf24d63202830","first_computed_at":"2026-07-05T11:32:49.562053Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:32:49.562053Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bDsLJfIFJlyEwN4qUElVwBx3A3zrS/ewbN5uo9LxJS22KmTj+g2MXQwL6ulSCLwUayGBwPYBobpzxrnJPd3lCw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:32:49.562530Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.04537","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5154eb264bf49d0ad7c330796b02ec685d58b4a80a638d37a74f3b7264d4779b","sha256:fc1f62868b770fa334d834279326128fc794e9156238306cea40e9b1adbb934e"],"state_sha256":"cf7bc9b00d93ca5121175095827c159925c9ce38a4c1f22f0b0c71856f9bd014"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2W1da1NXK43/MafYo/KYiIjGZH7MaVqfzNOnJeX+Ppa3lNPSyeFANZIhn8c9yy/Ir1BJ9rY1hj0uOqnj1nGLCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-24T01:30:46.673850Z","bundle_sha256":"37548a18612ed240f4a893996aeb9c355c07a6663ae12238c6f9904e8f02556b"}}