{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:U46GYSGOVR6UG3OFX6ZOZVTMOQ","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":"f2c74525779b0c5236240cb9f5ed329c0bb4dc14c71af21224f9c22e9109619b","cross_cats_sorted":["cs.DM","cs.GT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2022-02-13T05:56:30Z","title_canon_sha256":"6724b7ca27c5ed6104bb0191ae13de4f40e3536224b9b2cea9b5e4176aac9fdb"},"schema_version":"1.0","source":{"id":"2202.06949","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2202.06949","created_at":"2026-07-05T05:20:09Z"},{"alias_kind":"arxiv_version","alias_value":"2202.06949v3","created_at":"2026-07-05T05:20:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2202.06949","created_at":"2026-07-05T05:20:09Z"},{"alias_kind":"pith_short_12","alias_value":"U46GYSGOVR6U","created_at":"2026-07-05T05:20:09Z"},{"alias_kind":"pith_short_16","alias_value":"U46GYSGOVR6UG3OF","created_at":"2026-07-05T05:20:09Z"},{"alias_kind":"pith_short_8","alias_value":"U46GYSGO","created_at":"2026-07-05T05:20:09Z"}],"graph_snapshots":[{"event_id":"sha256:7a1000d0b0f25e1200922b6e466aa7f7fe7b7378ca032a7eacc430142a885ddb","target":"graph","created_at":"2026-07-05T05:20:09Z","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/2202.06949/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the problem of partitioning a line segment into two subsets, so that $n$ finite measures all have the same ratio of values for the subsets. Letting $\\alpha\\in[0,1]$ denote the desired ratio, this generalises the PPA-complete consensus-halving problem, in which $\\alpha=\\frac{1}{2}$. Stromquist and Woodall showed that for any $\\alpha$, there exists a solution using $2n$ cuts of the segment. They also showed that if $\\alpha$ is irrational, that upper bound is almost optimal. In this work, we elaborate the bounds for rational values $\\alpha$. For $\\alpha = \\frac{\\ell}{k}$, we show a lo","authors_text":"Jiawei Li, Paul W. Goldberg","cross_cats":["cs.DM","cs.GT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2022-02-13T05:56:30Z","title":"Consensus Division in an Arbitrary Ratio"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.06949","kind":"arxiv","version":3},"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":"sha256:6a4c4665c2bd13cafabeaf3dd332385bfb5cf5022d64ad718ea1aedb9fe284b6","target":"record","created_at":"2026-07-05T05:20:09Z","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":"f2c74525779b0c5236240cb9f5ed329c0bb4dc14c71af21224f9c22e9109619b","cross_cats_sorted":["cs.DM","cs.GT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2022-02-13T05:56:30Z","title_canon_sha256":"6724b7ca27c5ed6104bb0191ae13de4f40e3536224b9b2cea9b5e4176aac9fdb"},"schema_version":"1.0","source":{"id":"2202.06949","kind":"arxiv","version":3}},"canonical_sha256":"a73c6c48ceac7d436dc5bfb2ecd66c7421d71f9e1485750f3349a0b927838cd5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a73c6c48ceac7d436dc5bfb2ecd66c7421d71f9e1485750f3349a0b927838cd5","first_computed_at":"2026-07-05T05:20:09.951240Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:20:09.951240Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yBC7tRyzwMgtGNs+XYHKXh/ryn1bqtRb8RZIl8PENijpW5RWUgKuHjFZEkFx5ohVSpbTQE3z6sfNzjeyBgo9Cw==","signature_status":"signed_v1","signed_at":"2026-07-05T05:20:09.951779Z","signed_message":"canonical_sha256_bytes"},"source_id":"2202.06949","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6a4c4665c2bd13cafabeaf3dd332385bfb5cf5022d64ad718ea1aedb9fe284b6","sha256:7a1000d0b0f25e1200922b6e466aa7f7fe7b7378ca032a7eacc430142a885ddb"],"state_sha256":"f883b00692c4c084fdb268daa57b2fe7b13596b740d3aa5e0eb5037230caac49"}