{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:U4U5SHHIR4FLK323AWDPZKJWIH","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":"8d055e8b83be7d5a8353dfe5700d75622a7add2fa701615507087b65deceb47c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.GT","submitted_at":"2026-06-11T08:40:42Z","title_canon_sha256":"610471a0f0d4eb61f7146f06b16d050cd5169dba92da962cc9edd4c13be393cd"},"schema_version":"1.0","source":{"id":"2606.13057","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.13057","created_at":"2026-06-12T01:09:38Z"},{"alias_kind":"arxiv_version","alias_value":"2606.13057v1","created_at":"2026-06-12T01:09:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.13057","created_at":"2026-06-12T01:09:38Z"},{"alias_kind":"pith_short_12","alias_value":"U4U5SHHIR4FL","created_at":"2026-06-12T01:09:38Z"},{"alias_kind":"pith_short_16","alias_value":"U4U5SHHIR4FLK323","created_at":"2026-06-12T01:09:38Z"},{"alias_kind":"pith_short_8","alias_value":"U4U5SHHI","created_at":"2026-06-12T01:09:38Z"}],"graph_snapshots":[{"event_id":"sha256:7bedf47fa06739dcce67a521eb98e72970b1d2d9e8a80427cc9ccb0e4626dcf5","target":"graph","created_at":"2026-06-12T01:09:38Z","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/2606.13057/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Maximin share (MMS) stands out as a central notion in fair resource allocation. It is known that exact MMS fairness is not always attainable, especially when agents differ along two dimensions: their valuations and their perceptions of the divisibility of resources. The former case with heterogeneous valuations has been widely studied in the literature. The latter, referred to as subjective divisibility by Bei et al., [Games Econ. Behav. 2025], remains much less explored.\n  We study MMS approximation under subjective divisibility. First, we prove that even in the unary valuation setting, where","authors_text":"Bo Li, Fangxiao Wang, Ke Ding, Xiaohui Bei","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.GT","submitted_at":"2026-06-11T08:40:42Z","title":"Approximate Maximin Share with Subjective Divisibility: Beating the 1/2 Barrier"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.13057","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":"sha256:691e79ef172af841af3bc13612cd0949a638f731f03eebc52795213eca0ae596","target":"record","created_at":"2026-06-12T01:09:38Z","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":"8d055e8b83be7d5a8353dfe5700d75622a7add2fa701615507087b65deceb47c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.GT","submitted_at":"2026-06-11T08:40:42Z","title_canon_sha256":"610471a0f0d4eb61f7146f06b16d050cd5169dba92da962cc9edd4c13be393cd"},"schema_version":"1.0","source":{"id":"2606.13057","kind":"arxiv","version":1}},"canonical_sha256":"a729d91ce88f0ab56f5b0586fca93641d96c947022f01a6453786c2ad907a44a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a729d91ce88f0ab56f5b0586fca93641d96c947022f01a6453786c2ad907a44a","first_computed_at":"2026-06-12T01:09:38.692836Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-12T01:09:38.692836Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7BBXJu26q8liBNuC5D99Wd4Qabr4V9Qpm96fRdzDXw2rWCgvkG/V9QFw6fdYH7n0U3kd81GeONPqhy6JpEiRAA==","signature_status":"signed_v1","signed_at":"2026-06-12T01:09:38.693238Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.13057","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:691e79ef172af841af3bc13612cd0949a638f731f03eebc52795213eca0ae596","sha256:7bedf47fa06739dcce67a521eb98e72970b1d2d9e8a80427cc9ccb0e4626dcf5"],"state_sha256":"fe6019d36a3c82d48975fdf79b799094682f52d431dbd5833ac5315094fb3237"}