{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:D4LBNJHMXFRMLAD2KB7I3I7ABP","short_pith_number":"pith:D4LBNJHM","canonical_record":{"source":{"id":"2506.03638","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2025-06-04T07:32:13Z","cross_cats_sorted":[],"title_canon_sha256":"48f7e9c95ade7428976732a53dd33fc61ecc8166d16167265d4601f00b32417a","abstract_canon_sha256":"5611d27a902f29be4407d911479f9ef97a9d9392311e30f4c509875680ee2d06"},"schema_version":"1.0"},"canonical_sha256":"1f1616a4ecb962c5807a507e8da3e00bdcd93e26f2aa8bfd7c006447b061d2f8","source":{"kind":"arxiv","id":"2506.03638","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.03638","created_at":"2026-07-05T11:15:49Z"},{"alias_kind":"arxiv_version","alias_value":"2506.03638v1","created_at":"2026-07-05T11:15:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.03638","created_at":"2026-07-05T11:15:49Z"},{"alias_kind":"pith_short_12","alias_value":"D4LBNJHMXFRM","created_at":"2026-07-05T11:15:49Z"},{"alias_kind":"pith_short_16","alias_value":"D4LBNJHMXFRMLAD2","created_at":"2026-07-05T11:15:49Z"},{"alias_kind":"pith_short_8","alias_value":"D4LBNJHM","created_at":"2026-07-05T11:15:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:D4LBNJHMXFRMLAD2KB7I3I7ABP","target":"record","payload":{"canonical_record":{"source":{"id":"2506.03638","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2025-06-04T07:32:13Z","cross_cats_sorted":[],"title_canon_sha256":"48f7e9c95ade7428976732a53dd33fc61ecc8166d16167265d4601f00b32417a","abstract_canon_sha256":"5611d27a902f29be4407d911479f9ef97a9d9392311e30f4c509875680ee2d06"},"schema_version":"1.0"},"canonical_sha256":"1f1616a4ecb962c5807a507e8da3e00bdcd93e26f2aa8bfd7c006447b061d2f8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:15:49.179305Z","signature_b64":"m3zQ9KX9mzUPv6TMs8Fyyhij7PhgKnsVkanr5J6ZtSJXXf7mk2xU/1D1OWqwUkQCBMrFrLxRUeWqVs8mZD2sBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f1616a4ecb962c5807a507e8da3e00bdcd93e26f2aa8bfd7c006447b061d2f8","last_reissued_at":"2026-07-05T11:15:49.178840Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:15:49.178840Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.03638","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":"2026-07-05T11:15:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yiJYuZbFvUesS82eqpPqb1eC4Tc7vtfVUW1PCEzdHiHRjsgFhTkaG+1k3KF/ALeNi/upYAXiSe/G60EF3uJsAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T04:01:25.198432Z"},"content_sha256":"76740ef531c7a1351f36f6918427014060933e46c510c43ff26d8c8679f38764","schema_version":"1.0","event_id":"sha256:76740ef531c7a1351f36f6918427014060933e46c510c43ff26d8c8679f38764"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:D4LBNJHMXFRMLAD2KB7I3I7ABP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stability Notions for Hospital Residents with Sizes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Girija Limaye, Haricharan Balasundaram, J B Krishnashree, Meghana Nasre","submitted_at":"2025-06-04T07:32:13Z","abstract_excerpt":"The Hospital Residents problem with sizes (HRS) is a generalization of the well-studied hospital residents (HR) problem. In the HRS problem, an agent $a$ has a size $s(a)$ and the agent occupies $s(a)$ many positions of the hospital $h$ when assigned to $h$. The notion of stability in this setting is suitably modified, and it is known that deciding whether an HRS instance admits a stable matching is NP-hard under severe restrictions. In this work, we explore a variation of stability, which we term occupancy-based stability. This notion was defined by McDermid and Manlove in their work, however"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.03638","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/2506.03638/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":"2026-07-05T11:15:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nTe61jXs/a6iYSqueoeI8e11CQ64uMLNaChsZt23isNuvymLxjVXnYW27tWlfuJFxgO4U/Bc3mHWjlYvrYtlDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T04:01:25.199350Z"},"content_sha256":"485690769d820c4cacb34f165123c88b069f078b44933d54f2487fbc21767d2e","schema_version":"1.0","event_id":"sha256:485690769d820c4cacb34f165123c88b069f078b44933d54f2487fbc21767d2e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D4LBNJHMXFRMLAD2KB7I3I7ABP/bundle.json","state_url":"https://pith.science/pith/D4LBNJHMXFRMLAD2KB7I3I7ABP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D4LBNJHMXFRMLAD2KB7I3I7ABP/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":"2026-08-08T04:01:25Z","links":{"resolver":"https://pith.science/pith/D4LBNJHMXFRMLAD2KB7I3I7ABP","bundle":"https://pith.science/pith/D4LBNJHMXFRMLAD2KB7I3I7ABP/bundle.json","state":"https://pith.science/pith/D4LBNJHMXFRMLAD2KB7I3I7ABP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D4LBNJHMXFRMLAD2KB7I3I7ABP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:D4LBNJHMXFRMLAD2KB7I3I7ABP","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":"5611d27a902f29be4407d911479f9ef97a9d9392311e30f4c509875680ee2d06","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2025-06-04T07:32:13Z","title_canon_sha256":"48f7e9c95ade7428976732a53dd33fc61ecc8166d16167265d4601f00b32417a"},"schema_version":"1.0","source":{"id":"2506.03638","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.03638","created_at":"2026-07-05T11:15:49Z"},{"alias_kind":"arxiv_version","alias_value":"2506.03638v1","created_at":"2026-07-05T11:15:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.03638","created_at":"2026-07-05T11:15:49Z"},{"alias_kind":"pith_short_12","alias_value":"D4LBNJHMXFRM","created_at":"2026-07-05T11:15:49Z"},{"alias_kind":"pith_short_16","alias_value":"D4LBNJHMXFRMLAD2","created_at":"2026-07-05T11:15:49Z"},{"alias_kind":"pith_short_8","alias_value":"D4LBNJHM","created_at":"2026-07-05T11:15:49Z"}],"graph_snapshots":[{"event_id":"sha256:485690769d820c4cacb34f165123c88b069f078b44933d54f2487fbc21767d2e","target":"graph","created_at":"2026-07-05T11:15:49Z","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/2506.03638/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Hospital Residents problem with sizes (HRS) is a generalization of the well-studied hospital residents (HR) problem. In the HRS problem, an agent $a$ has a size $s(a)$ and the agent occupies $s(a)$ many positions of the hospital $h$ when assigned to $h$. The notion of stability in this setting is suitably modified, and it is known that deciding whether an HRS instance admits a stable matching is NP-hard under severe restrictions. In this work, we explore a variation of stability, which we term occupancy-based stability. This notion was defined by McDermid and Manlove in their work, however","authors_text":"Girija Limaye, Haricharan Balasundaram, J B Krishnashree, Meghana Nasre","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2025-06-04T07:32:13Z","title":"Stability Notions for Hospital Residents with Sizes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.03638","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":"sha256:76740ef531c7a1351f36f6918427014060933e46c510c43ff26d8c8679f38764","target":"record","created_at":"2026-07-05T11:15:49Z","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":"5611d27a902f29be4407d911479f9ef97a9d9392311e30f4c509875680ee2d06","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2025-06-04T07:32:13Z","title_canon_sha256":"48f7e9c95ade7428976732a53dd33fc61ecc8166d16167265d4601f00b32417a"},"schema_version":"1.0","source":{"id":"2506.03638","kind":"arxiv","version":1}},"canonical_sha256":"1f1616a4ecb962c5807a507e8da3e00bdcd93e26f2aa8bfd7c006447b061d2f8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f1616a4ecb962c5807a507e8da3e00bdcd93e26f2aa8bfd7c006447b061d2f8","first_computed_at":"2026-07-05T11:15:49.178840Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:15:49.178840Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"m3zQ9KX9mzUPv6TMs8Fyyhij7PhgKnsVkanr5J6ZtSJXXf7mk2xU/1D1OWqwUkQCBMrFrLxRUeWqVs8mZD2sBw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:15:49.179305Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.03638","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:76740ef531c7a1351f36f6918427014060933e46c510c43ff26d8c8679f38764","sha256:485690769d820c4cacb34f165123c88b069f078b44933d54f2487fbc21767d2e"],"state_sha256":"52bdfbb7162e01003315a552d9a08c61c7eb61aba591320eabbc726e592faec4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6uQilGWox7+FLzFQ2GUw3nh0zYuA9xKG4LVEFZQ+wd94zJ5vDHIl5HYznkmodEs7jlBJggWMA2HTMouNgK5DCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T04:01:25.205902Z","bundle_sha256":"46b2ae463ba82d91bfd27b1870aa9fc406c04f1d655ea37d4c22d9ea6c3f57b6"}}