{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:7D7QIE5VWF4IGBLLMBIG3MQXYO","short_pith_number":"pith:7D7QIE5V","canonical_record":{"source":{"id":"1405.3360","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2014-05-14T04:54:08Z","cross_cats_sorted":[],"title_canon_sha256":"b95cc0667539098f290783e65af8f3b933c820ea58326bf0f8bb52a885717951","abstract_canon_sha256":"cd59d3c1d5d0e7d9d7be400adb6be7d582bfe9b68e884112b83619ced12c43e3"},"schema_version":"1.0"},"canonical_sha256":"f8ff0413b5b17883056b60506db217c3b3ebcbbba545a77e91a182250fa4767a","source":{"kind":"arxiv","id":"1405.3360","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.3360","created_at":"2026-05-18T00:31:36Z"},{"alias_kind":"arxiv_version","alias_value":"1405.3360v2","created_at":"2026-05-18T00:31:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.3360","created_at":"2026-05-18T00:31:36Z"},{"alias_kind":"pith_short_12","alias_value":"7D7QIE5VWF4I","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"7D7QIE5VWF4IGBLL","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"7D7QIE5V","created_at":"2026-05-18T12:28:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:7D7QIE5VWF4IGBLLMBIG3MQXYO","target":"record","payload":{"canonical_record":{"source":{"id":"1405.3360","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2014-05-14T04:54:08Z","cross_cats_sorted":[],"title_canon_sha256":"b95cc0667539098f290783e65af8f3b933c820ea58326bf0f8bb52a885717951","abstract_canon_sha256":"cd59d3c1d5d0e7d9d7be400adb6be7d582bfe9b68e884112b83619ced12c43e3"},"schema_version":"1.0"},"canonical_sha256":"f8ff0413b5b17883056b60506db217c3b3ebcbbba545a77e91a182250fa4767a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:36.631249Z","signature_b64":"1lKWESBK0xONRsJTztax/9Fta/E4RgX2LbVoHiAfR6zsmN1MzPosrjnkQC7oBb248ve3apjdEGorv6XgXCuPBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f8ff0413b5b17883056b60506db217c3b3ebcbbba545a77e91a182250fa4767a","last_reissued_at":"2026-05-18T00:31:36.630396Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:36.630396Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.3360","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:31:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TSShtFCpcU/lqVEQNgSQWOc4o7Gs8ZP+7phnZ1r0b8ed5kr5mq1BQWXoeBlGSehrkwrl3WGiGJmL4mTgzEFTBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:21:18.285810Z"},"content_sha256":"94e8abc4e1efe7c48a424a3f3914ef720bf140cb80c9ee3e8bb7be9b3ba4242d","schema_version":"1.0","event_id":"sha256:94e8abc4e1efe7c48a424a3f3914ef720bf140cb80c9ee3e8bb7be9b3ba4242d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:7D7QIE5VWF4IGBLLMBIG3MQXYO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Nash Stability in the Hedonic Coalition Formation Games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.GT","authors_text":"Cengis Hasan, Eitan Altman, Jean-Marie Gorce","submitted_at":"2014-05-14T04:54:08Z","abstract_excerpt":"This paper studies the Nash stability in hedonic coalition formation games. We address the following issue: for a general problem formulation, is there any utility allocation method ensuring a Nash-stable partition? We propose the definition of the Nash-stable core. We study the conditions for having a non-empty Nash-stable core. More precisely, we show how relaxed efficiency in utility sharing method allows to ensure a non-empty Nash-stable core."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.3360","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T00:31:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EQNMplgD5qRhi8QSxLo5otlF0GeqFxcMuYLKl+8MjoHH36YGggaCJoeTnbwIsSTEMOLBXkz7wKR7ZIDUYlmeBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:21:18.286430Z"},"content_sha256":"67abc73e6e5235bed6f22a94cf652735c314ee1803d3bd51999567cbb9c6ba07","schema_version":"1.0","event_id":"sha256:67abc73e6e5235bed6f22a94cf652735c314ee1803d3bd51999567cbb9c6ba07"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7D7QIE5VWF4IGBLLMBIG3MQXYO/bundle.json","state_url":"https://pith.science/pith/7D7QIE5VWF4IGBLLMBIG3MQXYO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7D7QIE5VWF4IGBLLMBIG3MQXYO/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":"2026-05-26T21:21:18Z","links":{"resolver":"https://pith.science/pith/7D7QIE5VWF4IGBLLMBIG3MQXYO","bundle":"https://pith.science/pith/7D7QIE5VWF4IGBLLMBIG3MQXYO/bundle.json","state":"https://pith.science/pith/7D7QIE5VWF4IGBLLMBIG3MQXYO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7D7QIE5VWF4IGBLLMBIG3MQXYO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:7D7QIE5VWF4IGBLLMBIG3MQXYO","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":"cd59d3c1d5d0e7d9d7be400adb6be7d582bfe9b68e884112b83619ced12c43e3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2014-05-14T04:54:08Z","title_canon_sha256":"b95cc0667539098f290783e65af8f3b933c820ea58326bf0f8bb52a885717951"},"schema_version":"1.0","source":{"id":"1405.3360","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.3360","created_at":"2026-05-18T00:31:36Z"},{"alias_kind":"arxiv_version","alias_value":"1405.3360v2","created_at":"2026-05-18T00:31:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.3360","created_at":"2026-05-18T00:31:36Z"},{"alias_kind":"pith_short_12","alias_value":"7D7QIE5VWF4I","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"7D7QIE5VWF4IGBLL","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"7D7QIE5V","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:67abc73e6e5235bed6f22a94cf652735c314ee1803d3bd51999567cbb9c6ba07","target":"graph","created_at":"2026-05-18T00:31:36Z","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"},"paper":{"abstract_excerpt":"This paper studies the Nash stability in hedonic coalition formation games. We address the following issue: for a general problem formulation, is there any utility allocation method ensuring a Nash-stable partition? We propose the definition of the Nash-stable core. We study the conditions for having a non-empty Nash-stable core. More precisely, we show how relaxed efficiency in utility sharing method allows to ensure a non-empty Nash-stable core.","authors_text":"Cengis Hasan, Eitan Altman, Jean-Marie Gorce","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2014-05-14T04:54:08Z","title":"On the Nash Stability in the Hedonic Coalition Formation Games"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.3360","kind":"arxiv","version":2},"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":"sha256:94e8abc4e1efe7c48a424a3f3914ef720bf140cb80c9ee3e8bb7be9b3ba4242d","target":"record","created_at":"2026-05-18T00:31:36Z","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":"cd59d3c1d5d0e7d9d7be400adb6be7d582bfe9b68e884112b83619ced12c43e3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2014-05-14T04:54:08Z","title_canon_sha256":"b95cc0667539098f290783e65af8f3b933c820ea58326bf0f8bb52a885717951"},"schema_version":"1.0","source":{"id":"1405.3360","kind":"arxiv","version":2}},"canonical_sha256":"f8ff0413b5b17883056b60506db217c3b3ebcbbba545a77e91a182250fa4767a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f8ff0413b5b17883056b60506db217c3b3ebcbbba545a77e91a182250fa4767a","first_computed_at":"2026-05-18T00:31:36.630396Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:36.630396Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1lKWESBK0xONRsJTztax/9Fta/E4RgX2LbVoHiAfR6zsmN1MzPosrjnkQC7oBb248ve3apjdEGorv6XgXCuPBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:36.631249Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.3360","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:94e8abc4e1efe7c48a424a3f3914ef720bf140cb80c9ee3e8bb7be9b3ba4242d","sha256:67abc73e6e5235bed6f22a94cf652735c314ee1803d3bd51999567cbb9c6ba07"],"state_sha256":"a679936ef0ba5b926717ce123f5c7fcf1a4b59eceacda64bf74b7c748ba278e2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b6YOr6ZPIjq/Bbn2rSC/XdqhOk0nuFagseW6t6wEQnhhtB8wE5mW/z80aAttVdMynyAc5ZpHCLzUXQpQTElcAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T21:21:18.289564Z","bundle_sha256":"059e8b3a4962d8e90a26220328815e6b4eaa9d0f890317de4c0189fe1eb35542"}}