{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:TADQMKV7L6W6PPF7ZMKEW2KTWR","short_pith_number":"pith:TADQMKV7","canonical_record":{"source":{"id":"1401.6428","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-01-23T16:45:24Z","cross_cats_sorted":["cs.GT"],"title_canon_sha256":"69d1b0c7dcfe848117d1e8d74435b8ea663dd2367657e4c504e9612b878ba0f8","abstract_canon_sha256":"2632ad6ed7a93dcc4e7686f691214a2e2c81c4615881bb695de5f8a7c9810d33"},"schema_version":"1.0"},"canonical_sha256":"9807062abf5fade7bcbfcb144b6953b4588c8b922724ab36938bd743792feced","source":{"kind":"arxiv","id":"1401.6428","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.6428","created_at":"2026-05-18T03:01:12Z"},{"alias_kind":"arxiv_version","alias_value":"1401.6428v1","created_at":"2026-05-18T03:01:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.6428","created_at":"2026-05-18T03:01:12Z"},{"alias_kind":"pith_short_12","alias_value":"TADQMKV7L6W6","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"TADQMKV7L6W6PPF7","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"TADQMKV7","created_at":"2026-05-18T12:28:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:TADQMKV7L6W6PPF7ZMKEW2KTWR","target":"record","payload":{"canonical_record":{"source":{"id":"1401.6428","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-01-23T16:45:24Z","cross_cats_sorted":["cs.GT"],"title_canon_sha256":"69d1b0c7dcfe848117d1e8d74435b8ea663dd2367657e4c504e9612b878ba0f8","abstract_canon_sha256":"2632ad6ed7a93dcc4e7686f691214a2e2c81c4615881bb695de5f8a7c9810d33"},"schema_version":"1.0"},"canonical_sha256":"9807062abf5fade7bcbfcb144b6953b4588c8b922724ab36938bd743792feced","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:12.022387Z","signature_b64":"Tr5VxeVUG1SWufxukT9ykvekys1BHc1kTY61IQU5fL2YmkeWPPH9IbTxdP2jwROCZCsF3TUOTHWsibA5NCnxAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9807062abf5fade7bcbfcb144b6953b4588c8b922724ab36938bd743792feced","last_reissued_at":"2026-05-18T03:01:12.021662Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:12.021662Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.6428","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":"2026-05-18T03:01:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KNzo74fXbG0n9rmc0UO4bFcEzKiYDg8/Brc5RfczpaVVWnG7yh9OXg44w4tbP9SEcXJuqFaJFyYN/RIcO3c9DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T00:34:04.579037Z"},"content_sha256":"02e8b3f51d304c8bd22f7989dca1df1bf82fadb04be64878ecd7b7029c548cea","schema_version":"1.0","event_id":"sha256:02e8b3f51d304c8bd22f7989dca1df1bf82fadb04be64878ecd7b7029c548cea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:TADQMKV7L6W6PPF7ZMKEW2KTWR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Coalition Structure Generation over Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.GT"],"primary_cat":"cs.DS","authors_text":"Maria Polukarov, Nicholas R. Jennings, Thomas Voice","submitted_at":"2014-01-23T16:45:24Z","abstract_excerpt":"We give the analysis of the computational complexity of coalition structure generation over graphs. Given an undirected graph G = (N,E) and a valuation function v : P(N) \\to R over the subsets of nodes, the problem is to find a partition of N into connected subsets, that maximises the sum of the components values. This problem is generally NP-complete; in particular, it is hard for a defined class of valuation functions which are independent of disconnected members - that is, two nodes have no effect on each other's marginal contribution to their vertex separator. Nonetheless, for all such fun"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.6428","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":""},"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":"2026-05-18T03:01:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jNQQ+40B34J3/SDwU+o/XK/Vw1nGJA6dv7SRQ5X/aICsQYTunHzf07G6cBToteHdU5a9EM99AeMP9jlz+tRyBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T00:34:04.579679Z"},"content_sha256":"9aff57de51edd74b7ecc0d7998acb2b00b53791eba0656110c8fbeae3e4ca182","schema_version":"1.0","event_id":"sha256:9aff57de51edd74b7ecc0d7998acb2b00b53791eba0656110c8fbeae3e4ca182"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TADQMKV7L6W6PPF7ZMKEW2KTWR/bundle.json","state_url":"https://pith.science/pith/TADQMKV7L6W6PPF7ZMKEW2KTWR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TADQMKV7L6W6PPF7ZMKEW2KTWR/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":"2026-05-26T00:34:04Z","links":{"resolver":"https://pith.science/pith/TADQMKV7L6W6PPF7ZMKEW2KTWR","bundle":"https://pith.science/pith/TADQMKV7L6W6PPF7ZMKEW2KTWR/bundle.json","state":"https://pith.science/pith/TADQMKV7L6W6PPF7ZMKEW2KTWR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TADQMKV7L6W6PPF7ZMKEW2KTWR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:TADQMKV7L6W6PPF7ZMKEW2KTWR","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":"2632ad6ed7a93dcc4e7686f691214a2e2c81c4615881bb695de5f8a7c9810d33","cross_cats_sorted":["cs.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-01-23T16:45:24Z","title_canon_sha256":"69d1b0c7dcfe848117d1e8d74435b8ea663dd2367657e4c504e9612b878ba0f8"},"schema_version":"1.0","source":{"id":"1401.6428","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.6428","created_at":"2026-05-18T03:01:12Z"},{"alias_kind":"arxiv_version","alias_value":"1401.6428v1","created_at":"2026-05-18T03:01:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.6428","created_at":"2026-05-18T03:01:12Z"},{"alias_kind":"pith_short_12","alias_value":"TADQMKV7L6W6","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"TADQMKV7L6W6PPF7","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"TADQMKV7","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:9aff57de51edd74b7ecc0d7998acb2b00b53791eba0656110c8fbeae3e4ca182","target":"graph","created_at":"2026-05-18T03:01:12Z","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":"We give the analysis of the computational complexity of coalition structure generation over graphs. Given an undirected graph G = (N,E) and a valuation function v : P(N) \\to R over the subsets of nodes, the problem is to find a partition of N into connected subsets, that maximises the sum of the components values. This problem is generally NP-complete; in particular, it is hard for a defined class of valuation functions which are independent of disconnected members - that is, two nodes have no effect on each other's marginal contribution to their vertex separator. Nonetheless, for all such fun","authors_text":"Maria Polukarov, Nicholas R. Jennings, Thomas Voice","cross_cats":["cs.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-01-23T16:45:24Z","title":"Coalition Structure Generation over Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.6428","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":"sha256:02e8b3f51d304c8bd22f7989dca1df1bf82fadb04be64878ecd7b7029c548cea","target":"record","created_at":"2026-05-18T03:01:12Z","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":"2632ad6ed7a93dcc4e7686f691214a2e2c81c4615881bb695de5f8a7c9810d33","cross_cats_sorted":["cs.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-01-23T16:45:24Z","title_canon_sha256":"69d1b0c7dcfe848117d1e8d74435b8ea663dd2367657e4c504e9612b878ba0f8"},"schema_version":"1.0","source":{"id":"1401.6428","kind":"arxiv","version":1}},"canonical_sha256":"9807062abf5fade7bcbfcb144b6953b4588c8b922724ab36938bd743792feced","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9807062abf5fade7bcbfcb144b6953b4588c8b922724ab36938bd743792feced","first_computed_at":"2026-05-18T03:01:12.021662Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:01:12.021662Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Tr5VxeVUG1SWufxukT9ykvekys1BHc1kTY61IQU5fL2YmkeWPPH9IbTxdP2jwROCZCsF3TUOTHWsibA5NCnxAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:01:12.022387Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.6428","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:02e8b3f51d304c8bd22f7989dca1df1bf82fadb04be64878ecd7b7029c548cea","sha256:9aff57de51edd74b7ecc0d7998acb2b00b53791eba0656110c8fbeae3e4ca182"],"state_sha256":"c4cb323812554d3d0d07002611ca7f60f798049af15e77df2963800eb2936eb9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UAhvs4YDMPL/FuaAV/jEatq8gkew+sO/51fqyhHsu8JD/18Fv/bFvGtjLsSMu7SkXTRJH784JRAhJG1udQ0QCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T00:34:04.581916Z","bundle_sha256":"ec56c616b1dc33cef1af9627617c2be72d8b3a39c8816128d7b18c812f9a4563"}}