{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:TG5JSGPHF7V73D2FKCC344TTPO","short_pith_number":"pith:TG5JSGPH","canonical_record":{"source":{"id":"1407.5442","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2014-07-21T10:11:54Z","cross_cats_sorted":["cs.GT","physics.soc-ph"],"title_canon_sha256":"f23ac5a917ac3a6657fb44403848d829add6bf44370c69e5a80c7ce21bd0ebaf","abstract_canon_sha256":"aa0bb8b0714d91f08699a34ffc4d849aebd1764de3b5d8e92ea34cc36520dbdb"},"schema_version":"1.0"},"canonical_sha256":"99ba9919e72febfd8f455085be72737b8d60038e134b94d6d16ab453ecfb069d","source":{"kind":"arxiv","id":"1407.5442","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.5442","created_at":"2026-05-18T00:51:19Z"},{"alias_kind":"arxiv_version","alias_value":"1407.5442v2","created_at":"2026-05-18T00:51:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.5442","created_at":"2026-05-18T00:51:19Z"},{"alias_kind":"pith_short_12","alias_value":"TG5JSGPHF7V7","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"TG5JSGPHF7V73D2F","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"TG5JSGPH","created_at":"2026-05-18T12:28:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:TG5JSGPHF7V73D2FKCC344TTPO","target":"record","payload":{"canonical_record":{"source":{"id":"1407.5442","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2014-07-21T10:11:54Z","cross_cats_sorted":["cs.GT","physics.soc-ph"],"title_canon_sha256":"f23ac5a917ac3a6657fb44403848d829add6bf44370c69e5a80c7ce21bd0ebaf","abstract_canon_sha256":"aa0bb8b0714d91f08699a34ffc4d849aebd1764de3b5d8e92ea34cc36520dbdb"},"schema_version":"1.0"},"canonical_sha256":"99ba9919e72febfd8f455085be72737b8d60038e134b94d6d16ab453ecfb069d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:19.093787Z","signature_b64":"4zjb929WdX+GpHs9RXbP22Usbao7feLlpweemnd7lYLoWPXvF9dkEPNprLqZFC6EVU/K3W6xJEy0XT8b2P2xDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"99ba9919e72febfd8f455085be72737b8d60038e134b94d6d16ab453ecfb069d","last_reissued_at":"2026-05-18T00:51:19.093173Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:19.093173Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.5442","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":"2026-05-18T00:51:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nEePAmmjJSAcAceKd5//KsNGbaS1bkQlXQG8548QgrfqnZ26PwVwzFjD8cLdi1GL1Iso+VS9+q0HCjbhj7viCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T12:11:46.798689Z"},"content_sha256":"dccd486078538160319adeef72654df0c2a92786531bd36820b1332070d74063","schema_version":"1.0","event_id":"sha256:dccd486078538160319adeef72654df0c2a92786531bd36820b1332070d74063"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:TG5JSGPHF7V73D2FKCC344TTPO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cooperative Game Theoretic Solution Concepts for top-$k$ Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.GT","physics.soc-ph"],"primary_cat":"cs.SI","authors_text":"Akanksha Meghlan, Swapnil Dhamal, Y. Narahari","submitted_at":"2014-07-21T10:11:54Z","abstract_excerpt":"The problem of finding the $k$ most critical nodes, referred to as the $top\\text{-}k$ problem, is a very important one in several contexts such as information diffusion and preference aggregation in social networks, clustering of data points, etc. It has been observed in the literature that the value allotted to a node by most of the popular cooperative game theoretic solution concepts, acts as a good measure of appropriateness of that node (or a data point) to be included in the $top\\text{-}k$ set, by itself. However, in general, nodes having the highest $k$ values are not the desirable $top\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5442","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":"2026-05-18T00:51:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wFukS5efDy2CMe+GIjD9+ktzFsn1rjwvEKp7cusdZotpeTK8dwFOGvPjvWRWR/og0nmCimWpIRWcDNPhORw9Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T12:11:46.799165Z"},"content_sha256":"1e754330d01ee352c3513e9655cfec7c861a0ed34753516bdf49b185b65d2c9a","schema_version":"1.0","event_id":"sha256:1e754330d01ee352c3513e9655cfec7c861a0ed34753516bdf49b185b65d2c9a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TG5JSGPHF7V73D2FKCC344TTPO/bundle.json","state_url":"https://pith.science/pith/TG5JSGPHF7V73D2FKCC344TTPO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TG5JSGPHF7V73D2FKCC344TTPO/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":"2026-06-26T12:11:46Z","links":{"resolver":"https://pith.science/pith/TG5JSGPHF7V73D2FKCC344TTPO","bundle":"https://pith.science/pith/TG5JSGPHF7V73D2FKCC344TTPO/bundle.json","state":"https://pith.science/pith/TG5JSGPHF7V73D2FKCC344TTPO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TG5JSGPHF7V73D2FKCC344TTPO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:TG5JSGPHF7V73D2FKCC344TTPO","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":"aa0bb8b0714d91f08699a34ffc4d849aebd1764de3b5d8e92ea34cc36520dbdb","cross_cats_sorted":["cs.GT","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2014-07-21T10:11:54Z","title_canon_sha256":"f23ac5a917ac3a6657fb44403848d829add6bf44370c69e5a80c7ce21bd0ebaf"},"schema_version":"1.0","source":{"id":"1407.5442","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.5442","created_at":"2026-05-18T00:51:19Z"},{"alias_kind":"arxiv_version","alias_value":"1407.5442v2","created_at":"2026-05-18T00:51:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.5442","created_at":"2026-05-18T00:51:19Z"},{"alias_kind":"pith_short_12","alias_value":"TG5JSGPHF7V7","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"TG5JSGPHF7V73D2F","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"TG5JSGPH","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:1e754330d01ee352c3513e9655cfec7c861a0ed34753516bdf49b185b65d2c9a","target":"graph","created_at":"2026-05-18T00:51:19Z","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":"The problem of finding the $k$ most critical nodes, referred to as the $top\\text{-}k$ problem, is a very important one in several contexts such as information diffusion and preference aggregation in social networks, clustering of data points, etc. It has been observed in the literature that the value allotted to a node by most of the popular cooperative game theoretic solution concepts, acts as a good measure of appropriateness of that node (or a data point) to be included in the $top\\text{-}k$ set, by itself. However, in general, nodes having the highest $k$ values are not the desirable $top\\","authors_text":"Akanksha Meghlan, Swapnil Dhamal, Y. Narahari","cross_cats":["cs.GT","physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2014-07-21T10:11:54Z","title":"Cooperative Game Theoretic Solution Concepts for top-$k$ Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5442","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:dccd486078538160319adeef72654df0c2a92786531bd36820b1332070d74063","target":"record","created_at":"2026-05-18T00:51:19Z","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":"aa0bb8b0714d91f08699a34ffc4d849aebd1764de3b5d8e92ea34cc36520dbdb","cross_cats_sorted":["cs.GT","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2014-07-21T10:11:54Z","title_canon_sha256":"f23ac5a917ac3a6657fb44403848d829add6bf44370c69e5a80c7ce21bd0ebaf"},"schema_version":"1.0","source":{"id":"1407.5442","kind":"arxiv","version":2}},"canonical_sha256":"99ba9919e72febfd8f455085be72737b8d60038e134b94d6d16ab453ecfb069d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"99ba9919e72febfd8f455085be72737b8d60038e134b94d6d16ab453ecfb069d","first_computed_at":"2026-05-18T00:51:19.093173Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:19.093173Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4zjb929WdX+GpHs9RXbP22Usbao7feLlpweemnd7lYLoWPXvF9dkEPNprLqZFC6EVU/K3W6xJEy0XT8b2P2xDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:19.093787Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.5442","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dccd486078538160319adeef72654df0c2a92786531bd36820b1332070d74063","sha256:1e754330d01ee352c3513e9655cfec7c861a0ed34753516bdf49b185b65d2c9a"],"state_sha256":"58a05f67d51b43daf9db8b38eaf44f3ade02cf1958bbdccec51b271a74081417"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pUK3ZPiV4cvO2F1S4OqUpp9pw8xqtmMmL/jja5TMyXgPZQM6S/IKeY84HDgsn7Jc2RkBucsvnpKgPRS/nnPQDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T12:11:46.801748Z","bundle_sha256":"629a84932b2cfb365088ea4fda6222c072440f077c1bcc64720ba9c3efeea76e"}}