{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:LDCBNWQFGVZT2YJSPXHP2JZZUD","short_pith_number":"pith:LDCBNWQF","canonical_record":{"source":{"id":"1403.3881","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2014-03-16T04:12:57Z","cross_cats_sorted":["cs.CC","cs.DC","cs.DM","cs.MA"],"title_canon_sha256":"2b384c1997ec1e42ae16636b78e80621206d647182f2c90be5389425e95ff6a4","abstract_canon_sha256":"537efabae7ebc8f5f86ec7f8d52a400a3061bcabac8bed87bc6199513e485398"},"schema_version":"1.0"},"canonical_sha256":"58c416da0535733d61327dcefd2739a0e5bb7331b38be385a56a59a06a5bc89c","source":{"kind":"arxiv","id":"1403.3881","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.3881","created_at":"2026-05-18T01:55:53Z"},{"alias_kind":"arxiv_version","alias_value":"1403.3881v3","created_at":"2026-05-18T01:55:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.3881","created_at":"2026-05-18T01:55:53Z"},{"alias_kind":"pith_short_12","alias_value":"LDCBNWQFGVZT","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"LDCBNWQFGVZT2YJS","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"LDCBNWQF","created_at":"2026-05-18T12:28:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:LDCBNWQFGVZT2YJSPXHP2JZZUD","target":"record","payload":{"canonical_record":{"source":{"id":"1403.3881","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2014-03-16T04:12:57Z","cross_cats_sorted":["cs.CC","cs.DC","cs.DM","cs.MA"],"title_canon_sha256":"2b384c1997ec1e42ae16636b78e80621206d647182f2c90be5389425e95ff6a4","abstract_canon_sha256":"537efabae7ebc8f5f86ec7f8d52a400a3061bcabac8bed87bc6199513e485398"},"schema_version":"1.0"},"canonical_sha256":"58c416da0535733d61327dcefd2739a0e5bb7331b38be385a56a59a06a5bc89c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:55:53.505598Z","signature_b64":"0lL4lbeawSfU6t0Wh2hfEGBDATz8/qccu9/1Zx9gsaCOcvVmZHvWUcmkRqPmlHhDClRO/QW9giAGcFQmq/7cDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"58c416da0535733d61327dcefd2739a0e5bb7331b38be385a56a59a06a5bc89c","last_reissued_at":"2026-05-18T01:55:53.504995Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:55:53.504995Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.3881","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:55:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZladumgzW8XmmYwQTO2hWSDM04P02W0vRF67BKbePN8FgNOgHBDQu5QU+CjhRm1/dXkKl9C+gjTYROJ7nUMXCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T20:26:49.877829Z"},"content_sha256":"0a00397b2a128fd1419bdb5dad030b3f6394f6d76a8e5a2b3666b8c66fc4553b","schema_version":"1.0","event_id":"sha256:0a00397b2a128fd1419bdb5dad030b3f6394f6d76a8e5a2b3666b8c66fc4553b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:LDCBNWQFGVZT2YJSPXHP2JZZUD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Complexity of Equilibrium in Diffusion Games on Social Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DC","cs.DM","cs.MA"],"primary_cat":"cs.GT","authors_text":"Seyed Rasoul Etesami, Tamer Basar","submitted_at":"2014-03-16T04:12:57Z","abstract_excerpt":"In this paper, we consider the competitive diffusion game, and study the existence of its pure-strategy Nash equilibrium when defined over general undirected networks. We first determine the set of pure-strategy Nash equilibria for two special but well-known classes of networks, namely the lattice and the hypercube. Characterizing the utility of the players in terms of graphical distances of their initial seed placements to other nodes in the network, we show that in general networks the decision process on the existence of pure-strategy Nash equilibrium is an NP-hard problem. Following this, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3881","kind":"arxiv","version":3},"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":"2026-05-18T01:55:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7bNQcQr8t5zmmXvA1tIFbkXOP9j6m+TjntcLwJvDYZjcknCS8H6WU/MSNlm8qR8CYWSLwGYW1iu3rXwI9muMDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T20:26:49.878649Z"},"content_sha256":"23093d85b7941fd60593f0bb55c28e496ecb15d30f122abdf1bcabb1a5f2f7f1","schema_version":"1.0","event_id":"sha256:23093d85b7941fd60593f0bb55c28e496ecb15d30f122abdf1bcabb1a5f2f7f1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LDCBNWQFGVZT2YJSPXHP2JZZUD/bundle.json","state_url":"https://pith.science/pith/LDCBNWQFGVZT2YJSPXHP2JZZUD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LDCBNWQFGVZT2YJSPXHP2JZZUD/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":"2026-05-31T20:26:49Z","links":{"resolver":"https://pith.science/pith/LDCBNWQFGVZT2YJSPXHP2JZZUD","bundle":"https://pith.science/pith/LDCBNWQFGVZT2YJSPXHP2JZZUD/bundle.json","state":"https://pith.science/pith/LDCBNWQFGVZT2YJSPXHP2JZZUD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LDCBNWQFGVZT2YJSPXHP2JZZUD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:LDCBNWQFGVZT2YJSPXHP2JZZUD","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":"537efabae7ebc8f5f86ec7f8d52a400a3061bcabac8bed87bc6199513e485398","cross_cats_sorted":["cs.CC","cs.DC","cs.DM","cs.MA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2014-03-16T04:12:57Z","title_canon_sha256":"2b384c1997ec1e42ae16636b78e80621206d647182f2c90be5389425e95ff6a4"},"schema_version":"1.0","source":{"id":"1403.3881","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.3881","created_at":"2026-05-18T01:55:53Z"},{"alias_kind":"arxiv_version","alias_value":"1403.3881v3","created_at":"2026-05-18T01:55:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.3881","created_at":"2026-05-18T01:55:53Z"},{"alias_kind":"pith_short_12","alias_value":"LDCBNWQFGVZT","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"LDCBNWQFGVZT2YJS","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"LDCBNWQF","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:23093d85b7941fd60593f0bb55c28e496ecb15d30f122abdf1bcabb1a5f2f7f1","target":"graph","created_at":"2026-05-18T01:55:53Z","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":"In this paper, we consider the competitive diffusion game, and study the existence of its pure-strategy Nash equilibrium when defined over general undirected networks. We first determine the set of pure-strategy Nash equilibria for two special but well-known classes of networks, namely the lattice and the hypercube. Characterizing the utility of the players in terms of graphical distances of their initial seed placements to other nodes in the network, we show that in general networks the decision process on the existence of pure-strategy Nash equilibrium is an NP-hard problem. Following this, ","authors_text":"Seyed Rasoul Etesami, Tamer Basar","cross_cats":["cs.CC","cs.DC","cs.DM","cs.MA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2014-03-16T04:12:57Z","title":"Complexity of Equilibrium in Diffusion Games on Social Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3881","kind":"arxiv","version":3},"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":"sha256:0a00397b2a128fd1419bdb5dad030b3f6394f6d76a8e5a2b3666b8c66fc4553b","target":"record","created_at":"2026-05-18T01:55:53Z","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":"537efabae7ebc8f5f86ec7f8d52a400a3061bcabac8bed87bc6199513e485398","cross_cats_sorted":["cs.CC","cs.DC","cs.DM","cs.MA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2014-03-16T04:12:57Z","title_canon_sha256":"2b384c1997ec1e42ae16636b78e80621206d647182f2c90be5389425e95ff6a4"},"schema_version":"1.0","source":{"id":"1403.3881","kind":"arxiv","version":3}},"canonical_sha256":"58c416da0535733d61327dcefd2739a0e5bb7331b38be385a56a59a06a5bc89c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"58c416da0535733d61327dcefd2739a0e5bb7331b38be385a56a59a06a5bc89c","first_computed_at":"2026-05-18T01:55:53.504995Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:55:53.504995Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0lL4lbeawSfU6t0Wh2hfEGBDATz8/qccu9/1Zx9gsaCOcvVmZHvWUcmkRqPmlHhDClRO/QW9giAGcFQmq/7cDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:55:53.505598Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.3881","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0a00397b2a128fd1419bdb5dad030b3f6394f6d76a8e5a2b3666b8c66fc4553b","sha256:23093d85b7941fd60593f0bb55c28e496ecb15d30f122abdf1bcabb1a5f2f7f1"],"state_sha256":"1125edae756bab8e5e4453e3479c98e5f39ce3bc2f03c45ca938f021f8e664ea"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mC4xku7Rlc9kRwJiBY/iCSeLeXrgdnskkrYPqTIbdqEf2tSpIkiBjyQNT3GGgPIgLjCLSeR8WjU9yuG57i+EDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T20:26:49.883453Z","bundle_sha256":"b23d5b7c777da12442d1d5b1100d41ecbbe38b2940d46719f3f6511325264ddd"}}