{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:CO3TL5RWLNAIT6XX5QTMDF3P4Q","short_pith_number":"pith:CO3TL5RW","canonical_record":{"source":{"id":"1301.7592","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2013-01-31T12:31:05Z","cross_cats_sorted":["cs.SI"],"title_canon_sha256":"54a7a30cb0fc20e64cf765886e9e92538c431e91bd5fdfb775d39868b1df5a9e","abstract_canon_sha256":"c9dd593bcbfa6dbb691d30b6574b2c8346f9e21abbba04edd67a9d7b821b023c"},"schema_version":"1.0"},"canonical_sha256":"13b735f6365b4089faf7ec26c1976fe41ff3c77ec3843f465706e86bf6266807","source":{"kind":"arxiv","id":"1301.7592","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.7592","created_at":"2026-05-18T03:24:41Z"},{"alias_kind":"arxiv_version","alias_value":"1301.7592v2","created_at":"2026-05-18T03:24:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.7592","created_at":"2026-05-18T03:24:41Z"},{"alias_kind":"pith_short_12","alias_value":"CO3TL5RWLNAI","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"CO3TL5RWLNAIT6XX","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"CO3TL5RW","created_at":"2026-05-18T12:27:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:CO3TL5RWLNAIT6XX5QTMDF3P4Q","target":"record","payload":{"canonical_record":{"source":{"id":"1301.7592","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2013-01-31T12:31:05Z","cross_cats_sorted":["cs.SI"],"title_canon_sha256":"54a7a30cb0fc20e64cf765886e9e92538c431e91bd5fdfb775d39868b1df5a9e","abstract_canon_sha256":"c9dd593bcbfa6dbb691d30b6574b2c8346f9e21abbba04edd67a9d7b821b023c"},"schema_version":"1.0"},"canonical_sha256":"13b735f6365b4089faf7ec26c1976fe41ff3c77ec3843f465706e86bf6266807","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:24:41.405638Z","signature_b64":"chZ3aynKzlDML/KrAKDgZlO9vWOQIbYn0ie2Rnsa2amB+bFuIBVw70/abt3iFcGr0nQ8f3f/fivnq/8mwU1vBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"13b735f6365b4089faf7ec26c1976fe41ff3c77ec3843f465706e86bf6266807","last_reissued_at":"2026-05-18T03:24:41.405106Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:24:41.405106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.7592","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":"2026-05-18T03:24:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p6PT1tlDiSTLUFgsSDT6m3FcswxoIWEC3uvrDHpxZlPpwyEYtbAQP3AesWzFYqylB1S14L4vjHQ74er0TZTSDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T04:58:10.071094Z"},"content_sha256":"d3ded0267b95e986031c4e341df4e4f810f59cb63b97c93530e7473b355938c3","schema_version":"1.0","event_id":"sha256:d3ded0267b95e986031c4e341df4e4f810f59cb63b97c93530e7473b355938c3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:CO3TL5RWLNAIT6XX5QTMDF3P4Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Paradoxes in Social Networks with Multiple Products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SI"],"primary_cat":"cs.GT","authors_text":"Evangelos Markakis, Krzysztof R. Apt, Sunil Simon","submitted_at":"2013-01-31T12:31:05Z","abstract_excerpt":"Recently, we introduced in arXiv:1105.2434 a model for product adoption in social networks with multiple products, where the agents, influenced by their neighbours, can adopt one out of several alternatives. We identify and analyze here four types of paradoxes that can arise in these networks. To this end, we use social network games that we recently introduced in arxiv:1202.2209. These paradoxes shed light on possible inefficiencies arising when one modifies the sets of products available to the agents forming a social network. One of the paradoxes corresponds to the well-known Braess paradox"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.7592","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":"2026-05-18T03:24:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MxF691tbzA5Me1iGOnOqJI6J4qAHdO6JXkH+oRgOq+RKctvJI6mA5Q+V7PlDc/mI/v/R2b+KoyyltG9nxsR5BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T04:58:10.071784Z"},"content_sha256":"3c3356c93b5757411ae54fd8cd776fc1383195b6ff2b63511cb0d6742460800d","schema_version":"1.0","event_id":"sha256:3c3356c93b5757411ae54fd8cd776fc1383195b6ff2b63511cb0d6742460800d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CO3TL5RWLNAIT6XX5QTMDF3P4Q/bundle.json","state_url":"https://pith.science/pith/CO3TL5RWLNAIT6XX5QTMDF3P4Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CO3TL5RWLNAIT6XX5QTMDF3P4Q/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":"2026-05-26T04:58:10Z","links":{"resolver":"https://pith.science/pith/CO3TL5RWLNAIT6XX5QTMDF3P4Q","bundle":"https://pith.science/pith/CO3TL5RWLNAIT6XX5QTMDF3P4Q/bundle.json","state":"https://pith.science/pith/CO3TL5RWLNAIT6XX5QTMDF3P4Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CO3TL5RWLNAIT6XX5QTMDF3P4Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:CO3TL5RWLNAIT6XX5QTMDF3P4Q","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":"c9dd593bcbfa6dbb691d30b6574b2c8346f9e21abbba04edd67a9d7b821b023c","cross_cats_sorted":["cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2013-01-31T12:31:05Z","title_canon_sha256":"54a7a30cb0fc20e64cf765886e9e92538c431e91bd5fdfb775d39868b1df5a9e"},"schema_version":"1.0","source":{"id":"1301.7592","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.7592","created_at":"2026-05-18T03:24:41Z"},{"alias_kind":"arxiv_version","alias_value":"1301.7592v2","created_at":"2026-05-18T03:24:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.7592","created_at":"2026-05-18T03:24:41Z"},{"alias_kind":"pith_short_12","alias_value":"CO3TL5RWLNAI","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"CO3TL5RWLNAIT6XX","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"CO3TL5RW","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:3c3356c93b5757411ae54fd8cd776fc1383195b6ff2b63511cb0d6742460800d","target":"graph","created_at":"2026-05-18T03:24:41Z","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":"Recently, we introduced in arXiv:1105.2434 a model for product adoption in social networks with multiple products, where the agents, influenced by their neighbours, can adopt one out of several alternatives. We identify and analyze here four types of paradoxes that can arise in these networks. To this end, we use social network games that we recently introduced in arxiv:1202.2209. These paradoxes shed light on possible inefficiencies arising when one modifies the sets of products available to the agents forming a social network. One of the paradoxes corresponds to the well-known Braess paradox","authors_text":"Evangelos Markakis, Krzysztof R. Apt, Sunil Simon","cross_cats":["cs.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2013-01-31T12:31:05Z","title":"Paradoxes in Social Networks with Multiple Products"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.7592","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:d3ded0267b95e986031c4e341df4e4f810f59cb63b97c93530e7473b355938c3","target":"record","created_at":"2026-05-18T03:24:41Z","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":"c9dd593bcbfa6dbb691d30b6574b2c8346f9e21abbba04edd67a9d7b821b023c","cross_cats_sorted":["cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2013-01-31T12:31:05Z","title_canon_sha256":"54a7a30cb0fc20e64cf765886e9e92538c431e91bd5fdfb775d39868b1df5a9e"},"schema_version":"1.0","source":{"id":"1301.7592","kind":"arxiv","version":2}},"canonical_sha256":"13b735f6365b4089faf7ec26c1976fe41ff3c77ec3843f465706e86bf6266807","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"13b735f6365b4089faf7ec26c1976fe41ff3c77ec3843f465706e86bf6266807","first_computed_at":"2026-05-18T03:24:41.405106Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:24:41.405106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"chZ3aynKzlDML/KrAKDgZlO9vWOQIbYn0ie2Rnsa2amB+bFuIBVw70/abt3iFcGr0nQ8f3f/fivnq/8mwU1vBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:24:41.405638Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.7592","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d3ded0267b95e986031c4e341df4e4f810f59cb63b97c93530e7473b355938c3","sha256:3c3356c93b5757411ae54fd8cd776fc1383195b6ff2b63511cb0d6742460800d"],"state_sha256":"454473d12c73bb0411d33bb8d864a884730b2d07fdb939080180b5c899bf7163"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FCC/00P2nsL+FDjkoc4dReL7inGjRnvc5SegiSs/GcqdIyFR5aFzNOLQezN2cbH8GdP5HsSWSTAGBuNVQPdYCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T04:58:10.075359Z","bundle_sha256":"8b87881bfc91cc06602cb03b092715cc87de9e6db8e58317002364c86b496c89"}}