{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:PTNL4PO7Y5IXAQRIQKVNUT7TFN","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":"a06520383e81e5166f5cfbc6ab53a4122a2718a13b880c778216fc17e58b70af","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"econ.TH","submitted_at":"2026-07-10T10:35:28Z","title_canon_sha256":"8862bd9171b2821cda6ca4af0ebd2d7ea6cf0e219716e4c31f5dd24245eada4a"},"schema_version":"1.0","source":{"id":"2607.09269","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.09269","created_at":"2026-07-13T01:18:57Z"},{"alias_kind":"arxiv_version","alias_value":"2607.09269v1","created_at":"2026-07-13T01:18:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.09269","created_at":"2026-07-13T01:18:57Z"},{"alias_kind":"pith_short_12","alias_value":"PTNL4PO7Y5IX","created_at":"2026-07-13T01:18:57Z"},{"alias_kind":"pith_short_16","alias_value":"PTNL4PO7Y5IXAQRI","created_at":"2026-07-13T01:18:57Z"},{"alias_kind":"pith_short_8","alias_value":"PTNL4PO7","created_at":"2026-07-13T01:18:57Z"}],"graph_snapshots":[{"event_id":"sha256:ab10492b85e7e372b10b6c2ae39e5849c9381d0c819605addcc97a6761c809a3","target":"graph","created_at":"2026-07-13T01:18:57Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.09269/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study how interoperability reshapes competitive price discrimination when consumers are embedded in a social network. Two differentiated platforms set personalized prices; consumers benefit from neighbors' consumption of the same platform and, under interoperability, of the rival. Equilibrium prices obtain in closed form for arbitrary networks and contain a network-position term, proportional to Katz-Bonacich centrality, whose sign is determined by whether interoperability exceeds product substitutability. Below this threshold, platforms contest central consumers and grant centrality discou","authors_text":"Bin Wu, Jing Sun, Weiming Li, Xinxi Song","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"econ.TH","submitted_at":"2026-07-10T10:35:28Z","title":"From Centrality Discounts to Centrality Premia: Interoperability and Platform Competition in Social Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.09269","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:a2f29e124b3f68528d54620bc76b770e36537d0b3f453359dc909785ad0d4f30","target":"record","created_at":"2026-07-13T01:18:57Z","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":"a06520383e81e5166f5cfbc6ab53a4122a2718a13b880c778216fc17e58b70af","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"econ.TH","submitted_at":"2026-07-10T10:35:28Z","title_canon_sha256":"8862bd9171b2821cda6ca4af0ebd2d7ea6cf0e219716e4c31f5dd24245eada4a"},"schema_version":"1.0","source":{"id":"2607.09269","kind":"arxiv","version":1}},"canonical_sha256":"7cdabe3ddfc75170422882aada4ff32b42482353330d1671fec2f874f9edab42","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7cdabe3ddfc75170422882aada4ff32b42482353330d1671fec2f874f9edab42","first_computed_at":"2026-07-13T01:18:57.301776Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-13T01:18:57.301776Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WiUju+O+w8qfLTUJp47bOEyRECCxZzP11shWaf7PINjrsqCIKsu8IYvi5rzEKFU7PPxoEbixEG+ePNnzev7kDg==","signature_status":"signed_v1","signed_at":"2026-07-13T01:18:57.302899Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.09269","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a2f29e124b3f68528d54620bc76b770e36537d0b3f453359dc909785ad0d4f30","sha256:ab10492b85e7e372b10b6c2ae39e5849c9381d0c819605addcc97a6761c809a3"],"state_sha256":"43a3938f0b6e01a8efc672fc2d954406953f805c92f0df5b2668cc55f5d0a1bd"}