{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:SSSPNK2XTK3FM2YKU6UNI2NPDO","short_pith_number":"pith:SSSPNK2X","canonical_record":{"source":{"id":"1805.11871","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-05-30T09:11:50Z","cross_cats_sorted":[],"title_canon_sha256":"d374c27b3d6c86133dbc87303405c90fd1183d363f25379c722140cb2d5a4169","abstract_canon_sha256":"9b9ebd9f22347505ab5c4caf51433fd406c3038b5b94fe634b1a61db8b205504"},"schema_version":"1.0"},"canonical_sha256":"94a4f6ab579ab6566b0aa7a8d469af1bbbaec090a8b3cd91d25f05046482c4db","source":{"kind":"arxiv","id":"1805.11871","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.11871","created_at":"2026-05-18T00:14:36Z"},{"alias_kind":"arxiv_version","alias_value":"1805.11871v1","created_at":"2026-05-18T00:14:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.11871","created_at":"2026-05-18T00:14:36Z"},{"alias_kind":"pith_short_12","alias_value":"SSSPNK2XTK3F","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"SSSPNK2XTK3FM2YK","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"SSSPNK2X","created_at":"2026-05-18T12:32:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:SSSPNK2XTK3FM2YKU6UNI2NPDO","target":"record","payload":{"canonical_record":{"source":{"id":"1805.11871","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-05-30T09:11:50Z","cross_cats_sorted":[],"title_canon_sha256":"d374c27b3d6c86133dbc87303405c90fd1183d363f25379c722140cb2d5a4169","abstract_canon_sha256":"9b9ebd9f22347505ab5c4caf51433fd406c3038b5b94fe634b1a61db8b205504"},"schema_version":"1.0"},"canonical_sha256":"94a4f6ab579ab6566b0aa7a8d469af1bbbaec090a8b3cd91d25f05046482c4db","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:36.011170Z","signature_b64":"t0vGPg4nzswSrBuqcZPBCREaxE8hWi8DkODBaqST+R/3QqC1LmmYOmYNGCTvB5TvkxL3HVG4bP2qtviQwUhUBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"94a4f6ab579ab6566b0aa7a8d469af1bbbaec090a8b3cd91d25f05046482c4db","last_reissued_at":"2026-05-18T00:14:36.010454Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:36.010454Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.11871","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":"2026-05-18T00:14:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u3zJMlt1Yyr8RB+kNezrqgQBx+nB8fPgK5ymRRT0we98uinTEgK+o6QhucmRvIBU/z/gL/eMPVrxeQs7acbnCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T21:35:44.223565Z"},"content_sha256":"e241d8c2d729116bbca172da87fe4f4561ffcfc92a58949b16238502efd77133","schema_version":"1.0","event_id":"sha256:e241d8c2d729116bbca172da87fe4f4561ffcfc92a58949b16238502efd77133"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:SSSPNK2XTK3FM2YKU6UNI2NPDO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multidimensional free-mobility equilibrium: Tiebout revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Alexey Savvateev, Constantine Sorokin, Shlomo Weber","submitted_at":"2018-05-30T09:11:50Z","abstract_excerpt":"The paper provides consistent mathematical framework for seminal Tiebout free-mobility model (1956). Our setting supports continuum of consumers with multidimensional preferences and finite number of strategic public good providers. We accommodate the most general assumptions: providers' production function may have variable returns to scale, our framework is rich enough to incorporate possible externalities, spillovers, scale economies, network effects, etc.; consumers utility may depend on choice of other agents in almost arbitrary way. We focus on equilibrium existence, however the question"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.11871","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":"2026-05-18T00:14:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gdLOcSdJp+YePAN648zya+E5B1PjTtDm+HDK/qGNTrxp8OJJE4bZJuuclCVOQtcEW35c0+Mlk2C4Ay1Q4dmxDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T21:35:44.224266Z"},"content_sha256":"277db486a7a8a9f5eaf5ce9e42140122fc3cceec2c1d7e9a1fad8dece0bc74f5","schema_version":"1.0","event_id":"sha256:277db486a7a8a9f5eaf5ce9e42140122fc3cceec2c1d7e9a1fad8dece0bc74f5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SSSPNK2XTK3FM2YKU6UNI2NPDO/bundle.json","state_url":"https://pith.science/pith/SSSPNK2XTK3FM2YKU6UNI2NPDO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SSSPNK2XTK3FM2YKU6UNI2NPDO/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":"2026-06-10T21:35:44Z","links":{"resolver":"https://pith.science/pith/SSSPNK2XTK3FM2YKU6UNI2NPDO","bundle":"https://pith.science/pith/SSSPNK2XTK3FM2YKU6UNI2NPDO/bundle.json","state":"https://pith.science/pith/SSSPNK2XTK3FM2YKU6UNI2NPDO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SSSPNK2XTK3FM2YKU6UNI2NPDO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:SSSPNK2XTK3FM2YKU6UNI2NPDO","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":"9b9ebd9f22347505ab5c4caf51433fd406c3038b5b94fe634b1a61db8b205504","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-05-30T09:11:50Z","title_canon_sha256":"d374c27b3d6c86133dbc87303405c90fd1183d363f25379c722140cb2d5a4169"},"schema_version":"1.0","source":{"id":"1805.11871","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.11871","created_at":"2026-05-18T00:14:36Z"},{"alias_kind":"arxiv_version","alias_value":"1805.11871v1","created_at":"2026-05-18T00:14:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.11871","created_at":"2026-05-18T00:14:36Z"},{"alias_kind":"pith_short_12","alias_value":"SSSPNK2XTK3F","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"SSSPNK2XTK3FM2YK","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"SSSPNK2X","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:277db486a7a8a9f5eaf5ce9e42140122fc3cceec2c1d7e9a1fad8dece0bc74f5","target":"graph","created_at":"2026-05-18T00:14:36Z","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 paper provides consistent mathematical framework for seminal Tiebout free-mobility model (1956). Our setting supports continuum of consumers with multidimensional preferences and finite number of strategic public good providers. We accommodate the most general assumptions: providers' production function may have variable returns to scale, our framework is rich enough to incorporate possible externalities, spillovers, scale economies, network effects, etc.; consumers utility may depend on choice of other agents in almost arbitrary way. We focus on equilibrium existence, however the question","authors_text":"Alexey Savvateev, Constantine Sorokin, Shlomo Weber","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-05-30T09:11:50Z","title":"Multidimensional free-mobility equilibrium: Tiebout revisited"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.11871","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:e241d8c2d729116bbca172da87fe4f4561ffcfc92a58949b16238502efd77133","target":"record","created_at":"2026-05-18T00:14:36Z","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":"9b9ebd9f22347505ab5c4caf51433fd406c3038b5b94fe634b1a61db8b205504","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-05-30T09:11:50Z","title_canon_sha256":"d374c27b3d6c86133dbc87303405c90fd1183d363f25379c722140cb2d5a4169"},"schema_version":"1.0","source":{"id":"1805.11871","kind":"arxiv","version":1}},"canonical_sha256":"94a4f6ab579ab6566b0aa7a8d469af1bbbaec090a8b3cd91d25f05046482c4db","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"94a4f6ab579ab6566b0aa7a8d469af1bbbaec090a8b3cd91d25f05046482c4db","first_computed_at":"2026-05-18T00:14:36.010454Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:36.010454Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t0vGPg4nzswSrBuqcZPBCREaxE8hWi8DkODBaqST+R/3QqC1LmmYOmYNGCTvB5TvkxL3HVG4bP2qtviQwUhUBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:36.011170Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.11871","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e241d8c2d729116bbca172da87fe4f4561ffcfc92a58949b16238502efd77133","sha256:277db486a7a8a9f5eaf5ce9e42140122fc3cceec2c1d7e9a1fad8dece0bc74f5"],"state_sha256":"658b9341ff4ca747c7f1ce5c4cab831fa209e698b6687b2f57aa050a41a36828"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KL7dCohtnHmslRQDWFqQQtYJ+SG/YYod77PJQ6ymq2CzHQKU9L0IghkIFBYb+qZgKsYQ260wuAkcCtrCA7SNBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T21:35:44.228259Z","bundle_sha256":"67fce16c0a200de440277a19e72efca38d9f2b05393a1df2191a2e8cb819a4ec"}}