{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:5S7GZ7JEYAKMEDSOSNF5EGG7P7","short_pith_number":"pith:5S7GZ7JE","canonical_record":{"source":{"id":"1710.08110","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-10-23T06:56:04Z","cross_cats_sorted":[],"title_canon_sha256":"be865372502b720abc0e16e200691ec2dd9679c5f18b8e760137057a855e0f70","abstract_canon_sha256":"d953fd93acde1fea522101c99f09c6277f12ed8dde933b6a91f70f9e76b070c6"},"schema_version":"1.0"},"canonical_sha256":"ecbe6cfd24c014c20e4e934bd218df7fc17c7d7376c33131048f4806f704f8f8","source":{"kind":"arxiv","id":"1710.08110","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.08110","created_at":"2026-05-18T00:32:17Z"},{"alias_kind":"arxiv_version","alias_value":"1710.08110v1","created_at":"2026-05-18T00:32:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.08110","created_at":"2026-05-18T00:32:17Z"},{"alias_kind":"pith_short_12","alias_value":"5S7GZ7JEYAKM","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"5S7GZ7JEYAKMEDSO","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"5S7GZ7JE","created_at":"2026-05-18T12:31:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:5S7GZ7JEYAKMEDSOSNF5EGG7P7","target":"record","payload":{"canonical_record":{"source":{"id":"1710.08110","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-10-23T06:56:04Z","cross_cats_sorted":[],"title_canon_sha256":"be865372502b720abc0e16e200691ec2dd9679c5f18b8e760137057a855e0f70","abstract_canon_sha256":"d953fd93acde1fea522101c99f09c6277f12ed8dde933b6a91f70f9e76b070c6"},"schema_version":"1.0"},"canonical_sha256":"ecbe6cfd24c014c20e4e934bd218df7fc17c7d7376c33131048f4806f704f8f8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:17.185239Z","signature_b64":"MNC0CkIKewBN58ssy1Pw5S0HQfRC50fu+mszfRY8IDySTczym7zYPvO9mKnpS5i1DNiLwHnNMe3dg6zPiZERBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ecbe6cfd24c014c20e4e934bd218df7fc17c7d7376c33131048f4806f704f8f8","last_reissued_at":"2026-05-18T00:32:17.184646Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:17.184646Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.08110","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":"2026-05-18T00:32:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0zqFz/46ZfaV7Yssz/UNgcMrkE+6u+5AO92gmfxq3pHU4JdvcS8PXkVIP3Sl5eISlJSSF88qYL4H084T7aTuAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T06:42:25.398713Z"},"content_sha256":"706b8cf909a46f54420628f310665cb56aafb91bf22c6fa0493693df4d95b208","schema_version":"1.0","event_id":"sha256:706b8cf909a46f54420628f310665cb56aafb91bf22c6fa0493693df4d95b208"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:5S7GZ7JEYAKMEDSOSNF5EGG7P7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spatial rational expectations equilibria in the Ramsey model of optimal growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"A Xepapadeas, A Yannacopoulos, Filippo Santambrogio (LMO)","submitted_at":"2017-10-23T06:56:04Z","abstract_excerpt":"It is the aim of this work provide a rigorous treatment concerning the formation of spatial rational expectations equlibria in a general class of spatial economic models under the effect of externalities, using techniques from the calculus of variations. Using detailed estimates for a para-metric optimisation problem, the existence of spatial rational expectations equilibria is proved and they are characterised in terms of a nonlocal Euler-Lagrange equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.08110","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":"2026-05-18T00:32:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TpeqZ/JKiEt8jMSFma8s8ApF+u9uX2tHlMjJB5Wfr4+2GwF2jZeqkEhVySOyB4+d3oMYl03UFLjhFBgvGO+dCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T06:42:25.399040Z"},"content_sha256":"7dda73ef43828f2c07f7da27456ce31d6a1cb4a96394bd2a4748655ae188e047","schema_version":"1.0","event_id":"sha256:7dda73ef43828f2c07f7da27456ce31d6a1cb4a96394bd2a4748655ae188e047"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5S7GZ7JEYAKMEDSOSNF5EGG7P7/bundle.json","state_url":"https://pith.science/pith/5S7GZ7JEYAKMEDSOSNF5EGG7P7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5S7GZ7JEYAKMEDSOSNF5EGG7P7/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":"2026-06-23T06:42:25Z","links":{"resolver":"https://pith.science/pith/5S7GZ7JEYAKMEDSOSNF5EGG7P7","bundle":"https://pith.science/pith/5S7GZ7JEYAKMEDSOSNF5EGG7P7/bundle.json","state":"https://pith.science/pith/5S7GZ7JEYAKMEDSOSNF5EGG7P7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5S7GZ7JEYAKMEDSOSNF5EGG7P7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:5S7GZ7JEYAKMEDSOSNF5EGG7P7","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":"d953fd93acde1fea522101c99f09c6277f12ed8dde933b6a91f70f9e76b070c6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-10-23T06:56:04Z","title_canon_sha256":"be865372502b720abc0e16e200691ec2dd9679c5f18b8e760137057a855e0f70"},"schema_version":"1.0","source":{"id":"1710.08110","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.08110","created_at":"2026-05-18T00:32:17Z"},{"alias_kind":"arxiv_version","alias_value":"1710.08110v1","created_at":"2026-05-18T00:32:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.08110","created_at":"2026-05-18T00:32:17Z"},{"alias_kind":"pith_short_12","alias_value":"5S7GZ7JEYAKM","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"5S7GZ7JEYAKMEDSO","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"5S7GZ7JE","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:7dda73ef43828f2c07f7da27456ce31d6a1cb4a96394bd2a4748655ae188e047","target":"graph","created_at":"2026-05-18T00:32:17Z","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":"It is the aim of this work provide a rigorous treatment concerning the formation of spatial rational expectations equlibria in a general class of spatial economic models under the effect of externalities, using techniques from the calculus of variations. Using detailed estimates for a para-metric optimisation problem, the existence of spatial rational expectations equilibria is proved and they are characterised in terms of a nonlocal Euler-Lagrange equation.","authors_text":"A Xepapadeas, A Yannacopoulos, Filippo Santambrogio (LMO)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-10-23T06:56:04Z","title":"Spatial rational expectations equilibria in the Ramsey model of optimal growth"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.08110","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":"sha256:706b8cf909a46f54420628f310665cb56aafb91bf22c6fa0493693df4d95b208","target":"record","created_at":"2026-05-18T00:32:17Z","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":"d953fd93acde1fea522101c99f09c6277f12ed8dde933b6a91f70f9e76b070c6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-10-23T06:56:04Z","title_canon_sha256":"be865372502b720abc0e16e200691ec2dd9679c5f18b8e760137057a855e0f70"},"schema_version":"1.0","source":{"id":"1710.08110","kind":"arxiv","version":1}},"canonical_sha256":"ecbe6cfd24c014c20e4e934bd218df7fc17c7d7376c33131048f4806f704f8f8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ecbe6cfd24c014c20e4e934bd218df7fc17c7d7376c33131048f4806f704f8f8","first_computed_at":"2026-05-18T00:32:17.184646Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:17.184646Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MNC0CkIKewBN58ssy1Pw5S0HQfRC50fu+mszfRY8IDySTczym7zYPvO9mKnpS5i1DNiLwHnNMe3dg6zPiZERBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:17.185239Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.08110","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:706b8cf909a46f54420628f310665cb56aafb91bf22c6fa0493693df4d95b208","sha256:7dda73ef43828f2c07f7da27456ce31d6a1cb4a96394bd2a4748655ae188e047"],"state_sha256":"0284c3609e9568e73e6e7df5fb6359a0779d4523ca21f38c4a4e8acf4393fbf0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pxWHrF65sCyq47KxGvAAAeEs/BIyKJzIUyPEu4Esj1xzm1WS/A6WXIf5mO2J2Z4VBm751JBPDYlCj6luSM1RDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T06:42:25.400894Z","bundle_sha256":"9442842dd63e39b7fabbb28b61306f7cc88770b379e1a7b9bb2279261141e165"}}