{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:J5BK654KOFKHVZEJO266RYCSBK","short_pith_number":"pith:J5BK654K","canonical_record":{"source":{"id":"2607.10204","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"econ.TH","submitted_at":"2026-07-11T08:29:42Z","cross_cats_sorted":[],"title_canon_sha256":"640ea152af86785f39df944e6aba21c84c03bac4b9182610a91faa43e8d1c1f5","abstract_canon_sha256":"91b89c2d141bef971cd8d4895a289d0e9e8ae54763076de0fef355c3bfbcc02f"},"schema_version":"1.0"},"canonical_sha256":"4f42af778a71547ae48976bde8e0520a9da8843b6f375c4985efb8c66331ba41","source":{"kind":"arxiv","id":"2607.10204","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.10204","created_at":"2026-07-14T01:20:30Z"},{"alias_kind":"arxiv_version","alias_value":"2607.10204v1","created_at":"2026-07-14T01:20:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.10204","created_at":"2026-07-14T01:20:30Z"},{"alias_kind":"pith_short_12","alias_value":"J5BK654KOFKH","created_at":"2026-07-14T01:20:30Z"},{"alias_kind":"pith_short_16","alias_value":"J5BK654KOFKHVZEJ","created_at":"2026-07-14T01:20:30Z"},{"alias_kind":"pith_short_8","alias_value":"J5BK654K","created_at":"2026-07-14T01:20:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:J5BK654KOFKHVZEJO266RYCSBK","target":"record","payload":{"canonical_record":{"source":{"id":"2607.10204","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"econ.TH","submitted_at":"2026-07-11T08:29:42Z","cross_cats_sorted":[],"title_canon_sha256":"640ea152af86785f39df944e6aba21c84c03bac4b9182610a91faa43e8d1c1f5","abstract_canon_sha256":"91b89c2d141bef971cd8d4895a289d0e9e8ae54763076de0fef355c3bfbcc02f"},"schema_version":"1.0"},"canonical_sha256":"4f42af778a71547ae48976bde8e0520a9da8843b6f375c4985efb8c66331ba41","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-14T01:20:30.565204Z","signature_b64":"kDgXVplRDGXnYebRR4rdE4FRVpYPyRBWNnM+0QTPz24LzRAvRFme1QjNodOpPc95DO2G6KLxwQLPDgKzWp1lAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f42af778a71547ae48976bde8e0520a9da8843b6f375c4985efb8c66331ba41","last_reissued_at":"2026-07-14T01:20:30.564239Z","signature_status":"signed_v1","first_computed_at":"2026-07-14T01:20:30.564239Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.10204","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":"2026-07-14T01:20:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oK96/Wnt4GDmSSF3H2bH+Tuqk2qRCLa2WEo+OVe6SSPhrvXGAtkhQiDtU/sH18o+1lPDvj4ap8MOWKNfmnYbAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-31T15:21:35.341467Z"},"content_sha256":"5cee634d9ee5cdfe9813a2b8dc1f2e7e3f647153bc3e6b77108d1f13dfa5a973","schema_version":"1.0","event_id":"sha256:5cee634d9ee5cdfe9813a2b8dc1f2e7e3f647153bc3e6b77108d1f13dfa5a973"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:J5BK654KOFKHVZEJO266RYCSBK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bifurcation mechanism at a sustain point of a long narrow economy","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"econ.TH","authors_text":"Hiroki Aizawa, Jos\\'e M. Gaspar, Kyiohiro Ikeda","submitted_at":"2026-07-11T08:29:42Z","abstract_excerpt":"We investigate population agglomeration in a long narrow economy, in which an odd number of places are evenly distributed over a line segment. The bifurcation analysis of this economy elucidates the mechanism of the emergence of twin cities around the central city. The validity and usefulness of this analysis are confirmed using several well-known economic geography models that display various kinds of bifurcation behaviors. By this analysis, we investigate the historical change in the population distribution in a chain of cities on Japan's Main Island."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.10204","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.10204/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-14T01:20:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7jGhzAZS/R9vwIIa+NcdTfzsCrxEZ4mfKpgrUDikSAVc/jizowxFm2Nz+LvlJVfsO5rqMaB+fIu+Txc/U3NpAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-31T15:21:35.341974Z"},"content_sha256":"ae1af7c90c005cce6c2755c7938e0f97f5591099535347530f94a10ea170643a","schema_version":"1.0","event_id":"sha256:ae1af7c90c005cce6c2755c7938e0f97f5591099535347530f94a10ea170643a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J5BK654KOFKHVZEJO266RYCSBK/bundle.json","state_url":"https://pith.science/pith/J5BK654KOFKHVZEJO266RYCSBK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J5BK654KOFKHVZEJO266RYCSBK/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":"2026-07-31T15:21:35Z","links":{"resolver":"https://pith.science/pith/J5BK654KOFKHVZEJO266RYCSBK","bundle":"https://pith.science/pith/J5BK654KOFKHVZEJO266RYCSBK/bundle.json","state":"https://pith.science/pith/J5BK654KOFKHVZEJO266RYCSBK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J5BK654KOFKHVZEJO266RYCSBK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:J5BK654KOFKHVZEJO266RYCSBK","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":"91b89c2d141bef971cd8d4895a289d0e9e8ae54763076de0fef355c3bfbcc02f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"econ.TH","submitted_at":"2026-07-11T08:29:42Z","title_canon_sha256":"640ea152af86785f39df944e6aba21c84c03bac4b9182610a91faa43e8d1c1f5"},"schema_version":"1.0","source":{"id":"2607.10204","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.10204","created_at":"2026-07-14T01:20:30Z"},{"alias_kind":"arxiv_version","alias_value":"2607.10204v1","created_at":"2026-07-14T01:20:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.10204","created_at":"2026-07-14T01:20:30Z"},{"alias_kind":"pith_short_12","alias_value":"J5BK654KOFKH","created_at":"2026-07-14T01:20:30Z"},{"alias_kind":"pith_short_16","alias_value":"J5BK654KOFKHVZEJ","created_at":"2026-07-14T01:20:30Z"},{"alias_kind":"pith_short_8","alias_value":"J5BK654K","created_at":"2026-07-14T01:20:30Z"}],"graph_snapshots":[{"event_id":"sha256:ae1af7c90c005cce6c2755c7938e0f97f5591099535347530f94a10ea170643a","target":"graph","created_at":"2026-07-14T01:20:30Z","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/2607.10204/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate population agglomeration in a long narrow economy, in which an odd number of places are evenly distributed over a line segment. The bifurcation analysis of this economy elucidates the mechanism of the emergence of twin cities around the central city. The validity and usefulness of this analysis are confirmed using several well-known economic geography models that display various kinds of bifurcation behaviors. By this analysis, we investigate the historical change in the population distribution in a chain of cities on Japan's Main Island.","authors_text":"Hiroki Aizawa, Jos\\'e M. Gaspar, Kyiohiro Ikeda","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"econ.TH","submitted_at":"2026-07-11T08:29:42Z","title":"Bifurcation mechanism at a sustain point of a long narrow economy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.10204","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":"sha256:5cee634d9ee5cdfe9813a2b8dc1f2e7e3f647153bc3e6b77108d1f13dfa5a973","target":"record","created_at":"2026-07-14T01:20:30Z","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":"91b89c2d141bef971cd8d4895a289d0e9e8ae54763076de0fef355c3bfbcc02f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"econ.TH","submitted_at":"2026-07-11T08:29:42Z","title_canon_sha256":"640ea152af86785f39df944e6aba21c84c03bac4b9182610a91faa43e8d1c1f5"},"schema_version":"1.0","source":{"id":"2607.10204","kind":"arxiv","version":1}},"canonical_sha256":"4f42af778a71547ae48976bde8e0520a9da8843b6f375c4985efb8c66331ba41","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f42af778a71547ae48976bde8e0520a9da8843b6f375c4985efb8c66331ba41","first_computed_at":"2026-07-14T01:20:30.564239Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-14T01:20:30.564239Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kDgXVplRDGXnYebRR4rdE4FRVpYPyRBWNnM+0QTPz24LzRAvRFme1QjNodOpPc95DO2G6KLxwQLPDgKzWp1lAA==","signature_status":"signed_v1","signed_at":"2026-07-14T01:20:30.565204Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.10204","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5cee634d9ee5cdfe9813a2b8dc1f2e7e3f647153bc3e6b77108d1f13dfa5a973","sha256:ae1af7c90c005cce6c2755c7938e0f97f5591099535347530f94a10ea170643a"],"state_sha256":"4ef8007466adaa7952f3133b98289e94b3bd7fe9fbe464d23155fb767f10f8a3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VpuF3NQC/W4DUHPA2Y7Se6jQtGbnlkM+Jg/Oq3xpqG3wKO4/W37HL8zKuF+xHsx3iPs50OKqkzv6HdUkbzE6DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-31T15:21:35.347358Z","bundle_sha256":"c4078c1cbf24938d56773fb02a6dc3c0d685e0b2b61dacd1b03dd5fd92de17da"}}