{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:ABO4CGIUPMP5WF54U6FDKUUMMO","short_pith_number":"pith:ABO4CGIU","canonical_record":{"source":{"id":"1102.2834","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2011-02-14T17:31:35Z","cross_cats_sorted":["nlin.AO"],"title_canon_sha256":"27a81fbd204cbd5999a64729a0f73d4f2ccf6f307d2efe6b433335ec73267776","abstract_canon_sha256":"5bf7865d7a0b6f984d89436ea1a498f987d13f7a731f4c1f3289ef14f0781d8b"},"schema_version":"1.0"},"canonical_sha256":"005dc119147b1fdb17bca78a35528c63be03408f6cddb97506e8ac8c7f83cd1b","source":{"kind":"arxiv","id":"1102.2834","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.2834","created_at":"2026-05-18T02:03:11Z"},{"alias_kind":"arxiv_version","alias_value":"1102.2834v1","created_at":"2026-05-18T02:03:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.2834","created_at":"2026-05-18T02:03:11Z"},{"alias_kind":"pith_short_12","alias_value":"ABO4CGIUPMP5","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"ABO4CGIUPMP5WF54","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"ABO4CGIU","created_at":"2026-05-18T12:26:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:ABO4CGIUPMP5WF54U6FDKUUMMO","target":"record","payload":{"canonical_record":{"source":{"id":"1102.2834","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2011-02-14T17:31:35Z","cross_cats_sorted":["nlin.AO"],"title_canon_sha256":"27a81fbd204cbd5999a64729a0f73d4f2ccf6f307d2efe6b433335ec73267776","abstract_canon_sha256":"5bf7865d7a0b6f984d89436ea1a498f987d13f7a731f4c1f3289ef14f0781d8b"},"schema_version":"1.0"},"canonical_sha256":"005dc119147b1fdb17bca78a35528c63be03408f6cddb97506e8ac8c7f83cd1b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:03:11.318214Z","signature_b64":"WDdZS+xKhamJN2SP61KR3aVqHUzgxXsAowkr0InBhBE3qkqED9tt2Mur9u6h7O7CyHSfcMQ+cCwAaIq6Gr0NBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"005dc119147b1fdb17bca78a35528c63be03408f6cddb97506e8ac8c7f83cd1b","last_reissued_at":"2026-05-18T02:03:11.317534Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:03:11.317534Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.2834","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":"2026-05-18T02:03:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rNPJOwtXVUhAr1ux03mfuwLdUpyATxTz3WFvm+zdFVN0SfKWG4zgvcGsULmiKGpuwhHwQdwTAuN/Jm/qxI4KAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T07:05:31.449540Z"},"content_sha256":"3ca5494352fc4b07047f6e086f89e68418263339df92d8aa0d9516785c68b60c","schema_version":"1.0","event_id":"sha256:3ca5494352fc4b07047f6e086f89e68418263339df92d8aa0d9516785c68b60c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:ABO4CGIUPMP5WF54U6FDKUUMMO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Turing instability in oscillator chains with non-local coupling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.AO"],"primary_cat":"nlin.PS","authors_text":"F. A. dos S. Silva, R. L. Viana, S. R. Lopes","submitted_at":"2011-02-14T17:31:35Z","abstract_excerpt":"We investigate analytically and numerically the conditions for the Turing instability to occur in a one-dimensional chain of nonlinear oscillators coupled non-locally in such a way that the coupling strength decreases with the spatial distance as a power-law. A range parameter makes possible to cover the two limiting cases of local (nearest-neighbor) and a global (all-to-all) couplings. We consider an example from a non-linear auto-catalytic reaction-diffusion model."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.2834","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":"2026-05-18T02:03:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"27Agg22K36qhQS/VO3R/ojX+8cLCwP4Pnznmjvawe0ef12kMbCYDD3Ek5RJs+mVEGNxalg0mPur0OvSMeEVwBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T07:05:31.449886Z"},"content_sha256":"b0898e1449b7a1ff2b10564cef500b303115d4b1aee11d25acad69d0c1454196","schema_version":"1.0","event_id":"sha256:b0898e1449b7a1ff2b10564cef500b303115d4b1aee11d25acad69d0c1454196"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ABO4CGIUPMP5WF54U6FDKUUMMO/bundle.json","state_url":"https://pith.science/pith/ABO4CGIUPMP5WF54U6FDKUUMMO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ABO4CGIUPMP5WF54U6FDKUUMMO/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":"2026-06-22T07:05:31Z","links":{"resolver":"https://pith.science/pith/ABO4CGIUPMP5WF54U6FDKUUMMO","bundle":"https://pith.science/pith/ABO4CGIUPMP5WF54U6FDKUUMMO/bundle.json","state":"https://pith.science/pith/ABO4CGIUPMP5WF54U6FDKUUMMO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ABO4CGIUPMP5WF54U6FDKUUMMO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:ABO4CGIUPMP5WF54U6FDKUUMMO","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":"5bf7865d7a0b6f984d89436ea1a498f987d13f7a731f4c1f3289ef14f0781d8b","cross_cats_sorted":["nlin.AO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2011-02-14T17:31:35Z","title_canon_sha256":"27a81fbd204cbd5999a64729a0f73d4f2ccf6f307d2efe6b433335ec73267776"},"schema_version":"1.0","source":{"id":"1102.2834","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.2834","created_at":"2026-05-18T02:03:11Z"},{"alias_kind":"arxiv_version","alias_value":"1102.2834v1","created_at":"2026-05-18T02:03:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.2834","created_at":"2026-05-18T02:03:11Z"},{"alias_kind":"pith_short_12","alias_value":"ABO4CGIUPMP5","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"ABO4CGIUPMP5WF54","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"ABO4CGIU","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:b0898e1449b7a1ff2b10564cef500b303115d4b1aee11d25acad69d0c1454196","target":"graph","created_at":"2026-05-18T02:03:11Z","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":"We investigate analytically and numerically the conditions for the Turing instability to occur in a one-dimensional chain of nonlinear oscillators coupled non-locally in such a way that the coupling strength decreases with the spatial distance as a power-law. A range parameter makes possible to cover the two limiting cases of local (nearest-neighbor) and a global (all-to-all) couplings. We consider an example from a non-linear auto-catalytic reaction-diffusion model.","authors_text":"F. A. dos S. Silva, R. L. Viana, S. R. Lopes","cross_cats":["nlin.AO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2011-02-14T17:31:35Z","title":"Turing instability in oscillator chains with non-local coupling"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.2834","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":"sha256:3ca5494352fc4b07047f6e086f89e68418263339df92d8aa0d9516785c68b60c","target":"record","created_at":"2026-05-18T02:03:11Z","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":"5bf7865d7a0b6f984d89436ea1a498f987d13f7a731f4c1f3289ef14f0781d8b","cross_cats_sorted":["nlin.AO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2011-02-14T17:31:35Z","title_canon_sha256":"27a81fbd204cbd5999a64729a0f73d4f2ccf6f307d2efe6b433335ec73267776"},"schema_version":"1.0","source":{"id":"1102.2834","kind":"arxiv","version":1}},"canonical_sha256":"005dc119147b1fdb17bca78a35528c63be03408f6cddb97506e8ac8c7f83cd1b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"005dc119147b1fdb17bca78a35528c63be03408f6cddb97506e8ac8c7f83cd1b","first_computed_at":"2026-05-18T02:03:11.317534Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:03:11.317534Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WDdZS+xKhamJN2SP61KR3aVqHUzgxXsAowkr0InBhBE3qkqED9tt2Mur9u6h7O7CyHSfcMQ+cCwAaIq6Gr0NBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:03:11.318214Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.2834","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3ca5494352fc4b07047f6e086f89e68418263339df92d8aa0d9516785c68b60c","sha256:b0898e1449b7a1ff2b10564cef500b303115d4b1aee11d25acad69d0c1454196"],"state_sha256":"426f666112c2090f38584dd6ee95929987923be7f46d5c7577d508670bc6ac5b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ogvAa/w4/sT7WXGjGc86nLch5r6rSiYjE+M+VogVOy5JrzM1EgehA6Ls7CpT0UM2kTurFGkjSouNq484heX7Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T07:05:31.451776Z","bundle_sha256":"f1c0325207500a84b25aa0eaa80906a70bfbbc2b28110c4f28c7b65ceb2551ec"}}