{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:JKRSIYTV6JQRE3MHG4DQSGZRBP","short_pith_number":"pith:JKRSIYTV","canonical_record":{"source":{"id":"1805.04144","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-05-10T19:30:23Z","cross_cats_sorted":[],"title_canon_sha256":"c8b4edaedb65e6069f3c30c698d405e43e0f1cac50f49527bf623d608bd53a96","abstract_canon_sha256":"9c5144af143d403cf3ef9c6650d3b83f6dc63efcf72da20525b2b99aa5199d3c"},"schema_version":"1.0"},"canonical_sha256":"4aa3246275f261126d873707091b310bec3746554c4e7a2d5aa73fa5b72dd5bd","source":{"kind":"arxiv","id":"1805.04144","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.04144","created_at":"2026-05-17T23:52:18Z"},{"alias_kind":"arxiv_version","alias_value":"1805.04144v2","created_at":"2026-05-17T23:52:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.04144","created_at":"2026-05-17T23:52:18Z"},{"alias_kind":"pith_short_12","alias_value":"JKRSIYTV6JQR","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"JKRSIYTV6JQRE3MH","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"JKRSIYTV","created_at":"2026-05-18T12:32:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:JKRSIYTV6JQRE3MHG4DQSGZRBP","target":"record","payload":{"canonical_record":{"source":{"id":"1805.04144","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-05-10T19:30:23Z","cross_cats_sorted":[],"title_canon_sha256":"c8b4edaedb65e6069f3c30c698d405e43e0f1cac50f49527bf623d608bd53a96","abstract_canon_sha256":"9c5144af143d403cf3ef9c6650d3b83f6dc63efcf72da20525b2b99aa5199d3c"},"schema_version":"1.0"},"canonical_sha256":"4aa3246275f261126d873707091b310bec3746554c4e7a2d5aa73fa5b72dd5bd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:18.372741Z","signature_b64":"dz2Y03EVQ9mvofDAnDk104DJ2LXKrjGm86mD9TxXQqbJfTtddmDfCGK8GgkiVojbjN4LwG7IUsbHKHM3pQEWAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4aa3246275f261126d873707091b310bec3746554c4e7a2d5aa73fa5b72dd5bd","last_reissued_at":"2026-05-17T23:52:18.372112Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:18.372112Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.04144","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:52:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5UjoHk6k6TGU0zNpzC91LURmEPAeD7AaRPf6jmhpYxoz+ryUhJt2GKymt2y8JFTtW2FgPkNnbvi2LTPZlImQBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T10:44:15.076052Z"},"content_sha256":"adafd3984f37d352e59d8cf3c6f5a18dc1b96bc9297c9ed6bea097702fbbad42","schema_version":"1.0","event_id":"sha256:adafd3984f37d352e59d8cf3c6f5a18dc1b96bc9297c9ed6bea097702fbbad42"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:JKRSIYTV6JQRE3MHG4DQSGZRBP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Synchrony and Anti-Synchrony for Difference-Coupled Vector Fields on Graph Network Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"James W. Swift, John M. Neuberger, N\\'andor Sieben","submitted_at":"2018-05-10T19:30:23Z","abstract_excerpt":"We define a graph network to be a coupled cell network where there are only one type of cell and one type of symmetric coupling between the cells. For a difference-coupled vector field on a graph network system, all the cells have the same internal dynamics, and the coupling between cells is identical, symmetric, and depends only on the difference of the states of the interacting cells. We define four nested sets of difference-coupled vector fields by adding further restrictions on the internal dynamics and the coupling functions. These restrictions require that these functions preserve zero o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.04144","kind":"arxiv","version":2},"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":"2026-05-17T23:52:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5oqTzaExTe/o/Ty74VjIsdGWesK+PBS4AhafsMWQ8X/TmUJzc+Mw3eALHS9RTw8XFmNeAmsMpqqt9y6pZ6BbBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T10:44:15.076415Z"},"content_sha256":"99aede2ecba510420579fa5ce7be4a15dfe65765253d3d20f6b46d97c236f665","schema_version":"1.0","event_id":"sha256:99aede2ecba510420579fa5ce7be4a15dfe65765253d3d20f6b46d97c236f665"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JKRSIYTV6JQRE3MHG4DQSGZRBP/bundle.json","state_url":"https://pith.science/pith/JKRSIYTV6JQRE3MHG4DQSGZRBP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JKRSIYTV6JQRE3MHG4DQSGZRBP/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":"2026-06-24T10:44:15Z","links":{"resolver":"https://pith.science/pith/JKRSIYTV6JQRE3MHG4DQSGZRBP","bundle":"https://pith.science/pith/JKRSIYTV6JQRE3MHG4DQSGZRBP/bundle.json","state":"https://pith.science/pith/JKRSIYTV6JQRE3MHG4DQSGZRBP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JKRSIYTV6JQRE3MHG4DQSGZRBP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:JKRSIYTV6JQRE3MHG4DQSGZRBP","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":"9c5144af143d403cf3ef9c6650d3b83f6dc63efcf72da20525b2b99aa5199d3c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-05-10T19:30:23Z","title_canon_sha256":"c8b4edaedb65e6069f3c30c698d405e43e0f1cac50f49527bf623d608bd53a96"},"schema_version":"1.0","source":{"id":"1805.04144","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.04144","created_at":"2026-05-17T23:52:18Z"},{"alias_kind":"arxiv_version","alias_value":"1805.04144v2","created_at":"2026-05-17T23:52:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.04144","created_at":"2026-05-17T23:52:18Z"},{"alias_kind":"pith_short_12","alias_value":"JKRSIYTV6JQR","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"JKRSIYTV6JQRE3MH","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"JKRSIYTV","created_at":"2026-05-18T12:32:31Z"}],"graph_snapshots":[{"event_id":"sha256:99aede2ecba510420579fa5ce7be4a15dfe65765253d3d20f6b46d97c236f665","target":"graph","created_at":"2026-05-17T23:52:18Z","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 define a graph network to be a coupled cell network where there are only one type of cell and one type of symmetric coupling between the cells. For a difference-coupled vector field on a graph network system, all the cells have the same internal dynamics, and the coupling between cells is identical, symmetric, and depends only on the difference of the states of the interacting cells. We define four nested sets of difference-coupled vector fields by adding further restrictions on the internal dynamics and the coupling functions. These restrictions require that these functions preserve zero o","authors_text":"James W. Swift, John M. Neuberger, N\\'andor Sieben","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-05-10T19:30:23Z","title":"Synchrony and Anti-Synchrony for Difference-Coupled Vector Fields on Graph Network Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.04144","kind":"arxiv","version":2},"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:adafd3984f37d352e59d8cf3c6f5a18dc1b96bc9297c9ed6bea097702fbbad42","target":"record","created_at":"2026-05-17T23:52:18Z","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":"9c5144af143d403cf3ef9c6650d3b83f6dc63efcf72da20525b2b99aa5199d3c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-05-10T19:30:23Z","title_canon_sha256":"c8b4edaedb65e6069f3c30c698d405e43e0f1cac50f49527bf623d608bd53a96"},"schema_version":"1.0","source":{"id":"1805.04144","kind":"arxiv","version":2}},"canonical_sha256":"4aa3246275f261126d873707091b310bec3746554c4e7a2d5aa73fa5b72dd5bd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4aa3246275f261126d873707091b310bec3746554c4e7a2d5aa73fa5b72dd5bd","first_computed_at":"2026-05-17T23:52:18.372112Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:18.372112Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dz2Y03EVQ9mvofDAnDk104DJ2LXKrjGm86mD9TxXQqbJfTtddmDfCGK8GgkiVojbjN4LwG7IUsbHKHM3pQEWAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:18.372741Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.04144","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:adafd3984f37d352e59d8cf3c6f5a18dc1b96bc9297c9ed6bea097702fbbad42","sha256:99aede2ecba510420579fa5ce7be4a15dfe65765253d3d20f6b46d97c236f665"],"state_sha256":"ad4cb54538af4e065f5691f6d5f528d15488f4d63254e0cc5fdd0a9b5f1a5c9d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zyzU1/usvAVdA2NNjDuDBlHs1GKl5kPXc/7WWF5AcjW6Gm4Pn/mHDYjQobeAX0/tiFZR8Lww7zvr9b148YbfAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T10:44:15.078363Z","bundle_sha256":"235f02a744ea493fb6e85a70d967b9ec9b0826c60728604dfbe6dbdd4829c3e5"}}