{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:JJOUARV5NXZ62QVY5DXYNRHLZL","short_pith_number":"pith:JJOUARV5","canonical_record":{"source":{"id":"1612.02079","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-12-07T00:22:40Z","cross_cats_sorted":[],"title_canon_sha256":"204186eb2e24618921a7107634b77494bb609d10d2d36b6118e451d68640587f","abstract_canon_sha256":"840b48276b8c6a21ee8966551220908d5e983a16083612afa9dc478f2e95fcbb"},"schema_version":"1.0"},"canonical_sha256":"4a5d4046bd6df3ed42b8e8ef86c4ebcad144d41e9715d96e2757cad794879610","source":{"kind":"arxiv","id":"1612.02079","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.02079","created_at":"2026-05-18T00:54:59Z"},{"alias_kind":"arxiv_version","alias_value":"1612.02079v2","created_at":"2026-05-18T00:54:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.02079","created_at":"2026-05-18T00:54:59Z"},{"alias_kind":"pith_short_12","alias_value":"JJOUARV5NXZ6","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JJOUARV5NXZ62QVY","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JJOUARV5","created_at":"2026-05-18T12:30:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:JJOUARV5NXZ62QVY5DXYNRHLZL","target":"record","payload":{"canonical_record":{"source":{"id":"1612.02079","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-12-07T00:22:40Z","cross_cats_sorted":[],"title_canon_sha256":"204186eb2e24618921a7107634b77494bb609d10d2d36b6118e451d68640587f","abstract_canon_sha256":"840b48276b8c6a21ee8966551220908d5e983a16083612afa9dc478f2e95fcbb"},"schema_version":"1.0"},"canonical_sha256":"4a5d4046bd6df3ed42b8e8ef86c4ebcad144d41e9715d96e2757cad794879610","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:59.732500Z","signature_b64":"BR7sZaxEmkTwuUyLkPkMt+9Jf1iTNHblmvuePCdIzSi1/WFZ166R/w3WxY7IGxwYCsufNt9Uvm6EBZRhf5V6AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4a5d4046bd6df3ed42b8e8ef86c4ebcad144d41e9715d96e2757cad794879610","last_reissued_at":"2026-05-18T00:54:59.731644Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:59.731644Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.02079","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":"2026-05-18T00:54:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q142QIgdPQOKra9jXthZDS3p66Mz2jeZMjkDKUyx8tnjKTvymnpmO2xQzeMQOrKQ3bJed9QMOAzbGq6Da+/oCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T04:09:31.760850Z"},"content_sha256":"0a55223188289c6878e387c47f313821bbab3a22030d1e7b019848860b8849ca","schema_version":"1.0","event_id":"sha256:0a55223188289c6878e387c47f313821bbab3a22030d1e7b019848860b8849ca"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:JJOUARV5NXZ62QVY5DXYNRHLZL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Slowly varying, macroscale models emerge from microscale dynamics over multiscale domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"A. J. Roberts, J. E. Bunder","submitted_at":"2016-12-07T00:22:40Z","abstract_excerpt":"Many physical systems are well described on domains which are relatively large in some directions but relatively thin in other directions. In this scenario we typically expect the system to have emergent structures that vary slowly over the large dimensions. For practical mathematical modelling of such systems we require efficient and accurate methodologies for reducing the dimension of the original system and extracting the emergent dynamics. Common mathematical approximations for determining the emergent dynamics often rely on self-consistency arguments or limits as the aspect ratio of the '"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.02079","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":"2026-05-18T00:54:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/X5ZFpDNSl7S5zQyd9H+CRoiwtEv5RawW9w+89OFspJ2j/aea+eInO6wy+LHprknwovI/E7CFmvHhh5q6u8fBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T04:09:31.761199Z"},"content_sha256":"82c1ff16c3288243c799912be7164c64707035ba7c05e6a290bfe6e7046168dc","schema_version":"1.0","event_id":"sha256:82c1ff16c3288243c799912be7164c64707035ba7c05e6a290bfe6e7046168dc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JJOUARV5NXZ62QVY5DXYNRHLZL/bundle.json","state_url":"https://pith.science/pith/JJOUARV5NXZ62QVY5DXYNRHLZL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JJOUARV5NXZ62QVY5DXYNRHLZL/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":"2026-06-07T04:09:31Z","links":{"resolver":"https://pith.science/pith/JJOUARV5NXZ62QVY5DXYNRHLZL","bundle":"https://pith.science/pith/JJOUARV5NXZ62QVY5DXYNRHLZL/bundle.json","state":"https://pith.science/pith/JJOUARV5NXZ62QVY5DXYNRHLZL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JJOUARV5NXZ62QVY5DXYNRHLZL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:JJOUARV5NXZ62QVY5DXYNRHLZL","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":"840b48276b8c6a21ee8966551220908d5e983a16083612afa9dc478f2e95fcbb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-12-07T00:22:40Z","title_canon_sha256":"204186eb2e24618921a7107634b77494bb609d10d2d36b6118e451d68640587f"},"schema_version":"1.0","source":{"id":"1612.02079","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.02079","created_at":"2026-05-18T00:54:59Z"},{"alias_kind":"arxiv_version","alias_value":"1612.02079v2","created_at":"2026-05-18T00:54:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.02079","created_at":"2026-05-18T00:54:59Z"},{"alias_kind":"pith_short_12","alias_value":"JJOUARV5NXZ6","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JJOUARV5NXZ62QVY","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JJOUARV5","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:82c1ff16c3288243c799912be7164c64707035ba7c05e6a290bfe6e7046168dc","target":"graph","created_at":"2026-05-18T00:54:59Z","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":"Many physical systems are well described on domains which are relatively large in some directions but relatively thin in other directions. In this scenario we typically expect the system to have emergent structures that vary slowly over the large dimensions. For practical mathematical modelling of such systems we require efficient and accurate methodologies for reducing the dimension of the original system and extracting the emergent dynamics. Common mathematical approximations for determining the emergent dynamics often rely on self-consistency arguments or limits as the aspect ratio of the '","authors_text":"A. J. Roberts, J. E. Bunder","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-12-07T00:22:40Z","title":"Slowly varying, macroscale models emerge from microscale dynamics over multiscale domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.02079","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":"sha256:0a55223188289c6878e387c47f313821bbab3a22030d1e7b019848860b8849ca","target":"record","created_at":"2026-05-18T00:54:59Z","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":"840b48276b8c6a21ee8966551220908d5e983a16083612afa9dc478f2e95fcbb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-12-07T00:22:40Z","title_canon_sha256":"204186eb2e24618921a7107634b77494bb609d10d2d36b6118e451d68640587f"},"schema_version":"1.0","source":{"id":"1612.02079","kind":"arxiv","version":2}},"canonical_sha256":"4a5d4046bd6df3ed42b8e8ef86c4ebcad144d41e9715d96e2757cad794879610","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4a5d4046bd6df3ed42b8e8ef86c4ebcad144d41e9715d96e2757cad794879610","first_computed_at":"2026-05-18T00:54:59.731644Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:59.731644Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BR7sZaxEmkTwuUyLkPkMt+9Jf1iTNHblmvuePCdIzSi1/WFZ166R/w3WxY7IGxwYCsufNt9Uvm6EBZRhf5V6AA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:59.732500Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.02079","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0a55223188289c6878e387c47f313821bbab3a22030d1e7b019848860b8849ca","sha256:82c1ff16c3288243c799912be7164c64707035ba7c05e6a290bfe6e7046168dc"],"state_sha256":"9243b3d7e8af2d1ce7c4d4271f94476d3d549857a23a6b8eee7a1692f12a0065"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fjurB3bKGVlwK8n6jiNDVqg4pa97D0Q+mG21h4wbaogjX8RvxyjXcAPkpaGn0wPWHYgUz9ByZLnKWQsNDDGNAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T04:09:31.763647Z","bundle_sha256":"fcc10eddd92c917939da171803e19927a56fb2379be3f55fde8508824029724f"}}