{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:EYPOVHLVGKK4DJVZDZ2QVCXKXM","short_pith_number":"pith:EYPOVHLV","canonical_record":{"source":{"id":"1011.2910","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2010-11-12T13:58:04Z","cross_cats_sorted":[],"title_canon_sha256":"723634c52817360276972cc62301b86068066e464c1ae4efec81eb63142c13d8","abstract_canon_sha256":"9a962ae4f4dd98f496423d297e68b9d27b1de92b737cb2ccc10a247ebc40430a"},"schema_version":"1.0"},"canonical_sha256":"261eea9d753295c1a6b91e750a8aeabb1247fec44ace2dca77bd8dd086c94367","source":{"kind":"arxiv","id":"1011.2910","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.2910","created_at":"2026-05-18T04:36:07Z"},{"alias_kind":"arxiv_version","alias_value":"1011.2910v1","created_at":"2026-05-18T04:36:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.2910","created_at":"2026-05-18T04:36:07Z"},{"alias_kind":"pith_short_12","alias_value":"EYPOVHLVGKK4","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"EYPOVHLVGKK4DJVZ","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"EYPOVHLV","created_at":"2026-05-18T12:26:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:EYPOVHLVGKK4DJVZDZ2QVCXKXM","target":"record","payload":{"canonical_record":{"source":{"id":"1011.2910","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2010-11-12T13:58:04Z","cross_cats_sorted":[],"title_canon_sha256":"723634c52817360276972cc62301b86068066e464c1ae4efec81eb63142c13d8","abstract_canon_sha256":"9a962ae4f4dd98f496423d297e68b9d27b1de92b737cb2ccc10a247ebc40430a"},"schema_version":"1.0"},"canonical_sha256":"261eea9d753295c1a6b91e750a8aeabb1247fec44ace2dca77bd8dd086c94367","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:36:07.874194Z","signature_b64":"WufI+fiG7BOhXSaXcmB5aHWV8r1RKK6WifEbrP4HcI5P0DLBjg/qKBdpA3ZTfh1cuC++K8rZxQxOy7Jux2CsBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"261eea9d753295c1a6b91e750a8aeabb1247fec44ace2dca77bd8dd086c94367","last_reissued_at":"2026-05-18T04:36:07.873670Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:36:07.873670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.2910","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":"2026-05-18T04:36:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vo8atUTxRkgZJZRsY3xFCLzNwc8r0z1231G0xXxDSKWk/P3mdvtAdUcNBYNJh9sh/QHfKELWjvbqbH/MClA3Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T22:54:28.193519Z"},"content_sha256":"d024b5a8e721a474f63ff51ca18d41f7e4125180a114987aaae933d04be6b722","schema_version":"1.0","event_id":"sha256:d024b5a8e721a474f63ff51ca18d41f7e4125180a114987aaae933d04be6b722"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:EYPOVHLVGKK4DJVZDZ2QVCXKXM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Pattern Formation Induced by Time-Dependent Advection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.PS","authors_text":"A. Pikovsky, A. V. Straube","submitted_at":"2010-11-12T13:58:04Z","abstract_excerpt":"We study pattern-forming instabilities in reaction-advection-diffusion systems. We develop an approach based on Lyapunov-Bloch exponents to figure out the impact of a spatially periodic mixing flow on the stability of a spatially homogeneous state. We deal with the flows periodic in space that may have arbitrary time dependence. We propose a discrete in time model, where reaction, advection, and diffusion act as successive operators, and show that a mixing advection can lead to a pattern-forming instability in a two-component system where only one of the species is advected. Physically, this c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.2910","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":"2026-05-18T04:36:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sQFgfQe23/BXKET4BCSLy72sWTeo0269+0pSdZXgGGmavS4PwkQ3DVsLn1DxzdgU09LWGQoahCy9OpV94shRAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T22:54:28.193868Z"},"content_sha256":"f3868a049166b0e8fdef37afc875b0afcbbee13220b8de8bd8473455497f6f3e","schema_version":"1.0","event_id":"sha256:f3868a049166b0e8fdef37afc875b0afcbbee13220b8de8bd8473455497f6f3e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EYPOVHLVGKK4DJVZDZ2QVCXKXM/bundle.json","state_url":"https://pith.science/pith/EYPOVHLVGKK4DJVZDZ2QVCXKXM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EYPOVHLVGKK4DJVZDZ2QVCXKXM/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":"2026-06-10T22:54:28Z","links":{"resolver":"https://pith.science/pith/EYPOVHLVGKK4DJVZDZ2QVCXKXM","bundle":"https://pith.science/pith/EYPOVHLVGKK4DJVZDZ2QVCXKXM/bundle.json","state":"https://pith.science/pith/EYPOVHLVGKK4DJVZDZ2QVCXKXM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EYPOVHLVGKK4DJVZDZ2QVCXKXM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:EYPOVHLVGKK4DJVZDZ2QVCXKXM","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":"9a962ae4f4dd98f496423d297e68b9d27b1de92b737cb2ccc10a247ebc40430a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2010-11-12T13:58:04Z","title_canon_sha256":"723634c52817360276972cc62301b86068066e464c1ae4efec81eb63142c13d8"},"schema_version":"1.0","source":{"id":"1011.2910","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.2910","created_at":"2026-05-18T04:36:07Z"},{"alias_kind":"arxiv_version","alias_value":"1011.2910v1","created_at":"2026-05-18T04:36:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.2910","created_at":"2026-05-18T04:36:07Z"},{"alias_kind":"pith_short_12","alias_value":"EYPOVHLVGKK4","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"EYPOVHLVGKK4DJVZ","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"EYPOVHLV","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:f3868a049166b0e8fdef37afc875b0afcbbee13220b8de8bd8473455497f6f3e","target":"graph","created_at":"2026-05-18T04:36:07Z","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 study pattern-forming instabilities in reaction-advection-diffusion systems. We develop an approach based on Lyapunov-Bloch exponents to figure out the impact of a spatially periodic mixing flow on the stability of a spatially homogeneous state. We deal with the flows periodic in space that may have arbitrary time dependence. We propose a discrete in time model, where reaction, advection, and diffusion act as successive operators, and show that a mixing advection can lead to a pattern-forming instability in a two-component system where only one of the species is advected. Physically, this c","authors_text":"A. Pikovsky, A. V. Straube","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2010-11-12T13:58:04Z","title":"Pattern Formation Induced by Time-Dependent Advection"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.2910","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:d024b5a8e721a474f63ff51ca18d41f7e4125180a114987aaae933d04be6b722","target":"record","created_at":"2026-05-18T04:36:07Z","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":"9a962ae4f4dd98f496423d297e68b9d27b1de92b737cb2ccc10a247ebc40430a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2010-11-12T13:58:04Z","title_canon_sha256":"723634c52817360276972cc62301b86068066e464c1ae4efec81eb63142c13d8"},"schema_version":"1.0","source":{"id":"1011.2910","kind":"arxiv","version":1}},"canonical_sha256":"261eea9d753295c1a6b91e750a8aeabb1247fec44ace2dca77bd8dd086c94367","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"261eea9d753295c1a6b91e750a8aeabb1247fec44ace2dca77bd8dd086c94367","first_computed_at":"2026-05-18T04:36:07.873670Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:36:07.873670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WufI+fiG7BOhXSaXcmB5aHWV8r1RKK6WifEbrP4HcI5P0DLBjg/qKBdpA3ZTfh1cuC++K8rZxQxOy7Jux2CsBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:36:07.874194Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.2910","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d024b5a8e721a474f63ff51ca18d41f7e4125180a114987aaae933d04be6b722","sha256:f3868a049166b0e8fdef37afc875b0afcbbee13220b8de8bd8473455497f6f3e"],"state_sha256":"c90b38ecfe4012639fde3149b0bee18d59a77a890d62511eed49bf9a68c44502"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IIm517E/pNOz0wkbr47wIKmokPZh2q3qdYB18+45XTGEpaLZE1CnEQ+NOqHpPp080Sa7pYd5iEbonGD5lKMkBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T22:54:28.195864Z","bundle_sha256":"cf8371c38aee672f4c0bb59674b8ae25ac28256ff38022876feb36aa4993952c"}}