{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:25TIPNVLV6IPRD52FR3FQY6N5K","short_pith_number":"pith:25TIPNVL","canonical_record":{"source":{"id":"1604.01794","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2016-04-05T02:19:33Z","cross_cats_sorted":["math.DS","math.OC","physics.comp-ph"],"title_canon_sha256":"dce72de93b5d32aaae9e60c569f0c360e214cacd3607518b6f0ba7a02b4a66bd","abstract_canon_sha256":"659decbf163f5d76947fbe1c47cb93604d76c7dfe0757a60e5b8045d2d02f66b"},"schema_version":"1.0"},"canonical_sha256":"d76687b6abaf90f88fba2c765863cdea844064f919aeed12d728a8206616c499","source":{"kind":"arxiv","id":"1604.01794","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.01794","created_at":"2026-05-18T00:44:47Z"},{"alias_kind":"arxiv_version","alias_value":"1604.01794v2","created_at":"2026-05-18T00:44:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.01794","created_at":"2026-05-18T00:44:47Z"},{"alias_kind":"pith_short_12","alias_value":"25TIPNVLV6IP","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"25TIPNVLV6IPRD52","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"25TIPNVL","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:25TIPNVLV6IPRD52FR3FQY6N5K","target":"record","payload":{"canonical_record":{"source":{"id":"1604.01794","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2016-04-05T02:19:33Z","cross_cats_sorted":["math.DS","math.OC","physics.comp-ph"],"title_canon_sha256":"dce72de93b5d32aaae9e60c569f0c360e214cacd3607518b6f0ba7a02b4a66bd","abstract_canon_sha256":"659decbf163f5d76947fbe1c47cb93604d76c7dfe0757a60e5b8045d2d02f66b"},"schema_version":"1.0"},"canonical_sha256":"d76687b6abaf90f88fba2c765863cdea844064f919aeed12d728a8206616c499","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:47.718972Z","signature_b64":"GQUPfO/7/YXz1jTprMVY1+e7DD0YuUYzUpYaUAYECIserPNWj1p9/0ndK+frQcvbUBdE5ynv3nLz41rreSj7Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d76687b6abaf90f88fba2c765863cdea844064f919aeed12d728a8206616c499","last_reissued_at":"2026-05-18T00:44:47.718368Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:47.718368Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.01794","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":"2026-05-18T00:44:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ukq/bszUVIIdU4QSlHggWPm9Jkv4kSlLqpF3czHdPK361eya2fo+dD14ZJ7HCyLDchaBEQz5H3EnrcexFX1cCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T21:42:36.577271Z"},"content_sha256":"34504977a8eda442663a3ce86723db1602a80e5c151e1ea1c87a7b34758fbdb9","schema_version":"1.0","event_id":"sha256:34504977a8eda442663a3ce86723db1602a80e5c151e1ea1c87a7b34758fbdb9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:25TIPNVLV6IPRD52FR3FQY6N5K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal initial condition of passive tracers for their maximal mixing in finite time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.OC","physics.comp-ph"],"primary_cat":"physics.flu-dyn","authors_text":"Mohammad Farazmand","submitted_at":"2016-04-05T02:19:33Z","abstract_excerpt":"The efficiency of a fluid mixing device is often limited by fundamental laws and/or design constraints, such that a perfectly homogeneous mixture cannot be obtained in finite time. Here, we address the natural corollary question: Given the best available mixer, what is the optimal initial tracer pattern that leads to the most homogeneous mixture after a prescribed finite time? For ideal passive tracers, we show that this optimal initial condition coincides with the right singular vector (corresponding to the smallest singular value) of a suitably truncated Perron-Frobenius (PF) operator. The t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.01794","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":"2026-05-18T00:44:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IjXxJMXY7LdvwK3YitDWuevsJGhDgBgMmTWpAhrSbTOkyQUrCXD/sXtT1n7cq/6E9SdOEOh+nXjvVWKv7s3EDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T21:42:36.577833Z"},"content_sha256":"9fc9cd6fe0d2d10a2e590cfe1c748b26e6dac07331446cc32dbabdb4db762061","schema_version":"1.0","event_id":"sha256:9fc9cd6fe0d2d10a2e590cfe1c748b26e6dac07331446cc32dbabdb4db762061"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/25TIPNVLV6IPRD52FR3FQY6N5K/bundle.json","state_url":"https://pith.science/pith/25TIPNVLV6IPRD52FR3FQY6N5K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/25TIPNVLV6IPRD52FR3FQY6N5K/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":"2026-05-27T21:42:36Z","links":{"resolver":"https://pith.science/pith/25TIPNVLV6IPRD52FR3FQY6N5K","bundle":"https://pith.science/pith/25TIPNVLV6IPRD52FR3FQY6N5K/bundle.json","state":"https://pith.science/pith/25TIPNVLV6IPRD52FR3FQY6N5K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/25TIPNVLV6IPRD52FR3FQY6N5K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:25TIPNVLV6IPRD52FR3FQY6N5K","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":"659decbf163f5d76947fbe1c47cb93604d76c7dfe0757a60e5b8045d2d02f66b","cross_cats_sorted":["math.DS","math.OC","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2016-04-05T02:19:33Z","title_canon_sha256":"dce72de93b5d32aaae9e60c569f0c360e214cacd3607518b6f0ba7a02b4a66bd"},"schema_version":"1.0","source":{"id":"1604.01794","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.01794","created_at":"2026-05-18T00:44:47Z"},{"alias_kind":"arxiv_version","alias_value":"1604.01794v2","created_at":"2026-05-18T00:44:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.01794","created_at":"2026-05-18T00:44:47Z"},{"alias_kind":"pith_short_12","alias_value":"25TIPNVLV6IP","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"25TIPNVLV6IPRD52","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"25TIPNVL","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:9fc9cd6fe0d2d10a2e590cfe1c748b26e6dac07331446cc32dbabdb4db762061","target":"graph","created_at":"2026-05-18T00:44:47Z","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":"The efficiency of a fluid mixing device is often limited by fundamental laws and/or design constraints, such that a perfectly homogeneous mixture cannot be obtained in finite time. Here, we address the natural corollary question: Given the best available mixer, what is the optimal initial tracer pattern that leads to the most homogeneous mixture after a prescribed finite time? For ideal passive tracers, we show that this optimal initial condition coincides with the right singular vector (corresponding to the smallest singular value) of a suitably truncated Perron-Frobenius (PF) operator. The t","authors_text":"Mohammad Farazmand","cross_cats":["math.DS","math.OC","physics.comp-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2016-04-05T02:19:33Z","title":"Optimal initial condition of passive tracers for their maximal mixing in finite time"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.01794","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":"sha256:34504977a8eda442663a3ce86723db1602a80e5c151e1ea1c87a7b34758fbdb9","target":"record","created_at":"2026-05-18T00:44:47Z","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":"659decbf163f5d76947fbe1c47cb93604d76c7dfe0757a60e5b8045d2d02f66b","cross_cats_sorted":["math.DS","math.OC","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2016-04-05T02:19:33Z","title_canon_sha256":"dce72de93b5d32aaae9e60c569f0c360e214cacd3607518b6f0ba7a02b4a66bd"},"schema_version":"1.0","source":{"id":"1604.01794","kind":"arxiv","version":2}},"canonical_sha256":"d76687b6abaf90f88fba2c765863cdea844064f919aeed12d728a8206616c499","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d76687b6abaf90f88fba2c765863cdea844064f919aeed12d728a8206616c499","first_computed_at":"2026-05-18T00:44:47.718368Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:47.718368Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GQUPfO/7/YXz1jTprMVY1+e7DD0YuUYzUpYaUAYECIserPNWj1p9/0ndK+frQcvbUBdE5ynv3nLz41rreSj7Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:47.718972Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.01794","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:34504977a8eda442663a3ce86723db1602a80e5c151e1ea1c87a7b34758fbdb9","sha256:9fc9cd6fe0d2d10a2e590cfe1c748b26e6dac07331446cc32dbabdb4db762061"],"state_sha256":"79c83a28f21b1e1aefb4605717cdcacf8d93b11157cdaa98e21a0c52a9efb88d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8szvgLlGE4rEUPW/hOjwyDkX2TSmlQhiigAdoO0ySrNdhLdt9fikU6x12mSxDG5GhwGhpTmToAmZWbAGBsbzAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T21:42:36.581217Z","bundle_sha256":"bfc5384ce3d42080e3427e82ae7c377daabc955e1a85ce7646d532485640dc0c"}}