{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:3CWGZKMWD46BCDXRAXYHRETZB7","short_pith_number":"pith:3CWGZKMW","canonical_record":{"source":{"id":"2007.13637","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2020-07-27T15:34:31Z","cross_cats_sorted":["q-bio.QM"],"title_canon_sha256":"bbbd58caf831b828865e8edbea45c6e9fa0dd7948eec8aa4d5092ec2cf1a9499","abstract_canon_sha256":"c30a79e456ce2f56feca3c731e9485f50da609886f49a694e0c3eab0b64387b2"},"schema_version":"1.0"},"canonical_sha256":"d8ac6ca9961f3c110ef105f07892790ffe239b75c472ce7c5b96eba97bfc7f1b","source":{"kind":"arxiv","id":"2007.13637","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2007.13637","created_at":"2026-07-05T01:57:18Z"},{"alias_kind":"arxiv_version","alias_value":"2007.13637v2","created_at":"2026-07-05T01:57:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2007.13637","created_at":"2026-07-05T01:57:18Z"},{"alias_kind":"pith_short_12","alias_value":"3CWGZKMWD46B","created_at":"2026-07-05T01:57:18Z"},{"alias_kind":"pith_short_16","alias_value":"3CWGZKMWD46BCDXR","created_at":"2026-07-05T01:57:18Z"},{"alias_kind":"pith_short_8","alias_value":"3CWGZKMW","created_at":"2026-07-05T01:57:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:3CWGZKMWD46BCDXRAXYHRETZB7","target":"record","payload":{"canonical_record":{"source":{"id":"2007.13637","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2020-07-27T15:34:31Z","cross_cats_sorted":["q-bio.QM"],"title_canon_sha256":"bbbd58caf831b828865e8edbea45c6e9fa0dd7948eec8aa4d5092ec2cf1a9499","abstract_canon_sha256":"c30a79e456ce2f56feca3c731e9485f50da609886f49a694e0c3eab0b64387b2"},"schema_version":"1.0"},"canonical_sha256":"d8ac6ca9961f3c110ef105f07892790ffe239b75c472ce7c5b96eba97bfc7f1b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:57:18.763040Z","signature_b64":"NkM4WIE3fkFeKE7GkGGUGbFuZ4fMPeEDcwHFTgM+kumXuUnxy1XyOpl/rK5nQtl4oFzgBp/wKPhTAlhCsxsRAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d8ac6ca9961f3c110ef105f07892790ffe239b75c472ce7c5b96eba97bfc7f1b","last_reissued_at":"2026-07-05T01:57:18.762588Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:57:18.762588Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2007.13637","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":"2026-07-05T01:57:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uEtEIWly+4KmD0o24zXEnX4ujqJc73xTGmR2puaefNJ+FNbBR31k667ZWGFmkdbpASLV57o9wPm74o/Hnc90CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T18:17:42.083397Z"},"content_sha256":"7b5de5248a5fe73cbeb2b52190bdce7fc9604bc07b7e785a251baecf915c3159","schema_version":"1.0","event_id":"sha256:7b5de5248a5fe73cbeb2b52190bdce7fc9604bc07b7e785a251baecf915c3159"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:3CWGZKMWD46BCDXRAXYHRETZB7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal Mixing in Transport Networks: Numerical Optimization and Analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-bio.QM"],"primary_cat":"nlin.AO","authors_text":"Cassidy Mentus, Marcus Roper","submitted_at":"2020-07-27T15:34:31Z","abstract_excerpt":"Many foraging microorganisms rely upon cellular transport networks to deliver nutrients, fluid and organelles between different parts of the organism. Networked organisms ranging from filamentous fungi to slime molds demonstrate a remarkable ability to mix or disperse molecules and organelles in their transport media. Here we introduce mathematical tools to analyze the structure of energy efficient transport networks that maximize mixing and sending signals originating from and arriving at each node. We define two types of entropies on flows to quantify mixing and develop numerical algorithms "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.13637","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2007.13637/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T01:57:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pU7iBp8hmgxj8hbCBW1Bl9K5G/HOj9iV4OyMgmlFHalTGGcWvX9/FeaWutHiVUETUhkrACZKOIDHzjnCJw3IDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T18:17:42.083917Z"},"content_sha256":"e4adafe7b95716ddcee28ab6a35ef23a6ad31a11058236f2710a30d18487ac91","schema_version":"1.0","event_id":"sha256:e4adafe7b95716ddcee28ab6a35ef23a6ad31a11058236f2710a30d18487ac91"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3CWGZKMWD46BCDXRAXYHRETZB7/bundle.json","state_url":"https://pith.science/pith/3CWGZKMWD46BCDXRAXYHRETZB7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3CWGZKMWD46BCDXRAXYHRETZB7/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":"2026-08-19T18:17:42Z","links":{"resolver":"https://pith.science/pith/3CWGZKMWD46BCDXRAXYHRETZB7","bundle":"https://pith.science/pith/3CWGZKMWD46BCDXRAXYHRETZB7/bundle.json","state":"https://pith.science/pith/3CWGZKMWD46BCDXRAXYHRETZB7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3CWGZKMWD46BCDXRAXYHRETZB7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:3CWGZKMWD46BCDXRAXYHRETZB7","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":"c30a79e456ce2f56feca3c731e9485f50da609886f49a694e0c3eab0b64387b2","cross_cats_sorted":["q-bio.QM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2020-07-27T15:34:31Z","title_canon_sha256":"bbbd58caf831b828865e8edbea45c6e9fa0dd7948eec8aa4d5092ec2cf1a9499"},"schema_version":"1.0","source":{"id":"2007.13637","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2007.13637","created_at":"2026-07-05T01:57:18Z"},{"alias_kind":"arxiv_version","alias_value":"2007.13637v2","created_at":"2026-07-05T01:57:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2007.13637","created_at":"2026-07-05T01:57:18Z"},{"alias_kind":"pith_short_12","alias_value":"3CWGZKMWD46B","created_at":"2026-07-05T01:57:18Z"},{"alias_kind":"pith_short_16","alias_value":"3CWGZKMWD46BCDXR","created_at":"2026-07-05T01:57:18Z"},{"alias_kind":"pith_short_8","alias_value":"3CWGZKMW","created_at":"2026-07-05T01:57:18Z"}],"graph_snapshots":[{"event_id":"sha256:e4adafe7b95716ddcee28ab6a35ef23a6ad31a11058236f2710a30d18487ac91","target":"graph","created_at":"2026-07-05T01:57:18Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2007.13637/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Many foraging microorganisms rely upon cellular transport networks to deliver nutrients, fluid and organelles between different parts of the organism. Networked organisms ranging from filamentous fungi to slime molds demonstrate a remarkable ability to mix or disperse molecules and organelles in their transport media. Here we introduce mathematical tools to analyze the structure of energy efficient transport networks that maximize mixing and sending signals originating from and arriving at each node. We define two types of entropies on flows to quantify mixing and develop numerical algorithms ","authors_text":"Cassidy Mentus, Marcus Roper","cross_cats":["q-bio.QM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2020-07-27T15:34:31Z","title":"Optimal Mixing in Transport Networks: Numerical Optimization and Analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.13637","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":"sha256:7b5de5248a5fe73cbeb2b52190bdce7fc9604bc07b7e785a251baecf915c3159","target":"record","created_at":"2026-07-05T01:57:18Z","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":"c30a79e456ce2f56feca3c731e9485f50da609886f49a694e0c3eab0b64387b2","cross_cats_sorted":["q-bio.QM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2020-07-27T15:34:31Z","title_canon_sha256":"bbbd58caf831b828865e8edbea45c6e9fa0dd7948eec8aa4d5092ec2cf1a9499"},"schema_version":"1.0","source":{"id":"2007.13637","kind":"arxiv","version":2}},"canonical_sha256":"d8ac6ca9961f3c110ef105f07892790ffe239b75c472ce7c5b96eba97bfc7f1b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d8ac6ca9961f3c110ef105f07892790ffe239b75c472ce7c5b96eba97bfc7f1b","first_computed_at":"2026-07-05T01:57:18.762588Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:57:18.762588Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NkM4WIE3fkFeKE7GkGGUGbFuZ4fMPeEDcwHFTgM+kumXuUnxy1XyOpl/rK5nQtl4oFzgBp/wKPhTAlhCsxsRAA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:57:18.763040Z","signed_message":"canonical_sha256_bytes"},"source_id":"2007.13637","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7b5de5248a5fe73cbeb2b52190bdce7fc9604bc07b7e785a251baecf915c3159","sha256:e4adafe7b95716ddcee28ab6a35ef23a6ad31a11058236f2710a30d18487ac91"],"state_sha256":"dfd3ca2775bab700f864bc460abd52f7c7ab237644011845dfb0fe53258a945a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p6ClPQeDN6u64aQ7VPcEoRbvP27JE++eF9JzA/o/ITBAoYIJ8t1rSn6hpYmaSH2QwXd0gr8T6IfWFHKGt1s1Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T18:17:42.089085Z","bundle_sha256":"f5ef370c77b17945bb83c4b5f58793c824f8f68a9c199707a4991999f27ea4c4"}}