{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:S3L3ZR2XRIZOZYBLD6QY6W7JMK","short_pith_number":"pith:S3L3ZR2X","canonical_record":{"source":{"id":"2605.15158","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.soft","submitted_at":"2026-05-14T17:51:59Z","cross_cats_sorted":[],"title_canon_sha256":"adfcce83f903ff8b9d35d27c0c9868a82c42d45ce902750cf5921855aaca7921","abstract_canon_sha256":"ed6ff4199fe59fa2f233c909a935d9419b116de26f6e6dc4e43d242056f8e171"},"schema_version":"1.0"},"canonical_sha256":"96d7bcc7578a32ece02b1fa18f5be962bb113af074bbd164e3bc1651eaafda11","source":{"kind":"arxiv","id":"2605.15158","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.15158","created_at":"2026-05-17T21:18:33Z"},{"alias_kind":"arxiv_version","alias_value":"2605.15158v1","created_at":"2026-05-17T21:18:33Z"},{"alias_kind":"pith_short_12","alias_value":"S3L3ZR2XRIZO","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"S3L3ZR2XRIZOZYBL","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"S3L3ZR2X","created_at":"2026-05-18T12:33:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:S3L3ZR2XRIZOZYBLD6QY6W7JMK","target":"record","payload":{"canonical_record":{"source":{"id":"2605.15158","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.soft","submitted_at":"2026-05-14T17:51:59Z","cross_cats_sorted":[],"title_canon_sha256":"adfcce83f903ff8b9d35d27c0c9868a82c42d45ce902750cf5921855aaca7921","abstract_canon_sha256":"ed6ff4199fe59fa2f233c909a935d9419b116de26f6e6dc4e43d242056f8e171"},"schema_version":"1.0"},"canonical_sha256":"96d7bcc7578a32ece02b1fa18f5be962bb113af074bbd164e3bc1651eaafda11","receipt":{"kind":"pith_receipt","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.2","canonical_sha256":"96d7bcc7578a32ece02b1fa18f5be962bb113af074bbd164e3bc1651eaafda11","last_reissued_at":"2026-05-17T21:57:18.739757Z","signature_status":"unsigned_v0","first_computed_at":"2026-05-17T21:40:25.417710Z"},"source_kind":"arxiv","source_id":"2605.15158","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":"2026-05-17T21:18:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hwGMvspLcG2u8GbUMIWiabSXXATQyfv2ZsGaT5KflrkCYPU/HPA8KbKrC6osjX373rRQk+++iM0ruGx5bP1ODA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T05:50:42.908102Z"},"content_sha256":"2da2d8270d521f0d7d30419406c865d9d902e6f0ab23e9a7e1407f69362546bd","schema_version":"1.0","event_id":"sha256:2da2d8270d521f0d7d30419406c865d9d902e6f0ab23e9a7e1407f69362546bd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:S3L3ZR2XRIZOZYBLD6QY6W7JMK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Duality Between Chemical Potential Dynamics and Reaction-Diffusion Systems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Chemical-potential theories embed as slow manifolds in mass-conserving reaction-diffusion systems","cross_cats":[],"primary_cat":"cond-mat.soft","authors_text":"Daniel Zhou, Erwin Frey","submitted_at":"2026-05-14T17:51:59Z","abstract_excerpt":"Pattern formation in soft, active, and biological matter is described by two ostensibly distinct continuum frameworks: phase-field theories driven by chemical-potential gradients, and mass-conserving reaction-diffusion (McRD) dynamics governed by local interconversion kinetics. Here we establish a constructive, equation-level duality valid in the nonlinear, far-from-equilibrium regime. McRD is the broader class: every chemical-potential theory with conserved order parameters embeds as the slow dynamics on an attracting manifold of an McRD system; conversely, every McRD with attractive nullclin"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"McRD is the broader class: every chemical-potential theory with conserved order parameters embeds as the slow dynamics on an attracting manifold of an McRD system; conversely, every McRD with attractive nullcline admits an exact chemical-potential representation in the fast-interconversion limit, with the constitutive relation set by the nullcline.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The assumption that an attracting manifold exists for the slow dynamics and that the nullcline is attractive in the fast-interconversion limit, allowing the exact embedding and recovery of the chemical-potential representation.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"An exact equation-level duality maps every conserved chemical-potential theory onto the slow manifold of a mass-conserving reaction-diffusion system and recovers the chemical-potential form from any McRD system with an attractive nullcline in the fast-interconversion limit.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Chemical-potential theories embed as slow manifolds in mass-conserving reaction-diffusion systems","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"9fe2b3308d7e2644550864d22411ce7ae1855c026063d67baae8a3302f12980a"},"source":{"id":"2605.15158","kind":"arxiv","version":1},"verdict":{"id":"bca65b59-da87-465c-8b64-77ec6a16e908","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T03:14:42.711089Z","strongest_claim":"McRD is the broader class: every chemical-potential theory with conserved order parameters embeds as the slow dynamics on an attracting manifold of an McRD system; conversely, every McRD with attractive nullcline admits an exact chemical-potential representation in the fast-interconversion limit, with the constitutive relation set by the nullcline.","one_line_summary":"An exact equation-level duality maps every conserved chemical-potential theory onto the slow manifold of a mass-conserving reaction-diffusion system and recovers the chemical-potential form from any McRD system with an attractive nullcline in the fast-interconversion limit.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The assumption that an attracting manifold exists for the slow dynamics and that the nullcline is attractive in the fast-interconversion limit, allowing the exact embedding and recovery of the chemical-potential representation.","pith_extraction_headline":"Chemical-potential theories embed as slow manifolds in mass-conserving reaction-diffusion systems"},"references":{"count":80,"sample":[{"doi":"","year":null,"title":"The source–sink term is expanded in the same way as before, s(ϕ) =s α +s ′ α δϕ+O(δϕ 2),(C14) ForD m = 0 (so thatD c =M), the linearized dynamics read ∂tδc=M∇ 2δc−A c δc−A m δm+s α +s ′ αδϕ,(C15a) ∂tδ","work_id":"cf35591c-7e80-4cf6-a5e5-621a26cecf87","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"II D) Equations solved.For Figs","work_id":"4729944e-b8fd-48a1-b2ad-dc491a2cfd31","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"IV A) Equations solved.In Figs","work_id":"5c326fd1-8db8-4ca4-8ea2-17300fabbb01","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"V C) Equations solved.We integrate the original nonrecip- rocal two-component conserved dynamics [Eqs","work_id":"ae4a8c5e-86fb-4236-943f-edc5054484dc","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1977,"title":"P. C. Hohenberg and B. I. Halperin, Rev. Mod. Phys.49, 435 (1977)","work_id":"365934ad-efbe-450d-b219-34fa57437107","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":80,"snapshot_sha256":"37b677025ce4e7b0a3584da648514a8893cca69a4875d84dfdd407dd4b90209f","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"f1ba3ceb054fea37d1ff5ccc1ad8e89d424d67d0302a16f7fa5d57bcce2847f1"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":"bca65b59-da87-465c-8b64-77ec6a16e908"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T21:57:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Pb3Pla1Zfv8lhdvxZYGgj4ak8RHU1+RKJye3QfczUt874wv9S+cT3fKlL+A6SGSbFkQ98njvKArLdtxCVl0yDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T05:50:42.909419Z"},"content_sha256":"bcb35462522f8dee19f979ed340ff92aabcaef4e31f0ca0f5cb337ecbba45a64","schema_version":"1.0","event_id":"sha256:bcb35462522f8dee19f979ed340ff92aabcaef4e31f0ca0f5cb337ecbba45a64"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S3L3ZR2XRIZOZYBLD6QY6W7JMK/bundle.json","state_url":"https://pith.science/pith/S3L3ZR2XRIZOZYBLD6QY6W7JMK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S3L3ZR2XRIZOZYBLD6QY6W7JMK/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":"2026-06-10T05:50:42Z","links":{"resolver":"https://pith.science/pith/S3L3ZR2XRIZOZYBLD6QY6W7JMK","bundle":"https://pith.science/pith/S3L3ZR2XRIZOZYBLD6QY6W7JMK/bundle.json","state":"https://pith.science/pith/S3L3ZR2XRIZOZYBLD6QY6W7JMK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S3L3ZR2XRIZOZYBLD6QY6W7JMK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:S3L3ZR2XRIZOZYBLD6QY6W7JMK","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":"ed6ff4199fe59fa2f233c909a935d9419b116de26f6e6dc4e43d242056f8e171","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.soft","submitted_at":"2026-05-14T17:51:59Z","title_canon_sha256":"adfcce83f903ff8b9d35d27c0c9868a82c42d45ce902750cf5921855aaca7921"},"schema_version":"1.0","source":{"id":"2605.15158","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.15158","created_at":"2026-05-17T21:18:33Z"},{"alias_kind":"arxiv_version","alias_value":"2605.15158v1","created_at":"2026-05-17T21:18:33Z"},{"alias_kind":"pith_short_12","alias_value":"S3L3ZR2XRIZO","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"S3L3ZR2XRIZOZYBL","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"S3L3ZR2X","created_at":"2026-05-18T12:33:37Z"}],"graph_snapshots":[{"event_id":"sha256:bcb35462522f8dee19f979ed340ff92aabcaef4e31f0ca0f5cb337ecbba45a64","target":"graph","created_at":"2026-05-17T21:57:18Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"McRD is the broader class: every chemical-potential theory with conserved order parameters embeds as the slow dynamics on an attracting manifold of an McRD system; conversely, every McRD with attractive nullcline admits an exact chemical-potential representation in the fast-interconversion limit, with the constitutive relation set by the nullcline."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The assumption that an attracting manifold exists for the slow dynamics and that the nullcline is attractive in the fast-interconversion limit, allowing the exact embedding and recovery of the chemical-potential representation."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"An exact equation-level duality maps every conserved chemical-potential theory onto the slow manifold of a mass-conserving reaction-diffusion system and recovers the chemical-potential form from any McRD system with an attractive nullcline in the fast-interconversion limit."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Chemical-potential theories embed as slow manifolds in mass-conserving reaction-diffusion systems"}],"snapshot_sha256":"9fe2b3308d7e2644550864d22411ce7ae1855c026063d67baae8a3302f12980a"},"formal_canon":{"evidence_count":2,"snapshot_sha256":"f1ba3ceb054fea37d1ff5ccc1ad8e89d424d67d0302a16f7fa5d57bcce2847f1"},"paper":{"abstract_excerpt":"Pattern formation in soft, active, and biological matter is described by two ostensibly distinct continuum frameworks: phase-field theories driven by chemical-potential gradients, and mass-conserving reaction-diffusion (McRD) dynamics governed by local interconversion kinetics. Here we establish a constructive, equation-level duality valid in the nonlinear, far-from-equilibrium regime. McRD is the broader class: every chemical-potential theory with conserved order parameters embeds as the slow dynamics on an attracting manifold of an McRD system; conversely, every McRD with attractive nullclin","authors_text":"Daniel Zhou, Erwin Frey","cross_cats":[],"headline":"Chemical-potential theories embed as slow manifolds in mass-conserving reaction-diffusion systems","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.soft","submitted_at":"2026-05-14T17:51:59Z","title":"Duality Between Chemical Potential Dynamics and Reaction-Diffusion Systems"},"references":{"count":80,"internal_anchors":0,"resolved_work":80,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"The source–sink term is expanded in the same way as before, s(ϕ) =s α +s ′ α δϕ+O(δϕ 2),(C14) ForD m = 0 (so thatD c =M), the linearized dynamics read ∂tδc=M∇ 2δc−A c δc−A m δm+s α +s ′ αδϕ,(C15a) ∂tδ","work_id":"cf35591c-7e80-4cf6-a5e5-621a26cecf87","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"II D) Equations solved.For Figs","work_id":"4729944e-b8fd-48a1-b2ad-dc491a2cfd31","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"IV A) Equations solved.In Figs","work_id":"5c326fd1-8db8-4ca4-8ea2-17300fabbb01","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"V C) Equations solved.We integrate the original nonrecip- rocal two-component conserved dynamics [Eqs","work_id":"ae4a8c5e-86fb-4236-943f-edc5054484dc","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"P. C. Hohenberg and B. I. Halperin, Rev. Mod. Phys.49, 435 (1977)","work_id":"365934ad-efbe-450d-b219-34fa57437107","year":1977}],"snapshot_sha256":"37b677025ce4e7b0a3584da648514a8893cca69a4875d84dfdd407dd4b90209f"},"source":{"id":"2605.15158","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-15T03:14:42.711089Z","id":"bca65b59-da87-465c-8b64-77ec6a16e908","model_set":{"reader":"grok-4.3"},"one_line_summary":"An exact equation-level duality maps every conserved chemical-potential theory onto the slow manifold of a mass-conserving reaction-diffusion system and recovers the chemical-potential form from any McRD system with an attractive nullcline in the fast-interconversion limit.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Chemical-potential theories embed as slow manifolds in mass-conserving reaction-diffusion systems","strongest_claim":"McRD is the broader class: every chemical-potential theory with conserved order parameters embeds as the slow dynamics on an attracting manifold of an McRD system; conversely, every McRD with attractive nullcline admits an exact chemical-potential representation in the fast-interconversion limit, with the constitutive relation set by the nullcline.","weakest_assumption":"The assumption that an attracting manifold exists for the slow dynamics and that the nullcline is attractive in the fast-interconversion limit, allowing the exact embedding and recovery of the chemical-potential representation."}},"verdict_id":"bca65b59-da87-465c-8b64-77ec6a16e908"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:2da2d8270d521f0d7d30419406c865d9d902e6f0ab23e9a7e1407f69362546bd","target":"record","created_at":"2026-05-17T21:18:33Z","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":"ed6ff4199fe59fa2f233c909a935d9419b116de26f6e6dc4e43d242056f8e171","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.soft","submitted_at":"2026-05-14T17:51:59Z","title_canon_sha256":"adfcce83f903ff8b9d35d27c0c9868a82c42d45ce902750cf5921855aaca7921"},"schema_version":"1.0","source":{"id":"2605.15158","kind":"arxiv","version":1}},"canonical_sha256":"96d7bcc7578a32ece02b1fa18f5be962bb113af074bbd164e3bc1651eaafda11","receipt":{"builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"96d7bcc7578a32ece02b1fa18f5be962bb113af074bbd164e3bc1651eaafda11","first_computed_at":"2026-05-17T21:40:25.417710Z","kind":"pith_receipt","last_reissued_at":"2026-05-17T21:57:18.739757Z","receipt_version":"0.2","signature_status":"unsigned_v0"},"source_id":"2605.15158","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2da2d8270d521f0d7d30419406c865d9d902e6f0ab23e9a7e1407f69362546bd","sha256:bcb35462522f8dee19f979ed340ff92aabcaef4e31f0ca0f5cb337ecbba45a64"],"state_sha256":"7ed16e61a289bf32425e6b5a96ed060a32e31b11664c37c9fea15db64055c3c1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k/tBPrz6hRpVZtYdCazT1JI9g8llntSKnA0ib/NICPiY07DkpfZ1biUm22sxrLCXcAokHGqNnL2dhaJlb4/rDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T05:50:42.918883Z","bundle_sha256":"d30be8fbfbfe01f98dc42419e84057eb47663b54b68f51f2462cfdfaac36a2e5"}}