{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:TCAH545MLNO3K6HEH7HSXGBDAY","short_pith_number":"pith:TCAH545M","canonical_record":{"source":{"id":"1612.03007","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-09T13:13:20Z","cross_cats_sorted":[],"title_canon_sha256":"31052e2d0d04cd85f0f77698906fb133a11d76a3aee2a65569b15c31b79e9f45","abstract_canon_sha256":"dd742794e6a3241733bd51855087ecf85c73876fa5d31f12b7efe79b3043b96f"},"schema_version":"1.0"},"canonical_sha256":"98807ef3ac5b5db578e43fcf2b98230633fed2610a0d345afe93bc92049a5775","source":{"kind":"arxiv","id":"1612.03007","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.03007","created_at":"2026-05-18T00:29:51Z"},{"alias_kind":"arxiv_version","alias_value":"1612.03007v2","created_at":"2026-05-18T00:29:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.03007","created_at":"2026-05-18T00:29:51Z"},{"alias_kind":"pith_short_12","alias_value":"TCAH545MLNO3","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"TCAH545MLNO3K6HE","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"TCAH545M","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:TCAH545MLNO3K6HEH7HSXGBDAY","target":"record","payload":{"canonical_record":{"source":{"id":"1612.03007","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-09T13:13:20Z","cross_cats_sorted":[],"title_canon_sha256":"31052e2d0d04cd85f0f77698906fb133a11d76a3aee2a65569b15c31b79e9f45","abstract_canon_sha256":"dd742794e6a3241733bd51855087ecf85c73876fa5d31f12b7efe79b3043b96f"},"schema_version":"1.0"},"canonical_sha256":"98807ef3ac5b5db578e43fcf2b98230633fed2610a0d345afe93bc92049a5775","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:51.964929Z","signature_b64":"LMm7H0ZDII1VLNahJktakcvJ+K7IqMBre0da0LAxIpW6P1ByFMtTQvkjdRflqIpPr//68She6fRmG4+tvSMABg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"98807ef3ac5b5db578e43fcf2b98230633fed2610a0d345afe93bc92049a5775","last_reissued_at":"2026-05-18T00:29:51.964510Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:51.964510Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.03007","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":"2026-05-18T00:29:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+H4rBEjgL0Rrnhb00ML5vGHerfLVk82ULJY6KI5dxwqgbtMpm1fEI+/Zwf/xmkkLujw1w+Cfs77vrQDGuLhfDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T12:29:25.948461Z"},"content_sha256":"5c1a20bb6e335986ccf39afa281546eec4f88e65682060428a59c5cd15b34664","schema_version":"1.0","event_id":"sha256:5c1a20bb6e335986ccf39afa281546eec4f88e65682060428a59c5cd15b34664"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:TCAH545MLNO3K6HEH7HSXGBDAY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A coupled ligand-receptor bulk-surface system on a moving domain: well posedness, regularity and convergence to equilibrium","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Amal Alphonse, Charles M. Elliott, Joana Terra","submitted_at":"2016-12-09T13:13:20Z","abstract_excerpt":"We prove existence, uniqueness, and regularity for a reaction-diffusion system of coupled bulk-surface equations on a moving domain modelling receptor-ligand dynamics in cells. The nonlinear coupling between the three unknowns is through the Robin boundary condition for the bulk quantity and the right hand sides of the two surface equations. Our results are new even in the non-moving setting, and in this case we also show exponential convergence to a steady state. The primary complications in the analysis are indeed the nonlinear coupling and the Robin boundary condition. For the well posednes"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.03007","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":"2026-05-18T00:29:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YJluRSA/wuLtmkjWR484hmXgVM/wI6EllWhFciUhltST3YlqFSYdnt4R65xtuKahmmUlechb6aLMXbgb6lE2AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T12:29:25.948818Z"},"content_sha256":"51898d241639da063c6e369e625e3606daa9856729a5a1be17c3caf416816c37","schema_version":"1.0","event_id":"sha256:51898d241639da063c6e369e625e3606daa9856729a5a1be17c3caf416816c37"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TCAH545MLNO3K6HEH7HSXGBDAY/bundle.json","state_url":"https://pith.science/pith/TCAH545MLNO3K6HEH7HSXGBDAY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TCAH545MLNO3K6HEH7HSXGBDAY/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":"2026-06-03T12:29:25Z","links":{"resolver":"https://pith.science/pith/TCAH545MLNO3K6HEH7HSXGBDAY","bundle":"https://pith.science/pith/TCAH545MLNO3K6HEH7HSXGBDAY/bundle.json","state":"https://pith.science/pith/TCAH545MLNO3K6HEH7HSXGBDAY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TCAH545MLNO3K6HEH7HSXGBDAY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TCAH545MLNO3K6HEH7HSXGBDAY","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":"dd742794e6a3241733bd51855087ecf85c73876fa5d31f12b7efe79b3043b96f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-09T13:13:20Z","title_canon_sha256":"31052e2d0d04cd85f0f77698906fb133a11d76a3aee2a65569b15c31b79e9f45"},"schema_version":"1.0","source":{"id":"1612.03007","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.03007","created_at":"2026-05-18T00:29:51Z"},{"alias_kind":"arxiv_version","alias_value":"1612.03007v2","created_at":"2026-05-18T00:29:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.03007","created_at":"2026-05-18T00:29:51Z"},{"alias_kind":"pith_short_12","alias_value":"TCAH545MLNO3","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"TCAH545MLNO3K6HE","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"TCAH545M","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:51898d241639da063c6e369e625e3606daa9856729a5a1be17c3caf416816c37","target":"graph","created_at":"2026-05-18T00:29:51Z","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 prove existence, uniqueness, and regularity for a reaction-diffusion system of coupled bulk-surface equations on a moving domain modelling receptor-ligand dynamics in cells. The nonlinear coupling between the three unknowns is through the Robin boundary condition for the bulk quantity and the right hand sides of the two surface equations. Our results are new even in the non-moving setting, and in this case we also show exponential convergence to a steady state. The primary complications in the analysis are indeed the nonlinear coupling and the Robin boundary condition. For the well posednes","authors_text":"Amal Alphonse, Charles M. Elliott, Joana Terra","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-09T13:13:20Z","title":"A coupled ligand-receptor bulk-surface system on a moving domain: well posedness, regularity and convergence to equilibrium"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.03007","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":"sha256:5c1a20bb6e335986ccf39afa281546eec4f88e65682060428a59c5cd15b34664","target":"record","created_at":"2026-05-18T00:29:51Z","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":"dd742794e6a3241733bd51855087ecf85c73876fa5d31f12b7efe79b3043b96f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-09T13:13:20Z","title_canon_sha256":"31052e2d0d04cd85f0f77698906fb133a11d76a3aee2a65569b15c31b79e9f45"},"schema_version":"1.0","source":{"id":"1612.03007","kind":"arxiv","version":2}},"canonical_sha256":"98807ef3ac5b5db578e43fcf2b98230633fed2610a0d345afe93bc92049a5775","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"98807ef3ac5b5db578e43fcf2b98230633fed2610a0d345afe93bc92049a5775","first_computed_at":"2026-05-18T00:29:51.964510Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:51.964510Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LMm7H0ZDII1VLNahJktakcvJ+K7IqMBre0da0LAxIpW6P1ByFMtTQvkjdRflqIpPr//68She6fRmG4+tvSMABg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:51.964929Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.03007","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5c1a20bb6e335986ccf39afa281546eec4f88e65682060428a59c5cd15b34664","sha256:51898d241639da063c6e369e625e3606daa9856729a5a1be17c3caf416816c37"],"state_sha256":"0c835d2eca96979d1e9ae530a2c1266c7c46c336d4f525ee27c483d105fb7443"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yhUqxd8Z0HXG5rrjSYk2mLPiuvwYAxCHT31ToiYFdwvHRV/gIs+AzBeDMAffVMH6zZZxs8rg4Fpbr9M6kU2NCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T12:29:25.950776Z","bundle_sha256":"1bf7ec185532a117e747c2d3ae2aa518e6deaa0f56fdf420ab937123f991ef31"}}