{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:66GHM6JZAJ2UDK2NCMOWEMMMPW","short_pith_number":"pith:66GHM6JZ","canonical_record":{"source":{"id":"1508.06449","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-08-26T11:35:34Z","cross_cats_sorted":[],"title_canon_sha256":"17daf2c54adcb6908cb17723ecf0f0f58417bc83d6631561e1841548ba63b478","abstract_canon_sha256":"13337346ea7d92403d719de4a4901f39a725f1095da63f875717fcf7c02a17ea"},"schema_version":"1.0"},"canonical_sha256":"f78c767939027541ab4d131d62318c7d9405ac9d6c98d976f54152a493a8d866","source":{"kind":"arxiv","id":"1508.06449","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.06449","created_at":"2026-05-18T01:34:42Z"},{"alias_kind":"arxiv_version","alias_value":"1508.06449v1","created_at":"2026-05-18T01:34:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.06449","created_at":"2026-05-18T01:34:42Z"},{"alias_kind":"pith_short_12","alias_value":"66GHM6JZAJ2U","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"66GHM6JZAJ2UDK2N","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"66GHM6JZ","created_at":"2026-05-18T12:29:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:66GHM6JZAJ2UDK2NCMOWEMMMPW","target":"record","payload":{"canonical_record":{"source":{"id":"1508.06449","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-08-26T11:35:34Z","cross_cats_sorted":[],"title_canon_sha256":"17daf2c54adcb6908cb17723ecf0f0f58417bc83d6631561e1841548ba63b478","abstract_canon_sha256":"13337346ea7d92403d719de4a4901f39a725f1095da63f875717fcf7c02a17ea"},"schema_version":"1.0"},"canonical_sha256":"f78c767939027541ab4d131d62318c7d9405ac9d6c98d976f54152a493a8d866","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:42.942099Z","signature_b64":"cK2onT/hjsZ9A9YJYcMBsmHJEXYgLLRxf0q/LOzM6QnzSNB/c/mT3ubYS3YfmhZjncfVw0Spt6+laPixlctmBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f78c767939027541ab4d131d62318c7d9405ac9d6c98d976f54152a493a8d866","last_reissued_at":"2026-05-18T01:34:42.941410Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:42.941410Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.06449","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":"2026-05-18T01:34:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"faQlPIJWrI4x/2n+2Qp4WdFU0ZF25ZdTzZu1WBeROra7cgReKKbM7OK2UGrCdgdwh1R55KO8QLm7L3NKumfQAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T07:27:50.480484Z"},"content_sha256":"90a8199bc39660d690f28f75a109d01a3ea93e75dd9ebf0f10d5d70f91a33c08","schema_version":"1.0","event_id":"sha256:90a8199bc39660d690f28f75a109d01a3ea93e75dd9ebf0f10d5d70f91a33c08"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:66GHM6JZAJ2UDK2NCMOWEMMMPW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global existence of bounded weak solutions to degenerate cross-diffusion equations in moving domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Athmane Bakhta, Virginie Ehrlacher","submitted_at":"2015-08-26T11:35:34Z","abstract_excerpt":"The aim of this note is to present preliminary existence results for a system of cross-diffusion equations defined on a domain with moving boundaries, which model the evolution of the concentrations of different chemical species in a solid during a Chemical Vapor Deposition process. The system of equations, when the domain remains fixed over time, can be seen formally as a gradient flow system which can be analyzed using the boundedness by entropy method introduced by Burger and J\\\"ungel. Preliminary existence results are presented in the case of a one-dimensional moving boundary domain."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.06449","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":"2026-05-18T01:34:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FrePC6Ul5SYSzOqzyz6feNY5b0EB8CMiKpdpIEwGw5PiGa/5wlrXHxquhjp92PPLuKDslNeXEsbJ6Tr/LKe+Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T07:27:50.480864Z"},"content_sha256":"2f4864d1f5b5967e9f3ba6375b6c426dc9669cd52fe72ec4ecc8384bc780dbfa","schema_version":"1.0","event_id":"sha256:2f4864d1f5b5967e9f3ba6375b6c426dc9669cd52fe72ec4ecc8384bc780dbfa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/66GHM6JZAJ2UDK2NCMOWEMMMPW/bundle.json","state_url":"https://pith.science/pith/66GHM6JZAJ2UDK2NCMOWEMMMPW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/66GHM6JZAJ2UDK2NCMOWEMMMPW/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":"2026-06-09T07:27:50Z","links":{"resolver":"https://pith.science/pith/66GHM6JZAJ2UDK2NCMOWEMMMPW","bundle":"https://pith.science/pith/66GHM6JZAJ2UDK2NCMOWEMMMPW/bundle.json","state":"https://pith.science/pith/66GHM6JZAJ2UDK2NCMOWEMMMPW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/66GHM6JZAJ2UDK2NCMOWEMMMPW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:66GHM6JZAJ2UDK2NCMOWEMMMPW","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":"13337346ea7d92403d719de4a4901f39a725f1095da63f875717fcf7c02a17ea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-08-26T11:35:34Z","title_canon_sha256":"17daf2c54adcb6908cb17723ecf0f0f58417bc83d6631561e1841548ba63b478"},"schema_version":"1.0","source":{"id":"1508.06449","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.06449","created_at":"2026-05-18T01:34:42Z"},{"alias_kind":"arxiv_version","alias_value":"1508.06449v1","created_at":"2026-05-18T01:34:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.06449","created_at":"2026-05-18T01:34:42Z"},{"alias_kind":"pith_short_12","alias_value":"66GHM6JZAJ2U","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"66GHM6JZAJ2UDK2N","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"66GHM6JZ","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:2f4864d1f5b5967e9f3ba6375b6c426dc9669cd52fe72ec4ecc8384bc780dbfa","target":"graph","created_at":"2026-05-18T01:34:42Z","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 aim of this note is to present preliminary existence results for a system of cross-diffusion equations defined on a domain with moving boundaries, which model the evolution of the concentrations of different chemical species in a solid during a Chemical Vapor Deposition process. The system of equations, when the domain remains fixed over time, can be seen formally as a gradient flow system which can be analyzed using the boundedness by entropy method introduced by Burger and J\\\"ungel. Preliminary existence results are presented in the case of a one-dimensional moving boundary domain.","authors_text":"Athmane Bakhta, Virginie Ehrlacher","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-08-26T11:35:34Z","title":"Global existence of bounded weak solutions to degenerate cross-diffusion equations in moving domain"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.06449","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":"sha256:90a8199bc39660d690f28f75a109d01a3ea93e75dd9ebf0f10d5d70f91a33c08","target":"record","created_at":"2026-05-18T01:34:42Z","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":"13337346ea7d92403d719de4a4901f39a725f1095da63f875717fcf7c02a17ea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-08-26T11:35:34Z","title_canon_sha256":"17daf2c54adcb6908cb17723ecf0f0f58417bc83d6631561e1841548ba63b478"},"schema_version":"1.0","source":{"id":"1508.06449","kind":"arxiv","version":1}},"canonical_sha256":"f78c767939027541ab4d131d62318c7d9405ac9d6c98d976f54152a493a8d866","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f78c767939027541ab4d131d62318c7d9405ac9d6c98d976f54152a493a8d866","first_computed_at":"2026-05-18T01:34:42.941410Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:42.941410Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cK2onT/hjsZ9A9YJYcMBsmHJEXYgLLRxf0q/LOzM6QnzSNB/c/mT3ubYS3YfmhZjncfVw0Spt6+laPixlctmBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:42.942099Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.06449","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:90a8199bc39660d690f28f75a109d01a3ea93e75dd9ebf0f10d5d70f91a33c08","sha256:2f4864d1f5b5967e9f3ba6375b6c426dc9669cd52fe72ec4ecc8384bc780dbfa"],"state_sha256":"59ab9c6fd981c64386fc24ef1c385aba1ffe9c35f01eab5c3f3aa1a48b9db3c9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/iSqZC0Wn+fFYo41/OshIloPIOMOuSynuvV/NX+1432hmne1GI3auFedmI9am/GHv9Pld4QBj6BEZ09zGgkNAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T07:27:50.483658Z","bundle_sha256":"f569ebaf724c84804a6c984060d285df4e74ccdb620390bdfeb2011b0fe79430"}}