{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:QNTDT54Q7RQJVHWEEBP7NTORVH","short_pith_number":"pith:QNTDT54Q","canonical_record":{"source":{"id":"2504.18484","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-04-25T16:51:35Z","cross_cats_sorted":[],"title_canon_sha256":"b8273da76434977a17ef69eb7eac3b5834a4dc655a9e35c1df2e46b57c920611","abstract_canon_sha256":"7248de792d0ed3e0ad2dd5dadbcd78010c2626278d24f8501797e42a4b996ce1"},"schema_version":"1.0"},"canonical_sha256":"836639f790fc609a9ec4205ff6cdd1a9c61fc07ff8d98569411bf5a495cbad8d","source":{"kind":"arxiv","id":"2504.18484","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.18484","created_at":"2026-07-05T10:54:08Z"},{"alias_kind":"arxiv_version","alias_value":"2504.18484v1","created_at":"2026-07-05T10:54:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.18484","created_at":"2026-07-05T10:54:08Z"},{"alias_kind":"pith_short_12","alias_value":"QNTDT54Q7RQJ","created_at":"2026-07-05T10:54:08Z"},{"alias_kind":"pith_short_16","alias_value":"QNTDT54Q7RQJVHWE","created_at":"2026-07-05T10:54:08Z"},{"alias_kind":"pith_short_8","alias_value":"QNTDT54Q","created_at":"2026-07-05T10:54:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:QNTDT54Q7RQJVHWEEBP7NTORVH","target":"record","payload":{"canonical_record":{"source":{"id":"2504.18484","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-04-25T16:51:35Z","cross_cats_sorted":[],"title_canon_sha256":"b8273da76434977a17ef69eb7eac3b5834a4dc655a9e35c1df2e46b57c920611","abstract_canon_sha256":"7248de792d0ed3e0ad2dd5dadbcd78010c2626278d24f8501797e42a4b996ce1"},"schema_version":"1.0"},"canonical_sha256":"836639f790fc609a9ec4205ff6cdd1a9c61fc07ff8d98569411bf5a495cbad8d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:54:08.015161Z","signature_b64":"634Ddg6QWAKcde4W4AmJ5uQmoDKzZh8KSa9uiuGuLUfIbODAwkb2zsBi/NlTXuWlwYymKEO0qy3GAp4whPlACw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"836639f790fc609a9ec4205ff6cdd1a9c61fc07ff8d98569411bf5a495cbad8d","last_reissued_at":"2026-07-05T10:54:08.014671Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:54:08.014671Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2504.18484","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":"2026-07-05T10:54:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0sNmkvjkHrpApc2kCk+HMW5jI9VvWsgUapD5URhN/+10ozrGxBp4NufSTkFD4wrkiKnw0GkwzbRqyn33+jFbCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T10:38:02.856292Z"},"content_sha256":"27f1cdbcf94e5d2a0edee78def517a81c3082e0b602a958a991b2beb34cb287c","schema_version":"1.0","event_id":"sha256:27f1cdbcf94e5d2a0edee78def517a81c3082e0b602a958a991b2beb34cb287c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:QNTDT54Q7RQJVHWEEBP7NTORVH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On a Cross-Diffusion System with Independent Drifts and no Self-Diffusion: The Existence of Totally Mixed Solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alp\\'ar R. M\\'esz\\'aros, Guy Parker","submitted_at":"2025-04-25T16:51:35Z","abstract_excerpt":"We establish the global existence of weak solutions for a two-species cross-diffusion system, set on the 1-dimensional flat torus, in which the evolution of each species is governed by two mechanisms. The first of these is a diffusion which acts only on the sum of the species with a logarithmic pressure law, and the second of these is a drift term, which can differ between the two species. Our main results hold under a total mixing assumption on the initial data. This assumption, which allows the presence of vacuum, requires specific regularity properties for the ratio of the initial densities"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.18484","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2504.18484/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":"2026-07-05T10:54:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VTSgHH3QM3j6ORi8qSjtfMidZVx3dOREqPOE6Jyi8PzRsEcGnuwC25FPLG10cvklZxAsdKIRIL0HYqzlCFZCBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T10:38:02.857170Z"},"content_sha256":"b1598b35d3c903a6b424e68b39b6c35ca6db240ff3f9a855467c8804e7b5f7f9","schema_version":"1.0","event_id":"sha256:b1598b35d3c903a6b424e68b39b6c35ca6db240ff3f9a855467c8804e7b5f7f9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QNTDT54Q7RQJVHWEEBP7NTORVH/bundle.json","state_url":"https://pith.science/pith/QNTDT54Q7RQJVHWEEBP7NTORVH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QNTDT54Q7RQJVHWEEBP7NTORVH/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":"2026-08-20T10:38:02Z","links":{"resolver":"https://pith.science/pith/QNTDT54Q7RQJVHWEEBP7NTORVH","bundle":"https://pith.science/pith/QNTDT54Q7RQJVHWEEBP7NTORVH/bundle.json","state":"https://pith.science/pith/QNTDT54Q7RQJVHWEEBP7NTORVH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QNTDT54Q7RQJVHWEEBP7NTORVH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:QNTDT54Q7RQJVHWEEBP7NTORVH","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":"7248de792d0ed3e0ad2dd5dadbcd78010c2626278d24f8501797e42a4b996ce1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-04-25T16:51:35Z","title_canon_sha256":"b8273da76434977a17ef69eb7eac3b5834a4dc655a9e35c1df2e46b57c920611"},"schema_version":"1.0","source":{"id":"2504.18484","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.18484","created_at":"2026-07-05T10:54:08Z"},{"alias_kind":"arxiv_version","alias_value":"2504.18484v1","created_at":"2026-07-05T10:54:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.18484","created_at":"2026-07-05T10:54:08Z"},{"alias_kind":"pith_short_12","alias_value":"QNTDT54Q7RQJ","created_at":"2026-07-05T10:54:08Z"},{"alias_kind":"pith_short_16","alias_value":"QNTDT54Q7RQJVHWE","created_at":"2026-07-05T10:54:08Z"},{"alias_kind":"pith_short_8","alias_value":"QNTDT54Q","created_at":"2026-07-05T10:54:08Z"}],"graph_snapshots":[{"event_id":"sha256:b1598b35d3c903a6b424e68b39b6c35ca6db240ff3f9a855467c8804e7b5f7f9","target":"graph","created_at":"2026-07-05T10:54:08Z","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/2504.18484/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We establish the global existence of weak solutions for a two-species cross-diffusion system, set on the 1-dimensional flat torus, in which the evolution of each species is governed by two mechanisms. The first of these is a diffusion which acts only on the sum of the species with a logarithmic pressure law, and the second of these is a drift term, which can differ between the two species. Our main results hold under a total mixing assumption on the initial data. This assumption, which allows the presence of vacuum, requires specific regularity properties for the ratio of the initial densities","authors_text":"Alp\\'ar R. M\\'esz\\'aros, Guy Parker","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-04-25T16:51:35Z","title":"On a Cross-Diffusion System with Independent Drifts and no Self-Diffusion: The Existence of Totally Mixed Solutions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.18484","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":"sha256:27f1cdbcf94e5d2a0edee78def517a81c3082e0b602a958a991b2beb34cb287c","target":"record","created_at":"2026-07-05T10:54:08Z","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":"7248de792d0ed3e0ad2dd5dadbcd78010c2626278d24f8501797e42a4b996ce1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-04-25T16:51:35Z","title_canon_sha256":"b8273da76434977a17ef69eb7eac3b5834a4dc655a9e35c1df2e46b57c920611"},"schema_version":"1.0","source":{"id":"2504.18484","kind":"arxiv","version":1}},"canonical_sha256":"836639f790fc609a9ec4205ff6cdd1a9c61fc07ff8d98569411bf5a495cbad8d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"836639f790fc609a9ec4205ff6cdd1a9c61fc07ff8d98569411bf5a495cbad8d","first_computed_at":"2026-07-05T10:54:08.014671Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:54:08.014671Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"634Ddg6QWAKcde4W4AmJ5uQmoDKzZh8KSa9uiuGuLUfIbODAwkb2zsBi/NlTXuWlwYymKEO0qy3GAp4whPlACw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:54:08.015161Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.18484","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:27f1cdbcf94e5d2a0edee78def517a81c3082e0b602a958a991b2beb34cb287c","sha256:b1598b35d3c903a6b424e68b39b6c35ca6db240ff3f9a855467c8804e7b5f7f9"],"state_sha256":"bd89e23d37a810f62d7e3c0e2cada8a182bc5b1f645af1df66f3a32d810c5231"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"owJ57OUoxU7t9K9LBA+xJUp4olye0ctjTX5akLyFr25agVeLTPSTLxUVCRuR8rVyacFCkD2IaCaWcZ3lSUaxCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-20T10:38:02.861133Z","bundle_sha256":"a506424bf11331eec5c1ae2bd9a9744d56c44944bf9bc70276388dd1597a5e42"}}