{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:PC73GAZ6XP53SBGTXRXRMZPA5O","short_pith_number":"pith:PC73GAZ6","canonical_record":{"source":{"id":"2005.09915","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-05-20T08:52:01Z","cross_cats_sorted":[],"title_canon_sha256":"59ce184a55949807e5dd1d0cfe44ea36cc026aace3ab1be22307f58fc8aec0eb","abstract_canon_sha256":"e40f352bdff71a7e26058a01df7991e5b22b1a3203d29c82025ff6c972620f19"},"schema_version":"1.0"},"canonical_sha256":"78bfb3033ebbfbb904d3bc6f1665e0eb99b9df421d6ae4d7e32bdfb92145ba93","source":{"kind":"arxiv","id":"2005.09915","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2005.09915","created_at":"2026-07-05T01:04:35Z"},{"alias_kind":"arxiv_version","alias_value":"2005.09915v1","created_at":"2026-07-05T01:04:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2005.09915","created_at":"2026-07-05T01:04:35Z"},{"alias_kind":"pith_short_12","alias_value":"PC73GAZ6XP53","created_at":"2026-07-05T01:04:35Z"},{"alias_kind":"pith_short_16","alias_value":"PC73GAZ6XP53SBGT","created_at":"2026-07-05T01:04:35Z"},{"alias_kind":"pith_short_8","alias_value":"PC73GAZ6","created_at":"2026-07-05T01:04:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:PC73GAZ6XP53SBGTXRXRMZPA5O","target":"record","payload":{"canonical_record":{"source":{"id":"2005.09915","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-05-20T08:52:01Z","cross_cats_sorted":[],"title_canon_sha256":"59ce184a55949807e5dd1d0cfe44ea36cc026aace3ab1be22307f58fc8aec0eb","abstract_canon_sha256":"e40f352bdff71a7e26058a01df7991e5b22b1a3203d29c82025ff6c972620f19"},"schema_version":"1.0"},"canonical_sha256":"78bfb3033ebbfbb904d3bc6f1665e0eb99b9df421d6ae4d7e32bdfb92145ba93","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:04:35.266186Z","signature_b64":"pPNBi2hKTyaW06sSRolb0Jq/t5Uexfj6jX5I224OvO1lcpiHitsc2hulFxRwkf8RX7GesOvZJjXvgAusvCRbBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78bfb3033ebbfbb904d3bc6f1665e0eb99b9df421d6ae4d7e32bdfb92145ba93","last_reissued_at":"2026-07-05T01:04:35.265826Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:04:35.265826Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2005.09915","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":"2026-07-05T01:04:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y+v0xor1uyA/fFTiGBTo9OZ3bJbyEBGP53JMvGtGLqkX1PgFuMiUdbS9G4rV02qGWp0TQt1c4Mhk0zTnxSI/Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-15T21:41:49.270831Z"},"content_sha256":"4cbbbafc1dcc9753db027c6b613fd620880282a7731af320ba4a80f7271c0f82","schema_version":"1.0","event_id":"sha256:4cbbbafc1dcc9753db027c6b613fd620880282a7731af320ba4a80f7271c0f82"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:PC73GAZ6XP53SBGTXRXRMZPA5O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dampening effect of logistic source in a two-dimensional haptotaxis system with nonlinear zero-order interaction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chen Zhen","submitted_at":"2020-05-20T08:52:01Z","abstract_excerpt":"This paper deals with the oncolytic virotherapy model \\begin{equation}\\begin{split} \\begin{cases} &u_t = \\Delta u - \\nabla \\cdot (u\\nabla v)-uz +\\mu u(1-u),& \\\\[2ex] &v_t = - (u+w)v,& \\\\[2ex] &w_t = D_w \\Delta w - w + uz,& \\\\[2ex] &z_t = D_z \\Delta z - z - uz + \\beta w,& \\end{cases} \\end{split}\\end{equation} in a bounded domain $\\Omega$ $\\subset$ $\\Bbb{R}^2$ with smooth boundary, where $\\mu$, $D_w$, $D_z$ and $\\beta$ are prescribed positive parameters.\n  For any given suitably regular initial data, the global existence of classical solution to the corresponding homogeneous Neumann initial-boun"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2005.09915","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/2005.09915/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":"2026-07-05T01:04:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Cm/SKJKVqrEroP70H5ZSVrH3Gd6sSUmKeaGefp0aOCmlBkOCgRViGzdhliFZBL7lrWrjMYjibvbThLgoKeybBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-15T21:41:49.271214Z"},"content_sha256":"bbd9d1270f42bbcb60b3ae0337856e9162906e98ce7868409f98e96a32421f59","schema_version":"1.0","event_id":"sha256:bbd9d1270f42bbcb60b3ae0337856e9162906e98ce7868409f98e96a32421f59"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PC73GAZ6XP53SBGTXRXRMZPA5O/bundle.json","state_url":"https://pith.science/pith/PC73GAZ6XP53SBGTXRXRMZPA5O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PC73GAZ6XP53SBGTXRXRMZPA5O/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":"2026-07-15T21:41:49Z","links":{"resolver":"https://pith.science/pith/PC73GAZ6XP53SBGTXRXRMZPA5O","bundle":"https://pith.science/pith/PC73GAZ6XP53SBGTXRXRMZPA5O/bundle.json","state":"https://pith.science/pith/PC73GAZ6XP53SBGTXRXRMZPA5O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PC73GAZ6XP53SBGTXRXRMZPA5O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:PC73GAZ6XP53SBGTXRXRMZPA5O","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":"e40f352bdff71a7e26058a01df7991e5b22b1a3203d29c82025ff6c972620f19","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-05-20T08:52:01Z","title_canon_sha256":"59ce184a55949807e5dd1d0cfe44ea36cc026aace3ab1be22307f58fc8aec0eb"},"schema_version":"1.0","source":{"id":"2005.09915","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2005.09915","created_at":"2026-07-05T01:04:35Z"},{"alias_kind":"arxiv_version","alias_value":"2005.09915v1","created_at":"2026-07-05T01:04:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2005.09915","created_at":"2026-07-05T01:04:35Z"},{"alias_kind":"pith_short_12","alias_value":"PC73GAZ6XP53","created_at":"2026-07-05T01:04:35Z"},{"alias_kind":"pith_short_16","alias_value":"PC73GAZ6XP53SBGT","created_at":"2026-07-05T01:04:35Z"},{"alias_kind":"pith_short_8","alias_value":"PC73GAZ6","created_at":"2026-07-05T01:04:35Z"}],"graph_snapshots":[{"event_id":"sha256:bbd9d1270f42bbcb60b3ae0337856e9162906e98ce7868409f98e96a32421f59","target":"graph","created_at":"2026-07-05T01:04:35Z","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/2005.09915/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper deals with the oncolytic virotherapy model \\begin{equation}\\begin{split} \\begin{cases} &u_t = \\Delta u - \\nabla \\cdot (u\\nabla v)-uz +\\mu u(1-u),& \\\\[2ex] &v_t = - (u+w)v,& \\\\[2ex] &w_t = D_w \\Delta w - w + uz,& \\\\[2ex] &z_t = D_z \\Delta z - z - uz + \\beta w,& \\end{cases} \\end{split}\\end{equation} in a bounded domain $\\Omega$ $\\subset$ $\\Bbb{R}^2$ with smooth boundary, where $\\mu$, $D_w$, $D_z$ and $\\beta$ are prescribed positive parameters.\n  For any given suitably regular initial data, the global existence of classical solution to the corresponding homogeneous Neumann initial-boun","authors_text":"Chen Zhen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-05-20T08:52:01Z","title":"Dampening effect of logistic source in a two-dimensional haptotaxis system with nonlinear zero-order interaction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2005.09915","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":"sha256:4cbbbafc1dcc9753db027c6b613fd620880282a7731af320ba4a80f7271c0f82","target":"record","created_at":"2026-07-05T01:04:35Z","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":"e40f352bdff71a7e26058a01df7991e5b22b1a3203d29c82025ff6c972620f19","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-05-20T08:52:01Z","title_canon_sha256":"59ce184a55949807e5dd1d0cfe44ea36cc026aace3ab1be22307f58fc8aec0eb"},"schema_version":"1.0","source":{"id":"2005.09915","kind":"arxiv","version":1}},"canonical_sha256":"78bfb3033ebbfbb904d3bc6f1665e0eb99b9df421d6ae4d7e32bdfb92145ba93","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"78bfb3033ebbfbb904d3bc6f1665e0eb99b9df421d6ae4d7e32bdfb92145ba93","first_computed_at":"2026-07-05T01:04:35.265826Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:04:35.265826Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pPNBi2hKTyaW06sSRolb0Jq/t5Uexfj6jX5I224OvO1lcpiHitsc2hulFxRwkf8RX7GesOvZJjXvgAusvCRbBg==","signature_status":"signed_v1","signed_at":"2026-07-05T01:04:35.266186Z","signed_message":"canonical_sha256_bytes"},"source_id":"2005.09915","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4cbbbafc1dcc9753db027c6b613fd620880282a7731af320ba4a80f7271c0f82","sha256:bbd9d1270f42bbcb60b3ae0337856e9162906e98ce7868409f98e96a32421f59"],"state_sha256":"03604c096916b3cd24d691a01b57688932925654e960a3849be8b4c6ab9b3f6a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UPoG5opF/N+ftQtLqLpgIAN0oCrW1tX0Su1tqVSqb042QrCik1SDvqhgMla7jE3EQiCmylDqUpJePsWig9P1Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-15T21:41:49.273416Z","bundle_sha256":"8cb91254a005a81e1fcaffe548003feaf96d01d2d809393f5010730d25b10984"}}