{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:Z5WPTVULQVHCULPKQFFPP2V6B5","short_pith_number":"pith:Z5WPTVUL","canonical_record":{"source":{"id":"1805.07321","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-05-18T16:40:27Z","cross_cats_sorted":[],"title_canon_sha256":"34325f830d73bb59913bb864ea39f6182466ff089c8b021d825d0b2efe5b6d41","abstract_canon_sha256":"8243b03362625dd4429fd88301e8e4277588faa4bb226c655f4541e49a5023e3"},"schema_version":"1.0"},"canonical_sha256":"cf6cf9d68b854e2a2dea814af7eabe0f6dc665605e0b94a1ffd89d0d29d45e01","source":{"kind":"arxiv","id":"1805.07321","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.07321","created_at":"2026-05-18T00:15:38Z"},{"alias_kind":"arxiv_version","alias_value":"1805.07321v1","created_at":"2026-05-18T00:15:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.07321","created_at":"2026-05-18T00:15:38Z"},{"alias_kind":"pith_short_12","alias_value":"Z5WPTVULQVHC","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"Z5WPTVULQVHCULPK","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"Z5WPTVUL","created_at":"2026-05-18T12:33:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:Z5WPTVULQVHCULPKQFFPP2V6B5","target":"record","payload":{"canonical_record":{"source":{"id":"1805.07321","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-05-18T16:40:27Z","cross_cats_sorted":[],"title_canon_sha256":"34325f830d73bb59913bb864ea39f6182466ff089c8b021d825d0b2efe5b6d41","abstract_canon_sha256":"8243b03362625dd4429fd88301e8e4277588faa4bb226c655f4541e49a5023e3"},"schema_version":"1.0"},"canonical_sha256":"cf6cf9d68b854e2a2dea814af7eabe0f6dc665605e0b94a1ffd89d0d29d45e01","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:38.557137Z","signature_b64":"Or9VACRZn9ZWIbyvAFDGZt7jZw11xxFYxDUTb3vzB7SjO1fm+lAY+F5rjyvbX+qWR24IJaHqENZNnfiX5Fg8DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf6cf9d68b854e2a2dea814af7eabe0f6dc665605e0b94a1ffd89d0d29d45e01","last_reissued_at":"2026-05-18T00:15:38.556617Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:38.556617Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.07321","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":"2026-05-18T00:15:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"awDpBYlcIHezwLnl6pR+8BroOjX7g7bEW+TajyejsWUYXg3Cyj98MUTBVrvMXqiOwy8qk3QMVgu25Jt92GAABA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T05:44:00.243959Z"},"content_sha256":"796e18cbb35ad7e0036beea95a7cbb5e32f12ad6ca71d9054081099be414abf9","schema_version":"1.0","event_id":"sha256:796e18cbb35ad7e0036beea95a7cbb5e32f12ad6ca71d9054081099be414abf9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:Z5WPTVULQVHCULPKQFFPP2V6B5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global asymptotic stability of bifurcating, positive equilibria of p-Laplacian boundary value problems with p-concave nonlinearities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bryan P. Rynne","submitted_at":"2018-05-18T16:40:27Z","abstract_excerpt":"We consider the parabolic, initial value problem $$ v_t =\\Delta_p(v)+\\lambda g(x,v)\\phi_p(v), \\quad \\text{in $\\Omega \\times (0,\\infty),$} $$ \\[ v =0, \\text{in $\\partial\\Omega \\times (0,\\infty),$}\\tag{IVP} v =v_0\\ge0, \\text{in $\\Omega \\times \\{0\\},$} \\] where $\\Omega$ is a bounded domain in ${\\mathbb R}^N$, for some integer $N\\ge1$, with smooth boundary $\\partial\\Omega$, $\\phi_p(s):=|s|^{p-1} {\\rm sgn}s$, $s\\in{\\mathbb R}$, $\\Delta_p$ denotes the $p$-Laplacian, with $p>\\max\\{2,N\\}$, $v_0\\in C^0(\\overline{\\Omega})$, and $\\lambda>0$. The function $g:\\overline{\\Omega } \\times [0,\\infty)\\to(0,\\inft"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.07321","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":"2026-05-18T00:15:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TlU2KCVX22mo1XBsP7ElcDVL/kRFZ36kfdbcHKUEBAjPhkGU/B6XhbVXHqtyZ2y0wUYs4MI27ZzbVo1VF/rDDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T05:44:00.244302Z"},"content_sha256":"ac5765befb26e4a258c613e65695320612c4270945d65a04b023f90390e5a657","schema_version":"1.0","event_id":"sha256:ac5765befb26e4a258c613e65695320612c4270945d65a04b023f90390e5a657"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z5WPTVULQVHCULPKQFFPP2V6B5/bundle.json","state_url":"https://pith.science/pith/Z5WPTVULQVHCULPKQFFPP2V6B5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z5WPTVULQVHCULPKQFFPP2V6B5/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":"2026-06-24T05:44:00Z","links":{"resolver":"https://pith.science/pith/Z5WPTVULQVHCULPKQFFPP2V6B5","bundle":"https://pith.science/pith/Z5WPTVULQVHCULPKQFFPP2V6B5/bundle.json","state":"https://pith.science/pith/Z5WPTVULQVHCULPKQFFPP2V6B5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z5WPTVULQVHCULPKQFFPP2V6B5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:Z5WPTVULQVHCULPKQFFPP2V6B5","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":"8243b03362625dd4429fd88301e8e4277588faa4bb226c655f4541e49a5023e3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-05-18T16:40:27Z","title_canon_sha256":"34325f830d73bb59913bb864ea39f6182466ff089c8b021d825d0b2efe5b6d41"},"schema_version":"1.0","source":{"id":"1805.07321","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.07321","created_at":"2026-05-18T00:15:38Z"},{"alias_kind":"arxiv_version","alias_value":"1805.07321v1","created_at":"2026-05-18T00:15:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.07321","created_at":"2026-05-18T00:15:38Z"},{"alias_kind":"pith_short_12","alias_value":"Z5WPTVULQVHC","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"Z5WPTVULQVHCULPK","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"Z5WPTVUL","created_at":"2026-05-18T12:33:04Z"}],"graph_snapshots":[{"event_id":"sha256:ac5765befb26e4a258c613e65695320612c4270945d65a04b023f90390e5a657","target":"graph","created_at":"2026-05-18T00:15:38Z","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 consider the parabolic, initial value problem $$ v_t =\\Delta_p(v)+\\lambda g(x,v)\\phi_p(v), \\quad \\text{in $\\Omega \\times (0,\\infty),$} $$ \\[ v =0, \\text{in $\\partial\\Omega \\times (0,\\infty),$}\\tag{IVP} v =v_0\\ge0, \\text{in $\\Omega \\times \\{0\\},$} \\] where $\\Omega$ is a bounded domain in ${\\mathbb R}^N$, for some integer $N\\ge1$, with smooth boundary $\\partial\\Omega$, $\\phi_p(s):=|s|^{p-1} {\\rm sgn}s$, $s\\in{\\mathbb R}$, $\\Delta_p$ denotes the $p$-Laplacian, with $p>\\max\\{2,N\\}$, $v_0\\in C^0(\\overline{\\Omega})$, and $\\lambda>0$. The function $g:\\overline{\\Omega } \\times [0,\\infty)\\to(0,\\inft","authors_text":"Bryan P. Rynne","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-05-18T16:40:27Z","title":"Global asymptotic stability of bifurcating, positive equilibria of p-Laplacian boundary value problems with p-concave nonlinearities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.07321","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":"sha256:796e18cbb35ad7e0036beea95a7cbb5e32f12ad6ca71d9054081099be414abf9","target":"record","created_at":"2026-05-18T00:15:38Z","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":"8243b03362625dd4429fd88301e8e4277588faa4bb226c655f4541e49a5023e3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-05-18T16:40:27Z","title_canon_sha256":"34325f830d73bb59913bb864ea39f6182466ff089c8b021d825d0b2efe5b6d41"},"schema_version":"1.0","source":{"id":"1805.07321","kind":"arxiv","version":1}},"canonical_sha256":"cf6cf9d68b854e2a2dea814af7eabe0f6dc665605e0b94a1ffd89d0d29d45e01","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf6cf9d68b854e2a2dea814af7eabe0f6dc665605e0b94a1ffd89d0d29d45e01","first_computed_at":"2026-05-18T00:15:38.556617Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:38.556617Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Or9VACRZn9ZWIbyvAFDGZt7jZw11xxFYxDUTb3vzB7SjO1fm+lAY+F5rjyvbX+qWR24IJaHqENZNnfiX5Fg8DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:38.557137Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.07321","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:796e18cbb35ad7e0036beea95a7cbb5e32f12ad6ca71d9054081099be414abf9","sha256:ac5765befb26e4a258c613e65695320612c4270945d65a04b023f90390e5a657"],"state_sha256":"e15a0cafd98032c8ce9a7b801d0096060c11b0eb192afd92b8802beb1b83b7cd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MCuUm2Z6g7sUlwIm8HSPAB/qqCqxxAtZIMroDijzmr4CJmV3yAf5qTa1/bcJKB+bN8WSjPZtTAtWrrmGWjEpBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T05:44:00.246232Z","bundle_sha256":"63bcc3087b2e29692d8d8d0f877550e9b379b484f5d5a552761b6427c0d614f7"}}