{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:5BDJXNER3RI36AG45L5GNG6VXZ","short_pith_number":"pith:5BDJXNER","canonical_record":{"source":{"id":"1903.00341","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-28T09:39:39Z","cross_cats_sorted":[],"title_canon_sha256":"953b8c6138de220c39de078a378bbba1e350a371d1ab768de2836eb0b44a47d1","abstract_canon_sha256":"06d68956289886a4e48b69cda1ec66e771bdf94ccf345b7567d6835caeebac88"},"schema_version":"1.0"},"canonical_sha256":"e8469bb491dc51bf00dceafa669bd5be5150bdffdb12a77e2d29133d9e141e2d","source":{"kind":"arxiv","id":"1903.00341","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.00341","created_at":"2026-05-17T23:52:20Z"},{"alias_kind":"arxiv_version","alias_value":"1903.00341v1","created_at":"2026-05-17T23:52:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.00341","created_at":"2026-05-17T23:52:20Z"},{"alias_kind":"pith_short_12","alias_value":"5BDJXNER3RI3","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"5BDJXNER3RI36AG4","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"5BDJXNER","created_at":"2026-05-18T12:33:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:5BDJXNER3RI36AG45L5GNG6VXZ","target":"record","payload":{"canonical_record":{"source":{"id":"1903.00341","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-28T09:39:39Z","cross_cats_sorted":[],"title_canon_sha256":"953b8c6138de220c39de078a378bbba1e350a371d1ab768de2836eb0b44a47d1","abstract_canon_sha256":"06d68956289886a4e48b69cda1ec66e771bdf94ccf345b7567d6835caeebac88"},"schema_version":"1.0"},"canonical_sha256":"e8469bb491dc51bf00dceafa669bd5be5150bdffdb12a77e2d29133d9e141e2d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:20.038675Z","signature_b64":"Mf8nNKXf+jpp49xLooCzSZA+0zEmBW7C3qQxSo4VcF1ISntcUzVtDWfHH+r+NjGQg+lu+LmAdpn0WgapU6bOCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e8469bb491dc51bf00dceafa669bd5be5150bdffdb12a77e2d29133d9e141e2d","last_reissued_at":"2026-05-17T23:52:20.037897Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:20.037897Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.00341","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":"2026-05-17T23:52:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lmbwWicx9G7QEFlyOuRSBTCRoRDLG4yvQI7bwZ0vm3CPAEd9G5K4+/mSP8H1X+u3k/czAmC8xKFgNmnOMJwmCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T05:28:23.723267Z"},"content_sha256":"e6d5d713fe755bec81721e30bccd8539023595ab55614aa8cf9c24a4a549449d","schema_version":"1.0","event_id":"sha256:e6d5d713fe755bec81721e30bccd8539023595ab55614aa8cf9c24a4a549449d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:5BDJXNER3RI36AG45L5GNG6VXZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A note on Liouville type results for a fractional obstacle problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"J\\'er\\^ome Coville (BIOSP)","submitted_at":"2019-02-28T09:39:39Z","abstract_excerpt":"This note is a synthesis of my reflexions on some questions that have emerged during the MATRIX event \"Recent Trends on Nonlinear PDEs of Elliptic and Parabolic Type\" concerning the qualitative properties of solutions to some non local reaction-diffusion equations of the form L[u](x) + f (u(x)) = 0, for x $\\in$ R n \\ K, where K $\\subset$ R N is a bounded smooth compact \"obstacle\", L is non local operator and f is a bistable nonlinearity. When K is convex and the nonlocal operator L is a continuous operator of convolution type then some Liouville-type results for solutions satisfying some asymp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.00341","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":"2026-05-17T23:52:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kBnl3UJcMAK7E691dYRU99jq2ecdGYSSyj/Dbf3Vo0i6pmREsN6uYE3t1vo8nTCMrhyNJMV1vsYqjIVXkxM6AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T05:28:23.724000Z"},"content_sha256":"5f99e8680f2cc6cfa949a2e4469e94a6b9bc2049ed06a1fa0dc2d4c0fabe8b61","schema_version":"1.0","event_id":"sha256:5f99e8680f2cc6cfa949a2e4469e94a6b9bc2049ed06a1fa0dc2d4c0fabe8b61"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5BDJXNER3RI36AG45L5GNG6VXZ/bundle.json","state_url":"https://pith.science/pith/5BDJXNER3RI36AG45L5GNG6VXZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5BDJXNER3RI36AG45L5GNG6VXZ/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":"2026-06-11T05:28:23Z","links":{"resolver":"https://pith.science/pith/5BDJXNER3RI36AG45L5GNG6VXZ","bundle":"https://pith.science/pith/5BDJXNER3RI36AG45L5GNG6VXZ/bundle.json","state":"https://pith.science/pith/5BDJXNER3RI36AG45L5GNG6VXZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5BDJXNER3RI36AG45L5GNG6VXZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:5BDJXNER3RI36AG45L5GNG6VXZ","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":"06d68956289886a4e48b69cda1ec66e771bdf94ccf345b7567d6835caeebac88","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-28T09:39:39Z","title_canon_sha256":"953b8c6138de220c39de078a378bbba1e350a371d1ab768de2836eb0b44a47d1"},"schema_version":"1.0","source":{"id":"1903.00341","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.00341","created_at":"2026-05-17T23:52:20Z"},{"alias_kind":"arxiv_version","alias_value":"1903.00341v1","created_at":"2026-05-17T23:52:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.00341","created_at":"2026-05-17T23:52:20Z"},{"alias_kind":"pith_short_12","alias_value":"5BDJXNER3RI3","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"5BDJXNER3RI36AG4","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"5BDJXNER","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:5f99e8680f2cc6cfa949a2e4469e94a6b9bc2049ed06a1fa0dc2d4c0fabe8b61","target":"graph","created_at":"2026-05-17T23:52:20Z","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":"This note is a synthesis of my reflexions on some questions that have emerged during the MATRIX event \"Recent Trends on Nonlinear PDEs of Elliptic and Parabolic Type\" concerning the qualitative properties of solutions to some non local reaction-diffusion equations of the form L[u](x) + f (u(x)) = 0, for x $\\in$ R n \\ K, where K $\\subset$ R N is a bounded smooth compact \"obstacle\", L is non local operator and f is a bistable nonlinearity. When K is convex and the nonlocal operator L is a continuous operator of convolution type then some Liouville-type results for solutions satisfying some asymp","authors_text":"J\\'er\\^ome Coville (BIOSP)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-28T09:39:39Z","title":"A note on Liouville type results for a fractional obstacle problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.00341","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:e6d5d713fe755bec81721e30bccd8539023595ab55614aa8cf9c24a4a549449d","target":"record","created_at":"2026-05-17T23:52:20Z","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":"06d68956289886a4e48b69cda1ec66e771bdf94ccf345b7567d6835caeebac88","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-28T09:39:39Z","title_canon_sha256":"953b8c6138de220c39de078a378bbba1e350a371d1ab768de2836eb0b44a47d1"},"schema_version":"1.0","source":{"id":"1903.00341","kind":"arxiv","version":1}},"canonical_sha256":"e8469bb491dc51bf00dceafa669bd5be5150bdffdb12a77e2d29133d9e141e2d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e8469bb491dc51bf00dceafa669bd5be5150bdffdb12a77e2d29133d9e141e2d","first_computed_at":"2026-05-17T23:52:20.037897Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:20.037897Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Mf8nNKXf+jpp49xLooCzSZA+0zEmBW7C3qQxSo4VcF1ISntcUzVtDWfHH+r+NjGQg+lu+LmAdpn0WgapU6bOCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:20.038675Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.00341","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e6d5d713fe755bec81721e30bccd8539023595ab55614aa8cf9c24a4a549449d","sha256:5f99e8680f2cc6cfa949a2e4469e94a6b9bc2049ed06a1fa0dc2d4c0fabe8b61"],"state_sha256":"c584dc87d95761202794ba948adf7e1416a7af4b9d4d42913c5d16c115c81041"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TuwDiscLoGEvKCfjkQI95PBwikyiUrNSVYTV0fBNetzEovql889JoHwEn4svltUkwJayxJR28fhE9tYgpxhICQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T05:28:23.728380Z","bundle_sha256":"cddfbf9e5c68501eb345e9338a183baedd691b644249d932cbb0f89a0e869e27"}}