{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:B77Q27NJ7PWRHJF4IIX6FW44NJ","short_pith_number":"pith:B77Q27NJ","canonical_record":{"source":{"id":"1712.05223","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-14T13:52:08Z","cross_cats_sorted":[],"title_canon_sha256":"25fdeffe40cd792fb0ef84ffb939c8bda1eeb3f797f9b8b35a1e2d87c25478c1","abstract_canon_sha256":"c5fec88faa70ef4549e5dc257939f9ff794ca8c3f7b96d3e8fcac472df223a32"},"schema_version":"1.0"},"canonical_sha256":"0fff0d7da9fbed13a4bc422fe2db9c6a5eda6ff80e494a0f95b3118ac5894677","source":{"kind":"arxiv","id":"1712.05223","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.05223","created_at":"2026-05-18T00:02:28Z"},{"alias_kind":"arxiv_version","alias_value":"1712.05223v4","created_at":"2026-05-18T00:02:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.05223","created_at":"2026-05-18T00:02:28Z"},{"alias_kind":"pith_short_12","alias_value":"B77Q27NJ7PWR","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"B77Q27NJ7PWRHJF4","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"B77Q27NJ","created_at":"2026-05-18T12:31:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:B77Q27NJ7PWRHJF4IIX6FW44NJ","target":"record","payload":{"canonical_record":{"source":{"id":"1712.05223","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-14T13:52:08Z","cross_cats_sorted":[],"title_canon_sha256":"25fdeffe40cd792fb0ef84ffb939c8bda1eeb3f797f9b8b35a1e2d87c25478c1","abstract_canon_sha256":"c5fec88faa70ef4549e5dc257939f9ff794ca8c3f7b96d3e8fcac472df223a32"},"schema_version":"1.0"},"canonical_sha256":"0fff0d7da9fbed13a4bc422fe2db9c6a5eda6ff80e494a0f95b3118ac5894677","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:28.073454Z","signature_b64":"cP6ZGOTJJjK8erLB6zEEXRoDtuyBDFmYBzwO9km3YwPPdCuuJbpWG0Tz40eih+/ibf68uE4DrFqU2OIQZU68BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0fff0d7da9fbed13a4bc422fe2db9c6a5eda6ff80e494a0f95b3118ac5894677","last_reissued_at":"2026-05-18T00:02:28.072747Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:28.072747Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.05223","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:02:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QevCfecNUkLZfNRPHjv3eFfR1OZIXnFMUo85jp2h+KMrgk8uwzhC3YpwKqAOtEYm47FYQaSrEQ9cbzHE9+7WCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T19:58:58.418132Z"},"content_sha256":"e866aa952885cd38df3709cf8eb7a9f71d5e5484d2d7108627759545666f82a0","schema_version":"1.0","event_id":"sha256:e866aa952885cd38df3709cf8eb7a9f71d5e5484d2d7108627759545666f82a0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:B77Q27NJ7PWRHJF4IIX6FW44NJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Initial trace of positive solutions to fractional diffusion equation with absorption","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Huyuan Chen, Laurent Veron (LMPT)","submitted_at":"2017-12-14T13:52:08Z","abstract_excerpt":"In this paper, we prove the existence of an initial trace T u of any positive solution u of the semilinear fractional diffusion equation (H) $\\partial$ t u + (--$\\Delta$) $\\alpha$ u + f (t, x, u) = 0 in R * + $\\times$ R N , where N $\\ge$ 1 where the operator (--$\\Delta$) $\\alpha$ with $\\alpha$ $\\in$ (0, 1) is the fractional Laplacian and f : R + $\\times$ R N  $\\times$ R + $\\rightarrow$ R is a Caratheodory function satisfying f (t, x, u)u $\\ge$ 0 for all (t, x, u) $\\in$ R + $\\times$ R N $\\times$  R +. We define the regular set of the trace T u as an open subset of R u $\\subset$ R N carrying a n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.05223","kind":"arxiv","version":4},"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":"2026-05-18T00:02:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jEmrtiZKXCntzqvB2HqETpFA3JDqqal+k8F5J5FJrEite1oUQbvaxoAOoZV+PEahl6KRLzbCSMagoHTglHm5CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T19:58:58.418497Z"},"content_sha256":"dc1df7564ffb0038b9ca4c0ebac1d78d51c87bc7de33764aeccbe888f8ce55e6","schema_version":"1.0","event_id":"sha256:dc1df7564ffb0038b9ca4c0ebac1d78d51c87bc7de33764aeccbe888f8ce55e6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B77Q27NJ7PWRHJF4IIX6FW44NJ/bundle.json","state_url":"https://pith.science/pith/B77Q27NJ7PWRHJF4IIX6FW44NJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B77Q27NJ7PWRHJF4IIX6FW44NJ/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":"2026-05-22T19:58:58Z","links":{"resolver":"https://pith.science/pith/B77Q27NJ7PWRHJF4IIX6FW44NJ","bundle":"https://pith.science/pith/B77Q27NJ7PWRHJF4IIX6FW44NJ/bundle.json","state":"https://pith.science/pith/B77Q27NJ7PWRHJF4IIX6FW44NJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B77Q27NJ7PWRHJF4IIX6FW44NJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:B77Q27NJ7PWRHJF4IIX6FW44NJ","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":"c5fec88faa70ef4549e5dc257939f9ff794ca8c3f7b96d3e8fcac472df223a32","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-14T13:52:08Z","title_canon_sha256":"25fdeffe40cd792fb0ef84ffb939c8bda1eeb3f797f9b8b35a1e2d87c25478c1"},"schema_version":"1.0","source":{"id":"1712.05223","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.05223","created_at":"2026-05-18T00:02:28Z"},{"alias_kind":"arxiv_version","alias_value":"1712.05223v4","created_at":"2026-05-18T00:02:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.05223","created_at":"2026-05-18T00:02:28Z"},{"alias_kind":"pith_short_12","alias_value":"B77Q27NJ7PWR","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"B77Q27NJ7PWRHJF4","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"B77Q27NJ","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:dc1df7564ffb0038b9ca4c0ebac1d78d51c87bc7de33764aeccbe888f8ce55e6","target":"graph","created_at":"2026-05-18T00:02:28Z","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":"In this paper, we prove the existence of an initial trace T u of any positive solution u of the semilinear fractional diffusion equation (H) $\\partial$ t u + (--$\\Delta$) $\\alpha$ u + f (t, x, u) = 0 in R * + $\\times$ R N , where N $\\ge$ 1 where the operator (--$\\Delta$) $\\alpha$ with $\\alpha$ $\\in$ (0, 1) is the fractional Laplacian and f : R + $\\times$ R N  $\\times$ R + $\\rightarrow$ R is a Caratheodory function satisfying f (t, x, u)u $\\ge$ 0 for all (t, x, u) $\\in$ R + $\\times$ R N $\\times$  R +. We define the regular set of the trace T u as an open subset of R u $\\subset$ R N carrying a n","authors_text":"Huyuan Chen, Laurent Veron (LMPT)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-14T13:52:08Z","title":"Initial trace of positive solutions to fractional diffusion equation with absorption"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.05223","kind":"arxiv","version":4},"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:e866aa952885cd38df3709cf8eb7a9f71d5e5484d2d7108627759545666f82a0","target":"record","created_at":"2026-05-18T00:02:28Z","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":"c5fec88faa70ef4549e5dc257939f9ff794ca8c3f7b96d3e8fcac472df223a32","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-14T13:52:08Z","title_canon_sha256":"25fdeffe40cd792fb0ef84ffb939c8bda1eeb3f797f9b8b35a1e2d87c25478c1"},"schema_version":"1.0","source":{"id":"1712.05223","kind":"arxiv","version":4}},"canonical_sha256":"0fff0d7da9fbed13a4bc422fe2db9c6a5eda6ff80e494a0f95b3118ac5894677","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0fff0d7da9fbed13a4bc422fe2db9c6a5eda6ff80e494a0f95b3118ac5894677","first_computed_at":"2026-05-18T00:02:28.072747Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:28.072747Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cP6ZGOTJJjK8erLB6zEEXRoDtuyBDFmYBzwO9km3YwPPdCuuJbpWG0Tz40eih+/ibf68uE4DrFqU2OIQZU68BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:28.073454Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.05223","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e866aa952885cd38df3709cf8eb7a9f71d5e5484d2d7108627759545666f82a0","sha256:dc1df7564ffb0038b9ca4c0ebac1d78d51c87bc7de33764aeccbe888f8ce55e6"],"state_sha256":"11b33b0f324de104300267657d86d7d2e57e98dfe066334cdf007c843ca6612a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Kmh6+0d2dGcdxkxVSv3/r0uIlA7GejjbZRBvHxjoIcKNaHKBHnltYrZPp76bSU/SgM62+YZiohy16aRVscglBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T19:58:58.420426Z","bundle_sha256":"29a80a4335e75c62ae92f723c89e1c57bb3c98315a53c581d3fb433cadd0ff89"}}