{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:WI3Q27SIPP6C6MH5A6LB2XWJMM","short_pith_number":"pith:WI3Q27SI","canonical_record":{"source":{"id":"1505.02927","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-05-12T09:30:32Z","cross_cats_sorted":[],"title_canon_sha256":"55ee240e5539087dfc79c0cb09dd75f97e79038305365eeb2974f55a6dc69bb3","abstract_canon_sha256":"e61e85c31ffd4b520b9767f53f8957169384e0d9771557bc3a12ae030c93c040"},"schema_version":"1.0"},"canonical_sha256":"b2370d7e487bfc2f30fd07961d5ec9632ad96227c8d6f48909a2026995e02e60","source":{"kind":"arxiv","id":"1505.02927","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.02927","created_at":"2026-05-17T23:51:06Z"},{"alias_kind":"arxiv_version","alias_value":"1505.02927v3","created_at":"2026-05-17T23:51:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.02927","created_at":"2026-05-17T23:51:06Z"},{"alias_kind":"pith_short_12","alias_value":"WI3Q27SIPP6C","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WI3Q27SIPP6C6MH5","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WI3Q27SI","created_at":"2026-05-18T12:29:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:WI3Q27SIPP6C6MH5A6LB2XWJMM","target":"record","payload":{"canonical_record":{"source":{"id":"1505.02927","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-05-12T09:30:32Z","cross_cats_sorted":[],"title_canon_sha256":"55ee240e5539087dfc79c0cb09dd75f97e79038305365eeb2974f55a6dc69bb3","abstract_canon_sha256":"e61e85c31ffd4b520b9767f53f8957169384e0d9771557bc3a12ae030c93c040"},"schema_version":"1.0"},"canonical_sha256":"b2370d7e487bfc2f30fd07961d5ec9632ad96227c8d6f48909a2026995e02e60","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:06.509943Z","signature_b64":"sVQNdMq3ZTcw9nMgFFVPdbgWCIhWI76dtGxoIjYx+LbhNFgxU9b1LmJnwnWHTkwPbjhbGKlaeZBl5W/8W85dDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b2370d7e487bfc2f30fd07961d5ec9632ad96227c8d6f48909a2026995e02e60","last_reissued_at":"2026-05-17T23:51:06.509471Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:06.509471Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.02927","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:51:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gCz9kDQPE4nFf0T5mDQgJj09x7eScx86CaKh6qqn3eR6uFjDqYm1KOyFPx1u9sFpEEKwwldw+ucJ0oYHhhl+Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T06:16:21.130080Z"},"content_sha256":"98511118bed2c6b38d4ac7dfa50529ed55e4752f74afc9e9cbd202a3930dd6da","schema_version":"1.0","event_id":"sha256:98511118bed2c6b38d4ac7dfa50529ed55e4752f74afc9e9cbd202a3930dd6da"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:WI3Q27SIPP6C6MH5A6LB2XWJMM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Strong-viscosity Solutions: Semilinear Parabolic PDEs and Path-dependent PDEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Andrea Cosso (LPMA), Francesco Russo (UMA)","submitted_at":"2015-05-12T09:30:32Z","abstract_excerpt":"The aim of the present work is the introduction of a viscosity type solution, called strong-viscosity solution to distinguish it from the classical one, with the following peculiarities: it is a purely analytic object; it can be easily adapted to more general equations than classical partial differential equations. First, we introduce the notion of strong-viscosity solution for semilinear parabolic partial differential equations, defining it, in a few words, as the pointwise limit of classical solutions to perturbed semilinear parabolic partial differential equations; we compare it with the st"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.02927","kind":"arxiv","version":3},"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":"2026-05-17T23:51:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y3hgEnYYpPRjAcQFvuzFtQyCqJEJmDG19c+1sKopBtplaKvw6DOJcQd934tr9pW92lLCNvt6uWM+8e4cuHUxCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T06:16:21.130448Z"},"content_sha256":"c1d2070bb0aacbc2b3399d05f005362b32e071d98cd729240109da2f8b9654ee","schema_version":"1.0","event_id":"sha256:c1d2070bb0aacbc2b3399d05f005362b32e071d98cd729240109da2f8b9654ee"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WI3Q27SIPP6C6MH5A6LB2XWJMM/bundle.json","state_url":"https://pith.science/pith/WI3Q27SIPP6C6MH5A6LB2XWJMM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WI3Q27SIPP6C6MH5A6LB2XWJMM/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":"2026-05-28T06:16:21Z","links":{"resolver":"https://pith.science/pith/WI3Q27SIPP6C6MH5A6LB2XWJMM","bundle":"https://pith.science/pith/WI3Q27SIPP6C6MH5A6LB2XWJMM/bundle.json","state":"https://pith.science/pith/WI3Q27SIPP6C6MH5A6LB2XWJMM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WI3Q27SIPP6C6MH5A6LB2XWJMM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:WI3Q27SIPP6C6MH5A6LB2XWJMM","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":"e61e85c31ffd4b520b9767f53f8957169384e0d9771557bc3a12ae030c93c040","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-05-12T09:30:32Z","title_canon_sha256":"55ee240e5539087dfc79c0cb09dd75f97e79038305365eeb2974f55a6dc69bb3"},"schema_version":"1.0","source":{"id":"1505.02927","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.02927","created_at":"2026-05-17T23:51:06Z"},{"alias_kind":"arxiv_version","alias_value":"1505.02927v3","created_at":"2026-05-17T23:51:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.02927","created_at":"2026-05-17T23:51:06Z"},{"alias_kind":"pith_short_12","alias_value":"WI3Q27SIPP6C","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WI3Q27SIPP6C6MH5","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WI3Q27SI","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:c1d2070bb0aacbc2b3399d05f005362b32e071d98cd729240109da2f8b9654ee","target":"graph","created_at":"2026-05-17T23:51:06Z","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":"The aim of the present work is the introduction of a viscosity type solution, called strong-viscosity solution to distinguish it from the classical one, with the following peculiarities: it is a purely analytic object; it can be easily adapted to more general equations than classical partial differential equations. First, we introduce the notion of strong-viscosity solution for semilinear parabolic partial differential equations, defining it, in a few words, as the pointwise limit of classical solutions to perturbed semilinear parabolic partial differential equations; we compare it with the st","authors_text":"Andrea Cosso (LPMA), Francesco Russo (UMA)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-05-12T09:30:32Z","title":"Strong-viscosity Solutions: Semilinear Parabolic PDEs and Path-dependent PDEs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.02927","kind":"arxiv","version":3},"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":"sha256:98511118bed2c6b38d4ac7dfa50529ed55e4752f74afc9e9cbd202a3930dd6da","target":"record","created_at":"2026-05-17T23:51:06Z","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":"e61e85c31ffd4b520b9767f53f8957169384e0d9771557bc3a12ae030c93c040","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-05-12T09:30:32Z","title_canon_sha256":"55ee240e5539087dfc79c0cb09dd75f97e79038305365eeb2974f55a6dc69bb3"},"schema_version":"1.0","source":{"id":"1505.02927","kind":"arxiv","version":3}},"canonical_sha256":"b2370d7e487bfc2f30fd07961d5ec9632ad96227c8d6f48909a2026995e02e60","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b2370d7e487bfc2f30fd07961d5ec9632ad96227c8d6f48909a2026995e02e60","first_computed_at":"2026-05-17T23:51:06.509471Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:06.509471Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sVQNdMq3ZTcw9nMgFFVPdbgWCIhWI76dtGxoIjYx+LbhNFgxU9b1LmJnwnWHTkwPbjhbGKlaeZBl5W/8W85dDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:06.509943Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.02927","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:98511118bed2c6b38d4ac7dfa50529ed55e4752f74afc9e9cbd202a3930dd6da","sha256:c1d2070bb0aacbc2b3399d05f005362b32e071d98cd729240109da2f8b9654ee"],"state_sha256":"899d51c0460c15aa1a8f623dc5276f60a07febd73ec6c1615551bdcc9d4da390"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jdLj8DVyWazk0kR/OeLq5Y7Pdqx3g/PpvDjzp39wWBNpkJhm7vrHbnVus9WoSHEsdo9kpQrKnG/cY7d1w6DqCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T06:16:21.132310Z","bundle_sha256":"34610a5b4defccc53b76c8f73bc291534c8008610bb49d3ba3919e236f699a4d"}}