{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:4XXDW6Z66GCUB73YD5KAZL45CR","short_pith_number":"pith:4XXDW6Z6","canonical_record":{"source":{"id":"1712.08196","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-21T20:17:36Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"435346b28daee549a83ecbeb48f825b7ce4af50a296babae6d1d8eaef9881c88","abstract_canon_sha256":"2a91ec05e8aad996d7b2e9c544dbc0717b216698076281b08d526b6651d99d73"},"schema_version":"1.0"},"canonical_sha256":"e5ee3b7b3ef18540ff781f540caf9d146279b024f00f131b18c76e089a1bc643","source":{"kind":"arxiv","id":"1712.08196","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.08196","created_at":"2026-05-18T00:27:24Z"},{"alias_kind":"arxiv_version","alias_value":"1712.08196v1","created_at":"2026-05-18T00:27:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.08196","created_at":"2026-05-18T00:27:24Z"},{"alias_kind":"pith_short_12","alias_value":"4XXDW6Z66GCU","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"4XXDW6Z66GCUB73Y","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"4XXDW6Z6","created_at":"2026-05-18T12:31:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:4XXDW6Z66GCUB73YD5KAZL45CR","target":"record","payload":{"canonical_record":{"source":{"id":"1712.08196","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-21T20:17:36Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"435346b28daee549a83ecbeb48f825b7ce4af50a296babae6d1d8eaef9881c88","abstract_canon_sha256":"2a91ec05e8aad996d7b2e9c544dbc0717b216698076281b08d526b6651d99d73"},"schema_version":"1.0"},"canonical_sha256":"e5ee3b7b3ef18540ff781f540caf9d146279b024f00f131b18c76e089a1bc643","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:24.187045Z","signature_b64":"1iWx4W7bWuwbIB9M4ScR2bjaZSS1cEghDoEJDX47pDIyXEbcchjatztKnNVnWO7Xfastk9QUGl+m0GYKPxhzBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e5ee3b7b3ef18540ff781f540caf9d146279b024f00f131b18c76e089a1bc643","last_reissued_at":"2026-05-18T00:27:24.186434Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:24.186434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.08196","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":"2026-05-18T00:27:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9keSkDd1CgYXEx/reCSlogLQ21cmoW6WTBuc2GdvFizAPlidbv0r9KPpdau1UjO9vTwA0Fm7XhtH7v2CxWkXBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T01:06:27.158329Z"},"content_sha256":"a3fc176df83b578fb5e4166a41f99574e8f5edbcf62c83e855065e357fd94598","schema_version":"1.0","event_id":"sha256:a3fc176df83b578fb5e4166a41f99574e8f5edbcf62c83e855065e357fd94598"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:4XXDW6Z66GCUB73YD5KAZL45CR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Heat Equation With a Geometric Rough Path Potential in One Space Dimension: Existence and Regularity of Solution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"H.-J. Kim, S. V. Lototsky","submitted_at":"2017-12-21T20:17:36Z","abstract_excerpt":"A solution of the heat equation with a distribution-valued potential is constructed by regularization. When the potential is the generalized derivative of a H\\\"{o}lder continuous function, regularity of the resulting solution is in line with the standard parabolic theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.08196","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":"2026-05-18T00:27:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9W3tfTe1el6uAKUSECPkHs7IN0e2BPNjbEfEpBXxpbfz1k0zkGGQtrJ2gJKYPxMMtTtGoHnjoRSJewYhmzgFCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T01:06:27.159074Z"},"content_sha256":"3dbeee922ac1a8185a20d61702a6d4b0cb967457c4f1f8e10c6172af9cb4da03","schema_version":"1.0","event_id":"sha256:3dbeee922ac1a8185a20d61702a6d4b0cb967457c4f1f8e10c6172af9cb4da03"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4XXDW6Z66GCUB73YD5KAZL45CR/bundle.json","state_url":"https://pith.science/pith/4XXDW6Z66GCUB73YD5KAZL45CR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4XXDW6Z66GCUB73YD5KAZL45CR/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":"2026-06-12T01:06:27Z","links":{"resolver":"https://pith.science/pith/4XXDW6Z66GCUB73YD5KAZL45CR","bundle":"https://pith.science/pith/4XXDW6Z66GCUB73YD5KAZL45CR/bundle.json","state":"https://pith.science/pith/4XXDW6Z66GCUB73YD5KAZL45CR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4XXDW6Z66GCUB73YD5KAZL45CR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:4XXDW6Z66GCUB73YD5KAZL45CR","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":"2a91ec05e8aad996d7b2e9c544dbc0717b216698076281b08d526b6651d99d73","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-21T20:17:36Z","title_canon_sha256":"435346b28daee549a83ecbeb48f825b7ce4af50a296babae6d1d8eaef9881c88"},"schema_version":"1.0","source":{"id":"1712.08196","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.08196","created_at":"2026-05-18T00:27:24Z"},{"alias_kind":"arxiv_version","alias_value":"1712.08196v1","created_at":"2026-05-18T00:27:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.08196","created_at":"2026-05-18T00:27:24Z"},{"alias_kind":"pith_short_12","alias_value":"4XXDW6Z66GCU","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"4XXDW6Z66GCUB73Y","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"4XXDW6Z6","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:3dbeee922ac1a8185a20d61702a6d4b0cb967457c4f1f8e10c6172af9cb4da03","target":"graph","created_at":"2026-05-18T00:27:24Z","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":"A solution of the heat equation with a distribution-valued potential is constructed by regularization. When the potential is the generalized derivative of a H\\\"{o}lder continuous function, regularity of the resulting solution is in line with the standard parabolic theory.","authors_text":"H.-J. Kim, S. V. Lototsky","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-21T20:17:36Z","title":"Heat Equation With a Geometric Rough Path Potential in One Space Dimension: Existence and Regularity of Solution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.08196","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:a3fc176df83b578fb5e4166a41f99574e8f5edbcf62c83e855065e357fd94598","target":"record","created_at":"2026-05-18T00:27:24Z","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":"2a91ec05e8aad996d7b2e9c544dbc0717b216698076281b08d526b6651d99d73","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-21T20:17:36Z","title_canon_sha256":"435346b28daee549a83ecbeb48f825b7ce4af50a296babae6d1d8eaef9881c88"},"schema_version":"1.0","source":{"id":"1712.08196","kind":"arxiv","version":1}},"canonical_sha256":"e5ee3b7b3ef18540ff781f540caf9d146279b024f00f131b18c76e089a1bc643","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e5ee3b7b3ef18540ff781f540caf9d146279b024f00f131b18c76e089a1bc643","first_computed_at":"2026-05-18T00:27:24.186434Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:27:24.186434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1iWx4W7bWuwbIB9M4ScR2bjaZSS1cEghDoEJDX47pDIyXEbcchjatztKnNVnWO7Xfastk9QUGl+m0GYKPxhzBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:27:24.187045Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.08196","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a3fc176df83b578fb5e4166a41f99574e8f5edbcf62c83e855065e357fd94598","sha256:3dbeee922ac1a8185a20d61702a6d4b0cb967457c4f1f8e10c6172af9cb4da03"],"state_sha256":"d0f7672574b36f130d599eeaaa21bd5299d3d20f17ede135c532d34f44846654"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ODRS4f8AzMfTYUEDEU+IjRnh8rMjxScDv8WG/S3sjEhUTIAQZR7BCl+5kQ8cxfJgCOUfvHkR2t7CAxdGrQCGCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T01:06:27.163347Z","bundle_sha256":"8bc3fe7bea27d05e51c3b605aab6ec086a740fa919a13b10351029b87147320b"}}