{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:ZCLLTV3HQ2TATK35VULD7SCFCN","short_pith_number":"pith:ZCLLTV3H","canonical_record":{"source":{"id":"1412.2456","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-08T05:53:14Z","cross_cats_sorted":[],"title_canon_sha256":"b5bf8b4304b28b54d818d5c3821abf107e09029350b76392585ad67e2e2563e9","abstract_canon_sha256":"9d109c181b38d06ea352920e954b162e10cc4a25621fd36f8afd02a340360d12"},"schema_version":"1.0"},"canonical_sha256":"c896b9d76786a609ab7dad163fc8451359b327981219a5828b7d5135481d7c32","source":{"kind":"arxiv","id":"1412.2456","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.2456","created_at":"2026-05-18T02:31:57Z"},{"alias_kind":"arxiv_version","alias_value":"1412.2456v1","created_at":"2026-05-18T02:31:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.2456","created_at":"2026-05-18T02:31:57Z"},{"alias_kind":"pith_short_12","alias_value":"ZCLLTV3HQ2TA","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZCLLTV3HQ2TATK35","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZCLLTV3H","created_at":"2026-05-18T12:28:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:ZCLLTV3HQ2TATK35VULD7SCFCN","target":"record","payload":{"canonical_record":{"source":{"id":"1412.2456","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-08T05:53:14Z","cross_cats_sorted":[],"title_canon_sha256":"b5bf8b4304b28b54d818d5c3821abf107e09029350b76392585ad67e2e2563e9","abstract_canon_sha256":"9d109c181b38d06ea352920e954b162e10cc4a25621fd36f8afd02a340360d12"},"schema_version":"1.0"},"canonical_sha256":"c896b9d76786a609ab7dad163fc8451359b327981219a5828b7d5135481d7c32","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:31:57.940034Z","signature_b64":"9rlsB7Rj0CIXjhS7j9YuB20Ee6M3rIapUezXti1Z+dib1dojeIb4iY2vw/KVKaO9g9W65/C/SHcI1NACEjc9Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c896b9d76786a609ab7dad163fc8451359b327981219a5828b7d5135481d7c32","last_reissued_at":"2026-05-18T02:31:57.939333Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:31:57.939333Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.2456","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":"2026-05-18T02:31:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B4I7hnoiWDilCJ1i4JTPuioUTA5pZejqtkRyBX9Mh+L1Al/kchA4MJvXxun+3yh5yI0VMX0gjZKBRoSpR0e8BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T17:31:11.711717Z"},"content_sha256":"6d5c4011f3ee55afc6c77b1ae4746de71def08f60c5d3f92c4cec8ec794da7b0","schema_version":"1.0","event_id":"sha256:6d5c4011f3ee55afc6c77b1ae4746de71def08f60c5d3f92c4cec8ec794da7b0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:ZCLLTV3HQ2TATK35VULD7SCFCN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stochastic Convective Wave Equation in Two Space Dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Imbo Sim, Sang-Hyeon Park","submitted_at":"2014-12-08T05:53:14Z","abstract_excerpt":"We study the convective wave equation in two space dimension driven by spatially homogeneous Gaussian noise. The existence of the real-valued solution is proved by providing a necessary and sufficient condition of Gaussian noise source. Our approach is based on the mild solution of the convective wave equation which is constructed by Walsh's theory of martingale measures. H\\\"older continuity of the solution is proved by using Green's function and Kolmogorov continuity theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2456","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":"2026-05-18T02:31:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"47CDU4nCiRqI7zSGC5MRu26gogCvXaZFMEuwtDM5vQ+CKl9M+4yJFuBvfOrCSJ1/ESWohZLMagPL36uSXKFiDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T17:31:11.712060Z"},"content_sha256":"3565194fdbb972302457067566432cb4ac98b806b1c2460c2138f5465daa4fa2","schema_version":"1.0","event_id":"sha256:3565194fdbb972302457067566432cb4ac98b806b1c2460c2138f5465daa4fa2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZCLLTV3HQ2TATK35VULD7SCFCN/bundle.json","state_url":"https://pith.science/pith/ZCLLTV3HQ2TATK35VULD7SCFCN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZCLLTV3HQ2TATK35VULD7SCFCN/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":"2026-06-29T17:31:11Z","links":{"resolver":"https://pith.science/pith/ZCLLTV3HQ2TATK35VULD7SCFCN","bundle":"https://pith.science/pith/ZCLLTV3HQ2TATK35VULD7SCFCN/bundle.json","state":"https://pith.science/pith/ZCLLTV3HQ2TATK35VULD7SCFCN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZCLLTV3HQ2TATK35VULD7SCFCN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ZCLLTV3HQ2TATK35VULD7SCFCN","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":"9d109c181b38d06ea352920e954b162e10cc4a25621fd36f8afd02a340360d12","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-08T05:53:14Z","title_canon_sha256":"b5bf8b4304b28b54d818d5c3821abf107e09029350b76392585ad67e2e2563e9"},"schema_version":"1.0","source":{"id":"1412.2456","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.2456","created_at":"2026-05-18T02:31:57Z"},{"alias_kind":"arxiv_version","alias_value":"1412.2456v1","created_at":"2026-05-18T02:31:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.2456","created_at":"2026-05-18T02:31:57Z"},{"alias_kind":"pith_short_12","alias_value":"ZCLLTV3HQ2TA","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZCLLTV3HQ2TATK35","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZCLLTV3H","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:3565194fdbb972302457067566432cb4ac98b806b1c2460c2138f5465daa4fa2","target":"graph","created_at":"2026-05-18T02:31:57Z","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 study the convective wave equation in two space dimension driven by spatially homogeneous Gaussian noise. The existence of the real-valued solution is proved by providing a necessary and sufficient condition of Gaussian noise source. Our approach is based on the mild solution of the convective wave equation which is constructed by Walsh's theory of martingale measures. H\\\"older continuity of the solution is proved by using Green's function and Kolmogorov continuity theorem.","authors_text":"Imbo Sim, Sang-Hyeon Park","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-08T05:53:14Z","title":"Stochastic Convective Wave Equation in Two Space Dimension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2456","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":"sha256:6d5c4011f3ee55afc6c77b1ae4746de71def08f60c5d3f92c4cec8ec794da7b0","target":"record","created_at":"2026-05-18T02:31:57Z","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":"9d109c181b38d06ea352920e954b162e10cc4a25621fd36f8afd02a340360d12","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-08T05:53:14Z","title_canon_sha256":"b5bf8b4304b28b54d818d5c3821abf107e09029350b76392585ad67e2e2563e9"},"schema_version":"1.0","source":{"id":"1412.2456","kind":"arxiv","version":1}},"canonical_sha256":"c896b9d76786a609ab7dad163fc8451359b327981219a5828b7d5135481d7c32","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c896b9d76786a609ab7dad163fc8451359b327981219a5828b7d5135481d7c32","first_computed_at":"2026-05-18T02:31:57.939333Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:31:57.939333Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9rlsB7Rj0CIXjhS7j9YuB20Ee6M3rIapUezXti1Z+dib1dojeIb4iY2vw/KVKaO9g9W65/C/SHcI1NACEjc9Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:31:57.940034Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.2456","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d5c4011f3ee55afc6c77b1ae4746de71def08f60c5d3f92c4cec8ec794da7b0","sha256:3565194fdbb972302457067566432cb4ac98b806b1c2460c2138f5465daa4fa2"],"state_sha256":"7f4b5c447adff5e773b174b1bcb1aee5c0c96828f0310b2be890d1080ea63a8e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jhW6qY1r9KKZECB3J2hHsgZZmLuzDP4P+lLDJOmd2UOKbvcGdTyXwkc61i+WvCNAMzGd4tl1cfA26yIEgUjBDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T17:31:11.713934Z","bundle_sha256":"91eaa2cd49920e5e063d4369ab3e6f13ab3f12d37105d25d7f6a01eec3f536a9"}}