{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:3CQKWSOEMH2Q6UMR722LH5INLD","short_pith_number":"pith:3CQKWSOE","canonical_record":{"source":{"id":"1602.07004","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-02-23T00:57:37Z","cross_cats_sorted":[],"title_canon_sha256":"2a760f0a77e13fb4c7f81217d410257f7cbb8376b30384fc269eb25198500266","abstract_canon_sha256":"6922b02518956e1ef8aa28f7e0e39b204083b74e899eb9ea1b3921ec134f9046"},"schema_version":"1.0"},"canonical_sha256":"d8a0ab49c461f50f5191feb4b3f50d58de54961d0c222ecaa7943828741fcf79","source":{"kind":"arxiv","id":"1602.07004","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.07004","created_at":"2026-05-18T00:41:51Z"},{"alias_kind":"arxiv_version","alias_value":"1602.07004v2","created_at":"2026-05-18T00:41:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.07004","created_at":"2026-05-18T00:41:51Z"},{"alias_kind":"pith_short_12","alias_value":"3CQKWSOEMH2Q","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"3CQKWSOEMH2Q6UMR","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"3CQKWSOE","created_at":"2026-05-18T12:29:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:3CQKWSOEMH2Q6UMR722LH5INLD","target":"record","payload":{"canonical_record":{"source":{"id":"1602.07004","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-02-23T00:57:37Z","cross_cats_sorted":[],"title_canon_sha256":"2a760f0a77e13fb4c7f81217d410257f7cbb8376b30384fc269eb25198500266","abstract_canon_sha256":"6922b02518956e1ef8aa28f7e0e39b204083b74e899eb9ea1b3921ec134f9046"},"schema_version":"1.0"},"canonical_sha256":"d8a0ab49c461f50f5191feb4b3f50d58de54961d0c222ecaa7943828741fcf79","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:51.498861Z","signature_b64":"qWSRo8XuCKian9H4yLb1f5nw5+fZ34eSChXxc7zSOMplsorWbf4x7sxZPtYcFjwdGPVA+MvDgzaRQxA1XRpkBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d8a0ab49c461f50f5191feb4b3f50d58de54961d0c222ecaa7943828741fcf79","last_reissued_at":"2026-05-18T00:41:51.498295Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:51.498295Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.07004","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:41:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vp/1LisKKcKjNJM7iZQkpHdO+fD6nqvFSmMTkubc4DoeN0jNNBupMEy36WBP9SYyCam0O2Q94AzNMmzjBmZYAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T22:57:28.934731Z"},"content_sha256":"e956e1106a4287406eaf6515d1fa62b1dd9ccc490d1005cebbc0074d1a44fa2b","schema_version":"1.0","event_id":"sha256:e956e1106a4287406eaf6515d1fa62b1dd9ccc490d1005cebbc0074d1a44fa2b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:3CQKWSOEMH2Q6UMR722LH5INLD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hyperbolic Anderson Model with space-time homogeneous Gaussian noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jian Song, Raluca M. Balan","submitted_at":"2016-02-23T00:57:37Z","abstract_excerpt":"In this article, we study the stochastic wave equation in arbitrary spatial dimension $d$, with a multiplicative term of the form $\\sigma(u)=u$, also known in the literature as the Hyperbolic Anderson Model. This equation is perturbed by a general Gaussian noise, which is homogeneous in both space and time. We prove the existence and uniqueness of a solution of this equation (in the Skorohod sense) and the H\\\"older continuity of its sample paths, under the same respective conditions on the spatial spectral measure of the noise as in the case of the white noise in time, regardless of the tempor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.07004","kind":"arxiv","version":2},"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":"2026-05-18T00:41:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gqejD9a2dG1ilw314ac5sjRyhktwJjLl59mhwby7hMNJTeSq3p3giqmjWxnJIPZFeuTF1NSD8wsTgA78ctAACQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T22:57:28.935506Z"},"content_sha256":"7c5dc11db2e88c0fae44b312f54984b503d73f7383b7699d0e3a92ec3c304835","schema_version":"1.0","event_id":"sha256:7c5dc11db2e88c0fae44b312f54984b503d73f7383b7699d0e3a92ec3c304835"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3CQKWSOEMH2Q6UMR722LH5INLD/bundle.json","state_url":"https://pith.science/pith/3CQKWSOEMH2Q6UMR722LH5INLD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3CQKWSOEMH2Q6UMR722LH5INLD/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":"2026-06-11T22:57:28Z","links":{"resolver":"https://pith.science/pith/3CQKWSOEMH2Q6UMR722LH5INLD","bundle":"https://pith.science/pith/3CQKWSOEMH2Q6UMR722LH5INLD/bundle.json","state":"https://pith.science/pith/3CQKWSOEMH2Q6UMR722LH5INLD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3CQKWSOEMH2Q6UMR722LH5INLD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:3CQKWSOEMH2Q6UMR722LH5INLD","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":"6922b02518956e1ef8aa28f7e0e39b204083b74e899eb9ea1b3921ec134f9046","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-02-23T00:57:37Z","title_canon_sha256":"2a760f0a77e13fb4c7f81217d410257f7cbb8376b30384fc269eb25198500266"},"schema_version":"1.0","source":{"id":"1602.07004","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.07004","created_at":"2026-05-18T00:41:51Z"},{"alias_kind":"arxiv_version","alias_value":"1602.07004v2","created_at":"2026-05-18T00:41:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.07004","created_at":"2026-05-18T00:41:51Z"},{"alias_kind":"pith_short_12","alias_value":"3CQKWSOEMH2Q","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"3CQKWSOEMH2Q6UMR","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"3CQKWSOE","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:7c5dc11db2e88c0fae44b312f54984b503d73f7383b7699d0e3a92ec3c304835","target":"graph","created_at":"2026-05-18T00:41:51Z","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 article, we study the stochastic wave equation in arbitrary spatial dimension $d$, with a multiplicative term of the form $\\sigma(u)=u$, also known in the literature as the Hyperbolic Anderson Model. This equation is perturbed by a general Gaussian noise, which is homogeneous in both space and time. We prove the existence and uniqueness of a solution of this equation (in the Skorohod sense) and the H\\\"older continuity of its sample paths, under the same respective conditions on the spatial spectral measure of the noise as in the case of the white noise in time, regardless of the tempor","authors_text":"Jian Song, Raluca M. Balan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-02-23T00:57:37Z","title":"Hyperbolic Anderson Model with space-time homogeneous Gaussian noise"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.07004","kind":"arxiv","version":2},"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:e956e1106a4287406eaf6515d1fa62b1dd9ccc490d1005cebbc0074d1a44fa2b","target":"record","created_at":"2026-05-18T00:41:51Z","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":"6922b02518956e1ef8aa28f7e0e39b204083b74e899eb9ea1b3921ec134f9046","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-02-23T00:57:37Z","title_canon_sha256":"2a760f0a77e13fb4c7f81217d410257f7cbb8376b30384fc269eb25198500266"},"schema_version":"1.0","source":{"id":"1602.07004","kind":"arxiv","version":2}},"canonical_sha256":"d8a0ab49c461f50f5191feb4b3f50d58de54961d0c222ecaa7943828741fcf79","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d8a0ab49c461f50f5191feb4b3f50d58de54961d0c222ecaa7943828741fcf79","first_computed_at":"2026-05-18T00:41:51.498295Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:51.498295Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qWSRo8XuCKian9H4yLb1f5nw5+fZ34eSChXxc7zSOMplsorWbf4x7sxZPtYcFjwdGPVA+MvDgzaRQxA1XRpkBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:51.498861Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.07004","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e956e1106a4287406eaf6515d1fa62b1dd9ccc490d1005cebbc0074d1a44fa2b","sha256:7c5dc11db2e88c0fae44b312f54984b503d73f7383b7699d0e3a92ec3c304835"],"state_sha256":"52813541d593bc89f18a4993f23bdf43eaaa4da171b68c97b1a1264ab44e5ec6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k5jxlVpPi4l0v98ZJ6jtwT5XJ8eTg7mIrLK++H4XjHeSBBpl74ddHwPnZCcTOVCWH/C/OCYNJQmGnJIRvqeUBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T22:57:28.940412Z","bundle_sha256":"9a4c12a939a5fcaba4e3d4b0c2763b7b11e037e033360957336862a0f519ae3b"}}