{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:JTYOAN7J6Z3WIBCB6IXON4BD5Y","short_pith_number":"pith:JTYOAN7J","canonical_record":{"source":{"id":"1605.00024","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-04-29T21:06:11Z","cross_cats_sorted":[],"title_canon_sha256":"c0007a049b94f48e2ad54f7e06a2d798bd3f5aa3c464f5688e09b47c6187a4ac","abstract_canon_sha256":"cae1bee0b655ce949691b1edec7e738f6c1dca601159c6f7e22c09ab381179aa"},"schema_version":"1.0"},"canonical_sha256":"4cf0e037e9f677640441f22ee6f023ee2335c0f4db9ad3821a713f7da12681a4","source":{"kind":"arxiv","id":"1605.00024","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.00024","created_at":"2026-05-18T01:15:57Z"},{"alias_kind":"arxiv_version","alias_value":"1605.00024v1","created_at":"2026-05-18T01:15:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.00024","created_at":"2026-05-18T01:15:57Z"},{"alias_kind":"pith_short_12","alias_value":"JTYOAN7J6Z3W","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JTYOAN7J6Z3WIBCB","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JTYOAN7J","created_at":"2026-05-18T12:30:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:JTYOAN7J6Z3WIBCB6IXON4BD5Y","target":"record","payload":{"canonical_record":{"source":{"id":"1605.00024","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-04-29T21:06:11Z","cross_cats_sorted":[],"title_canon_sha256":"c0007a049b94f48e2ad54f7e06a2d798bd3f5aa3c464f5688e09b47c6187a4ac","abstract_canon_sha256":"cae1bee0b655ce949691b1edec7e738f6c1dca601159c6f7e22c09ab381179aa"},"schema_version":"1.0"},"canonical_sha256":"4cf0e037e9f677640441f22ee6f023ee2335c0f4db9ad3821a713f7da12681a4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:57.064693Z","signature_b64":"4OuCbQw1LO9p3m37DUE0JxWmZDg7dKjsNf3WvnZ/pPiT7V2x314biBgDkp5TbvwGo6PmaOsuryKUlG+yCGd0Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4cf0e037e9f677640441f22ee6f023ee2335c0f4db9ad3821a713f7da12681a4","last_reissued_at":"2026-05-18T01:15:57.064081Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:57.064081Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.00024","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":"2026-05-18T01:15:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M7whgn9SigJ2aq2cptR+a0ei+CLcX715rsEtIX3x3HyzG0gsTCndiIXLofjYJZcpuVFfzTOhLUH1cLS80i2rDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T01:29:51.326376Z"},"content_sha256":"aaa57356a165f5b570ad6de807acb3976c947b541e5000f7f6483d62290002b7","schema_version":"1.0","event_id":"sha256:aaa57356a165f5b570ad6de807acb3976c947b541e5000f7f6483d62290002b7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:JTYOAN7J6Z3WIBCB6IXON4BD5Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Intermittency for the Hyperbolic Anderson Model with rough noise in space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Llu\\'is Quer-Sardanyons, Maria Jolis, Raluca M. Balan","submitted_at":"2016-04-29T21:06:11Z","abstract_excerpt":"In this article, we consider the stochastic wave equation on the real line driven by a linear multiplicative Gaussian noise, which is white in time and whose spatial correlation corresponds to that of a fractional Brownian motion with Hurst index $H\\in (\\frac14,\\frac12)$. Initial data are assumed to be constant. First, we prove that this equation has a unique solution (in the Skorohod sense) and obtain an exponential upper bound for the $p$-th moment of the solution, for any $p\\geq 2$. Condition $H>\\frac14$ turns out to be necessary for the existence of solution. Secondly, we show that this so"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00024","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":"2026-05-18T01:15:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xcjvifN5zKNIcgIyYbB6nSmXAxsT0AhlFAllkKKLN19K/mh+Scg51SG1ecW/qJHlhtmLvVSzPL3ZhRmOXBMyAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T01:29:51.326730Z"},"content_sha256":"550f8514c5ae50be0a0d1c2d3c3b7ac2532378b4feecccc516ae31ed75e0c89a","schema_version":"1.0","event_id":"sha256:550f8514c5ae50be0a0d1c2d3c3b7ac2532378b4feecccc516ae31ed75e0c89a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JTYOAN7J6Z3WIBCB6IXON4BD5Y/bundle.json","state_url":"https://pith.science/pith/JTYOAN7J6Z3WIBCB6IXON4BD5Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JTYOAN7J6Z3WIBCB6IXON4BD5Y/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":"2026-05-30T01:29:51Z","links":{"resolver":"https://pith.science/pith/JTYOAN7J6Z3WIBCB6IXON4BD5Y","bundle":"https://pith.science/pith/JTYOAN7J6Z3WIBCB6IXON4BD5Y/bundle.json","state":"https://pith.science/pith/JTYOAN7J6Z3WIBCB6IXON4BD5Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JTYOAN7J6Z3WIBCB6IXON4BD5Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:JTYOAN7J6Z3WIBCB6IXON4BD5Y","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":"cae1bee0b655ce949691b1edec7e738f6c1dca601159c6f7e22c09ab381179aa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-04-29T21:06:11Z","title_canon_sha256":"c0007a049b94f48e2ad54f7e06a2d798bd3f5aa3c464f5688e09b47c6187a4ac"},"schema_version":"1.0","source":{"id":"1605.00024","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.00024","created_at":"2026-05-18T01:15:57Z"},{"alias_kind":"arxiv_version","alias_value":"1605.00024v1","created_at":"2026-05-18T01:15:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.00024","created_at":"2026-05-18T01:15:57Z"},{"alias_kind":"pith_short_12","alias_value":"JTYOAN7J6Z3W","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JTYOAN7J6Z3WIBCB","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JTYOAN7J","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:550f8514c5ae50be0a0d1c2d3c3b7ac2532378b4feecccc516ae31ed75e0c89a","target":"graph","created_at":"2026-05-18T01:15:57Z","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":"In this article, we consider the stochastic wave equation on the real line driven by a linear multiplicative Gaussian noise, which is white in time and whose spatial correlation corresponds to that of a fractional Brownian motion with Hurst index $H\\in (\\frac14,\\frac12)$. Initial data are assumed to be constant. First, we prove that this equation has a unique solution (in the Skorohod sense) and obtain an exponential upper bound for the $p$-th moment of the solution, for any $p\\geq 2$. Condition $H>\\frac14$ turns out to be necessary for the existence of solution. Secondly, we show that this so","authors_text":"Llu\\'is Quer-Sardanyons, Maria Jolis, Raluca M. Balan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-04-29T21:06:11Z","title":"Intermittency for the Hyperbolic Anderson Model with rough noise in space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00024","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:aaa57356a165f5b570ad6de807acb3976c947b541e5000f7f6483d62290002b7","target":"record","created_at":"2026-05-18T01:15:57Z","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":"cae1bee0b655ce949691b1edec7e738f6c1dca601159c6f7e22c09ab381179aa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-04-29T21:06:11Z","title_canon_sha256":"c0007a049b94f48e2ad54f7e06a2d798bd3f5aa3c464f5688e09b47c6187a4ac"},"schema_version":"1.0","source":{"id":"1605.00024","kind":"arxiv","version":1}},"canonical_sha256":"4cf0e037e9f677640441f22ee6f023ee2335c0f4db9ad3821a713f7da12681a4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4cf0e037e9f677640441f22ee6f023ee2335c0f4db9ad3821a713f7da12681a4","first_computed_at":"2026-05-18T01:15:57.064081Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:57.064081Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4OuCbQw1LO9p3m37DUE0JxWmZDg7dKjsNf3WvnZ/pPiT7V2x314biBgDkp5TbvwGo6PmaOsuryKUlG+yCGd0Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:57.064693Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.00024","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aaa57356a165f5b570ad6de807acb3976c947b541e5000f7f6483d62290002b7","sha256:550f8514c5ae50be0a0d1c2d3c3b7ac2532378b4feecccc516ae31ed75e0c89a"],"state_sha256":"372755b45f960b601e6075a0907ed864066d6e43efd93eae7f0f2ff170385e45"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"spghAG1SqNwLN3TmTwWTEjhkmUYx+xG1Qcn4lVoJWcO+xtP5EkovCrp/dm+si+pNLAhI3GeInSN0o7ime4mFBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T01:29:51.328999Z","bundle_sha256":"ea682c80ae7dc83ee6601eca9d5f7970441248a007ccbafdbc45e09e0508ecea"}}