{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:52YN5VP7HIK5ICBLZ2MCXNFPNJ","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":"7ebed8557072d1c6a16f781575d8612412b80daffb3cd8fde35f14999cb6f17c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-10-09T18:52:36Z","title_canon_sha256":"6e5eb99130284d8a07b26b14cdc25527b9c68b91c749e5be42204b11c7a762ab"},"schema_version":"1.0","source":{"id":"1810.04212","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.04212","created_at":"2026-05-18T00:03:40Z"},{"alias_kind":"arxiv_version","alias_value":"1810.04212v1","created_at":"2026-05-18T00:03:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.04212","created_at":"2026-05-18T00:03:40Z"},{"alias_kind":"pith_short_12","alias_value":"52YN5VP7HIK5","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"52YN5VP7HIK5ICBL","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"52YN5VP7","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:7c668e6e93978abe4dd6ae3bb5e5abc55207dfb969cea42aa51e4087d551cc08","target":"graph","created_at":"2026-05-18T00:03:40Z","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 note we consider the parabolic Anderson model in one dimension with time-independent fractional noise $\\dot{W}$ in space. We consider the case $H<\\frac{1}{2}$ and get existence and uniqueness of solution. In order to find the quenched asymptotics for the solution we consider its Feynman-Kac representation and explore the asymptotics of the principal eigenvalue for a random operator of the form $\\frac{1}{2} \\Delta + \\dot{W}$.","authors_text":"Bo Gao, Prakash Chakraborty, Samy Tindel, Xia Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-10-09T18:52:36Z","title":"Quenched asymptotics for a 1-d stochastic heat equation driven by a rough spatial noise"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.04212","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":"sha256:32a5271c0d0eac2cbf49f71a65af5d1176bededc88b450f8eeb24fd3cb8aa29a","target":"record","created_at":"2026-05-18T00:03:40Z","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":"7ebed8557072d1c6a16f781575d8612412b80daffb3cd8fde35f14999cb6f17c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-10-09T18:52:36Z","title_canon_sha256":"6e5eb99130284d8a07b26b14cdc25527b9c68b91c749e5be42204b11c7a762ab"},"schema_version":"1.0","source":{"id":"1810.04212","kind":"arxiv","version":1}},"canonical_sha256":"eeb0ded5ff3a15d4082bce982bb4af6a61051619e6d5e3071650495d688b6f2b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eeb0ded5ff3a15d4082bce982bb4af6a61051619e6d5e3071650495d688b6f2b","first_computed_at":"2026-05-18T00:03:40.808936Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:40.808936Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QHE6N2CRVzHjbpRPFKJ95XqY9Oymef5s/h+t5+qwCO9SFKVqd4zDrO10Gd6hL+2zT0/9NqHMvwPhJJqwovCJCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:40.809723Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.04212","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:32a5271c0d0eac2cbf49f71a65af5d1176bededc88b450f8eeb24fd3cb8aa29a","sha256:7c668e6e93978abe4dd6ae3bb5e5abc55207dfb969cea42aa51e4087d551cc08"],"state_sha256":"ba65d406d1355872a8b5f049462aad26a16b4ddcb0296e3989bcc26c36eba2ca"}