{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:LLXZYBVNINVZYSXO3ICC7ZWKDB","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":"9b4ae2198aad57023754be31e8613d334a3460ce61a2229da0f0edd225cd5861","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-10T11:25:58Z","title_canon_sha256":"7298150063b3ae16abe1c1512a67ca1715462cf261b9924a7946ed535847ce61"},"schema_version":"1.0","source":{"id":"2606.11951","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.11951","created_at":"2026-06-11T01:10:17Z"},{"alias_kind":"arxiv_version","alias_value":"2606.11951v1","created_at":"2026-06-11T01:10:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.11951","created_at":"2026-06-11T01:10:17Z"},{"alias_kind":"pith_short_12","alias_value":"LLXZYBVNINVZ","created_at":"2026-06-11T01:10:17Z"},{"alias_kind":"pith_short_16","alias_value":"LLXZYBVNINVZYSXO","created_at":"2026-06-11T01:10:17Z"},{"alias_kind":"pith_short_8","alias_value":"LLXZYBVN","created_at":"2026-06-11T01:10:17Z"}],"graph_snapshots":[{"event_id":"sha256:d07c08b9d2f6df32cae7c2a4b6563760fe4a4296c5244220b6dcb1888619d940","target":"graph","created_at":"2026-06-11T01:10:17Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.11951/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove a Skorokhod decomposition for the Markov processes $X^a$ and $X$ associated to the gradient Dirichlet forms with respect to the measures $\\rho^a\\mu^{\\beta}$ and $\\rho\\mu^{\\beta}$, respectively. Here, $\\mu^{\\beta}$ is the law of the standard Brownian bridge $\\beta$, while $\\rho^a$ and $\\rho$ denote densities which are given by $\\rho^a(z) := \\mathbf{1}_{[0,\\infty)}(\\bar{z}_a)$ and $\\rho(z) := \\int_0^1 \\mathbf{1}_{[0,\\infty)}(\\bar{z}_x) \\, dx$, respectively, for all $z\\in L^2(0,1)$ which have a (unique) continuous representative $\\bar{z}$ which vanishes at zero and one. To this end, we d","authors_text":"Martin Grothaus, Nicolas Renner","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-10T11:25:58Z","title":"On Skorokhod Problems for Reflected and Singular Stochastic Heat Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.11951","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":"sha256:966db2e2cd5fdda638acb8598cda118788f9499b78c43a4ab932b30f61105080","target":"record","created_at":"2026-06-11T01:10:17Z","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":"9b4ae2198aad57023754be31e8613d334a3460ce61a2229da0f0edd225cd5861","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-10T11:25:58Z","title_canon_sha256":"7298150063b3ae16abe1c1512a67ca1715462cf261b9924a7946ed535847ce61"},"schema_version":"1.0","source":{"id":"2606.11951","kind":"arxiv","version":1}},"canonical_sha256":"5aef9c06ad436b9c4aeeda042fe6ca1866173926ecfdfadc873296093c39e7a6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5aef9c06ad436b9c4aeeda042fe6ca1866173926ecfdfadc873296093c39e7a6","first_computed_at":"2026-06-11T01:10:17.564809Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-11T01:10:17.564809Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uRIzJe/Z/JJe2I8slft8EWEHuLbv2az+IkT22D8PotCkoYzzs818sDczwK0HbBH7IgX919LxvGubZXsx5tY7Bg==","signature_status":"signed_v1","signed_at":"2026-06-11T01:10:17.565997Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.11951","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:966db2e2cd5fdda638acb8598cda118788f9499b78c43a4ab932b30f61105080","sha256:d07c08b9d2f6df32cae7c2a4b6563760fe4a4296c5244220b6dcb1888619d940"],"state_sha256":"41d5170051eae0547e3495bf2c7b602137499659b226f27c7841c66aee13fcd9"}