{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:WZ7SUHIDKG2CCDSAD3ITQZD2GO","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":"c9fdde344d2d1359a5de8714706bcf99bda0fc8e5f0cedc50108ea8267206a18","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-09T17:18:18Z","title_canon_sha256":"16dd8eb9447418a5f72f97b630219f7807ebb141e7d6ae2a2ee93188739ff980"},"schema_version":"1.0","source":{"id":"1509.02855","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.02855","created_at":"2026-05-18T00:59:59Z"},{"alias_kind":"arxiv_version","alias_value":"1509.02855v3","created_at":"2026-05-18T00:59:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.02855","created_at":"2026-05-18T00:59:59Z"},{"alias_kind":"pith_short_12","alias_value":"WZ7SUHIDKG2C","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WZ7SUHIDKG2CCDSA","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WZ7SUHID","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:7ddd856a2d99ce4790d98279757e9cd2f7690a3dac04803063f4bc307843cdba","target":"graph","created_at":"2026-05-18T00:59:59Z","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":"Skorokhod's M1 topology is defined for c\\`adl\\`ag paths taking values in the space of tempered distributions (more generally, in the dual of a countably Hilbertian nuclear space). Compactness and tightness characterisations are derived which allow us to study a collection of stochastic processes through their projections on the familiar space of real-valued c\\`adl\\`ag processes. It is shown how this topological space can be used in analysing the convergence of empirical process approximations to distribution-valued evolution equations with Dirichlet boundary conditions.","authors_text":"Sean Ledger","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-09T17:18:18Z","title":"Skorokhod's M1 topology for distribution-valued processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.02855","kind":"arxiv","version":3},"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":"sha256:6d280d7e3e38cf746b0af4eafebdb3900f1a5c6ecb6dfb756f8405a777c91ec0","target":"record","created_at":"2026-05-18T00:59:59Z","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":"c9fdde344d2d1359a5de8714706bcf99bda0fc8e5f0cedc50108ea8267206a18","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-09T17:18:18Z","title_canon_sha256":"16dd8eb9447418a5f72f97b630219f7807ebb141e7d6ae2a2ee93188739ff980"},"schema_version":"1.0","source":{"id":"1509.02855","kind":"arxiv","version":3}},"canonical_sha256":"b67f2a1d0351b4210e401ed138647a339a43984410e802eeaee3739b12cde53f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b67f2a1d0351b4210e401ed138647a339a43984410e802eeaee3739b12cde53f","first_computed_at":"2026-05-18T00:59:59.057774Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:59.057774Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SZynLzM89qJC2DpatAEOoScBd3tttMQoavIr7WOHUHvTHY8PUiYJfQShhGkEBM1/9y2+AKaL8XXXUSiG/dxDCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:59.058247Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.02855","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d280d7e3e38cf746b0af4eafebdb3900f1a5c6ecb6dfb756f8405a777c91ec0","sha256:7ddd856a2d99ce4790d98279757e9cd2f7690a3dac04803063f4bc307843cdba"],"state_sha256":"6e510a94dd8f82396e32a433a81dadd48b7da27546ba45f52ec35a284a504cc1"}