{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:DSQYAE6IEDYH5H5QFCX4EUNTIT","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":"b8199248bfccdd86b80bdbea29908f2e250366ebfd980d7865b9957c23783121","cross_cats_sorted":["math.MG","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2020-09-07T14:12:39Z","title_canon_sha256":"126d600531b39226fb97dda8cb9716ef193eaa782415e4f700ed720d6fcc6359"},"schema_version":"1.0","source":{"id":"2009.03121","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2009.03121","created_at":"2026-07-05T01:33:29Z"},{"alias_kind":"arxiv_version","alias_value":"2009.03121v1","created_at":"2026-07-05T01:33:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.03121","created_at":"2026-07-05T01:33:29Z"},{"alias_kind":"pith_short_12","alias_value":"DSQYAE6IEDYH","created_at":"2026-07-05T01:33:29Z"},{"alias_kind":"pith_short_16","alias_value":"DSQYAE6IEDYH5H5Q","created_at":"2026-07-05T01:33:29Z"},{"alias_kind":"pith_short_8","alias_value":"DSQYAE6I","created_at":"2026-07-05T01:33:29Z"}],"graph_snapshots":[{"event_id":"sha256:0d8ed733a76ff87f930001b19103c69c3f0a8c0328911d54d9284e9bbc4507ed","target":"graph","created_at":"2026-07-05T01:33:29Z","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/2009.03121/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop the theory of tamed spaces which are Dirichlet spaces with distribution-valued lower bounds on the Ricci curvature and investigate these from an Eulerian point of view. To this end we analyze in detail singular perturbations of Dirichlet form by a broad class of distributions. The distributional Ricci bound is then formulated in terms of an integrated version of the Bochner inequality using the perturbed energy form and generalizing the well-known Bakry-\\'Emery curvature-dimension condition. Among other things we show the equivalence of distributional Ricci bounds to gradient estima","authors_text":"Chiara Rigoni, Karl-Theodor Sturm, Luca Tamanini, Matthias Erbar","cross_cats":["math.MG","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2020-09-07T14:12:39Z","title":"Tamed spaces -- Dirichlet spaces with distribution-valued Ricci bounds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.03121","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:ff25b77658ade5977319f9d390cba75a29205a844e31b858c341f496f61713a5","target":"record","created_at":"2026-07-05T01:33:29Z","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":"b8199248bfccdd86b80bdbea29908f2e250366ebfd980d7865b9957c23783121","cross_cats_sorted":["math.MG","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2020-09-07T14:12:39Z","title_canon_sha256":"126d600531b39226fb97dda8cb9716ef193eaa782415e4f700ed720d6fcc6359"},"schema_version":"1.0","source":{"id":"2009.03121","kind":"arxiv","version":1}},"canonical_sha256":"1ca18013c820f07e9fb028afc251b344edc109ec1ed8253539b6eb8fe5191963","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ca18013c820f07e9fb028afc251b344edc109ec1ed8253539b6eb8fe5191963","first_computed_at":"2026-07-05T01:33:29.190795Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:33:29.190795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RPw2erLZfaQeRwkRd8DaRrZzXkTkb1p3wzjGhkHDI0kv78R9ktsTi05yyaTLznB+/DtHeDfafNB+o9fnzYelBg==","signature_status":"signed_v1","signed_at":"2026-07-05T01:33:29.191159Z","signed_message":"canonical_sha256_bytes"},"source_id":"2009.03121","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ff25b77658ade5977319f9d390cba75a29205a844e31b858c341f496f61713a5","sha256:0d8ed733a76ff87f930001b19103c69c3f0a8c0328911d54d9284e9bbc4507ed"],"state_sha256":"780d191565ffd74536849d5d39691c635b891d08a96fcb4bcd95ef231a4caa8a"}