{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:5GLMIZ42R6ZQHB4YGKISP3UVV3","short_pith_number":"pith:5GLMIZ42","canonical_record":{"source":{"id":"1502.07490","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-02-26T10:05:58Z","cross_cats_sorted":[],"title_canon_sha256":"9985f61ee3087b2212c04e96738e73876fd4bfda26a0df7cd39133bd63319da8","abstract_canon_sha256":"c1b6e088601d6835aa7dab704ca90ba11f5239f36b3b826e06bb38cb5288ea33"},"schema_version":"1.0"},"canonical_sha256":"e996c4679a8fb3038798329127ee95aed730140f50d7f03f0472705a64f6d65d","source":{"kind":"arxiv","id":"1502.07490","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.07490","created_at":"2026-05-18T02:26:03Z"},{"alias_kind":"arxiv_version","alias_value":"1502.07490v1","created_at":"2026-05-18T02:26:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.07490","created_at":"2026-05-18T02:26:03Z"},{"alias_kind":"pith_short_12","alias_value":"5GLMIZ42R6ZQ","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"5GLMIZ42R6ZQHB4Y","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"5GLMIZ42","created_at":"2026-05-18T12:29:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:5GLMIZ42R6ZQHB4YGKISP3UVV3","target":"record","payload":{"canonical_record":{"source":{"id":"1502.07490","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-02-26T10:05:58Z","cross_cats_sorted":[],"title_canon_sha256":"9985f61ee3087b2212c04e96738e73876fd4bfda26a0df7cd39133bd63319da8","abstract_canon_sha256":"c1b6e088601d6835aa7dab704ca90ba11f5239f36b3b826e06bb38cb5288ea33"},"schema_version":"1.0"},"canonical_sha256":"e996c4679a8fb3038798329127ee95aed730140f50d7f03f0472705a64f6d65d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:26:03.556737Z","signature_b64":"bYCthgl27XhSe45MMadIBBnJKeRUSqJVnpcY/tEpiL/zoXocvTpUD9rf3K9htIopgaMWn2ki2Ie67/CGnhkqCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e996c4679a8fb3038798329127ee95aed730140f50d7f03f0472705a64f6d65d","last_reissued_at":"2026-05-18T02:26:03.556173Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:26:03.556173Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.07490","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":"2026-05-18T02:26:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iOZQIHoK04A/hjbYw++5hzX3bM8sl0g7g9BXYh1o8S1UdoP4UaBqsA/Quj8FyTVa8eihqasW9D/efdUJq6kDCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T17:56:51.911149Z"},"content_sha256":"c40fc04525eccbeb4100f90c1d9688029191112f04859cc1726ea04ca1ff8b7c","schema_version":"1.0","event_id":"sha256:c40fc04525eccbeb4100f90c1d9688029191112f04859cc1726ea04ca1ff8b7c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:5GLMIZ42R6ZQHB4YGKISP3UVV3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Existence of the Fomin derivative of the invariant measure of a stochastic reaction--diffusion equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Arnaud Debussche, Giuseppe Da Prato","submitted_at":"2015-02-26T10:05:58Z","abstract_excerpt":"We consider a reaction--diffusion equation perturbed by noise (not necessarily white). We prove existence of the Fomin derivative of the corresponding transition semigroup $P_t$. The main tool is a new estimate for $P_tD\\varphi$ in terms of $\\|\\varphi\\|_{L^2(H,\\nu)}$, where $\\nu$ is the invariant measure of $P_t$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.07490","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":"2026-05-18T02:26:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LaMvZVLpFf9JijJxHKTLjUvy4vhjSDW+LCkoptLbBp9ihYH5uIGttE5+mN6sLvbtwqrVQXB7m6E6R+ZElkpADA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T17:56:51.911516Z"},"content_sha256":"ba5b9432472e1997e7abb281007e5082caae15b511b36bc9144b35018a41c7ed","schema_version":"1.0","event_id":"sha256:ba5b9432472e1997e7abb281007e5082caae15b511b36bc9144b35018a41c7ed"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5GLMIZ42R6ZQHB4YGKISP3UVV3/bundle.json","state_url":"https://pith.science/pith/5GLMIZ42R6ZQHB4YGKISP3UVV3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5GLMIZ42R6ZQHB4YGKISP3UVV3/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":"2026-06-09T17:56:51Z","links":{"resolver":"https://pith.science/pith/5GLMIZ42R6ZQHB4YGKISP3UVV3","bundle":"https://pith.science/pith/5GLMIZ42R6ZQHB4YGKISP3UVV3/bundle.json","state":"https://pith.science/pith/5GLMIZ42R6ZQHB4YGKISP3UVV3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5GLMIZ42R6ZQHB4YGKISP3UVV3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:5GLMIZ42R6ZQHB4YGKISP3UVV3","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":"c1b6e088601d6835aa7dab704ca90ba11f5239f36b3b826e06bb38cb5288ea33","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-02-26T10:05:58Z","title_canon_sha256":"9985f61ee3087b2212c04e96738e73876fd4bfda26a0df7cd39133bd63319da8"},"schema_version":"1.0","source":{"id":"1502.07490","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.07490","created_at":"2026-05-18T02:26:03Z"},{"alias_kind":"arxiv_version","alias_value":"1502.07490v1","created_at":"2026-05-18T02:26:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.07490","created_at":"2026-05-18T02:26:03Z"},{"alias_kind":"pith_short_12","alias_value":"5GLMIZ42R6ZQ","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"5GLMIZ42R6ZQHB4Y","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"5GLMIZ42","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:ba5b9432472e1997e7abb281007e5082caae15b511b36bc9144b35018a41c7ed","target":"graph","created_at":"2026-05-18T02:26:03Z","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":"We consider a reaction--diffusion equation perturbed by noise (not necessarily white). We prove existence of the Fomin derivative of the corresponding transition semigroup $P_t$. The main tool is a new estimate for $P_tD\\varphi$ in terms of $\\|\\varphi\\|_{L^2(H,\\nu)}$, where $\\nu$ is the invariant measure of $P_t$.","authors_text":"Arnaud Debussche, Giuseppe Da Prato","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-02-26T10:05:58Z","title":"Existence of the Fomin derivative of the invariant measure of a stochastic reaction--diffusion equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.07490","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:c40fc04525eccbeb4100f90c1d9688029191112f04859cc1726ea04ca1ff8b7c","target":"record","created_at":"2026-05-18T02:26:03Z","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":"c1b6e088601d6835aa7dab704ca90ba11f5239f36b3b826e06bb38cb5288ea33","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-02-26T10:05:58Z","title_canon_sha256":"9985f61ee3087b2212c04e96738e73876fd4bfda26a0df7cd39133bd63319da8"},"schema_version":"1.0","source":{"id":"1502.07490","kind":"arxiv","version":1}},"canonical_sha256":"e996c4679a8fb3038798329127ee95aed730140f50d7f03f0472705a64f6d65d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e996c4679a8fb3038798329127ee95aed730140f50d7f03f0472705a64f6d65d","first_computed_at":"2026-05-18T02:26:03.556173Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:26:03.556173Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bYCthgl27XhSe45MMadIBBnJKeRUSqJVnpcY/tEpiL/zoXocvTpUD9rf3K9htIopgaMWn2ki2Ie67/CGnhkqCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:26:03.556737Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.07490","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c40fc04525eccbeb4100f90c1d9688029191112f04859cc1726ea04ca1ff8b7c","sha256:ba5b9432472e1997e7abb281007e5082caae15b511b36bc9144b35018a41c7ed"],"state_sha256":"a980059f3ae3f9f2df57d408cce21d44823a9110471ed92766e6358099011fba"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+ur60xrb8vp0Qo3QujAqFfx0JRRgD5taDCeOdxVbBAw6SV5cnuO8EC9VZIHNT7uQSnbT0eTxSzBTks9K7D5rAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T17:56:51.913451Z","bundle_sha256":"d27208b7c8a1ffa8151428a46a3189c7675900ba151346cd8c6ba6b631e2ebe1"}}