{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:JPDQZ6GRE667JVT2OFPEMP4D2O","short_pith_number":"pith:JPDQZ6GR","canonical_record":{"source":{"id":"1310.4431","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-10-16T16:14:50Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"126801c1282638d027e9c889e80dcd95fc8f066412b4ebea50c26fd6d841cc13","abstract_canon_sha256":"928f1ccd736079703ece98eb420d4447eab50e628d41f8f4626723a19a479819"},"schema_version":"1.0"},"canonical_sha256":"4bc70cf8d127bdf4d67a715e463f83d3a5c7e67e54d511d11ccbb6dcb6555197","source":{"kind":"arxiv","id":"1310.4431","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.4431","created_at":"2026-05-18T01:27:54Z"},{"alias_kind":"arxiv_version","alias_value":"1310.4431v1","created_at":"2026-05-18T01:27:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.4431","created_at":"2026-05-18T01:27:54Z"},{"alias_kind":"pith_short_12","alias_value":"JPDQZ6GRE667","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JPDQZ6GRE667JVT2","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JPDQZ6GR","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:JPDQZ6GRE667JVT2OFPEMP4D2O","target":"record","payload":{"canonical_record":{"source":{"id":"1310.4431","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-10-16T16:14:50Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"126801c1282638d027e9c889e80dcd95fc8f066412b4ebea50c26fd6d841cc13","abstract_canon_sha256":"928f1ccd736079703ece98eb420d4447eab50e628d41f8f4626723a19a479819"},"schema_version":"1.0"},"canonical_sha256":"4bc70cf8d127bdf4d67a715e463f83d3a5c7e67e54d511d11ccbb6dcb6555197","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:54.983090Z","signature_b64":"o7iVflf6PbdZUPjK3MI1lgPb9lGKbX6LMeZOT4uzT/tSv3UdQPd50QPxIApuVeVLllFaBo7F7ZCB6WlZxYp2Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4bc70cf8d127bdf4d67a715e463f83d3a5c7e67e54d511d11ccbb6dcb6555197","last_reissued_at":"2026-05-18T01:27:54.982291Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:54.982291Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.4431","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":"2026-05-18T01:27:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UoKr8qJjvHoJhDWDq68lKouHidDrm73GXzUS5/MKs43xQTMKweYqMBw+RrcNSyVoViGK2jF01gqte6Tgtw9LBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T05:02:28.466927Z"},"content_sha256":"ea9cace06f6fbc3c2120fdfae80e0cc016981e3d3c6c82b1fef9337bcf4372d8","schema_version":"1.0","event_id":"sha256:ea9cace06f6fbc3c2120fdfae80e0cc016981e3d3c6c82b1fef9337bcf4372d8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:JPDQZ6GRE667JVT2OFPEMP4D2O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Tauberian theorem for strong Feller semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.FA","authors_text":"Moritz Gerlach","submitted_at":"2013-10-16T16:14:50Z","abstract_excerpt":"We prove that a weakly ergodic, eventually strong Feller semigroup on the space of measures on a Polish space converges strongly to a projection onto its fixed space."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.4431","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":"2026-05-18T01:27:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bWugH03Gu+AaecDqYhGO0v+QBnB5KNXiZ3gpHcT7I12Bqq7UP/Ph+8QZdTwDDMijZPWl9eDdF+GgzcCPi7cmBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T05:02:28.467272Z"},"content_sha256":"1faa60bdfc6161e84121b6856e2e6f80c513b16f9911ddc6ba45af3081cf77d1","schema_version":"1.0","event_id":"sha256:1faa60bdfc6161e84121b6856e2e6f80c513b16f9911ddc6ba45af3081cf77d1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JPDQZ6GRE667JVT2OFPEMP4D2O/bundle.json","state_url":"https://pith.science/pith/JPDQZ6GRE667JVT2OFPEMP4D2O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JPDQZ6GRE667JVT2OFPEMP4D2O/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":"2026-06-04T05:02:28Z","links":{"resolver":"https://pith.science/pith/JPDQZ6GRE667JVT2OFPEMP4D2O","bundle":"https://pith.science/pith/JPDQZ6GRE667JVT2OFPEMP4D2O/bundle.json","state":"https://pith.science/pith/JPDQZ6GRE667JVT2OFPEMP4D2O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JPDQZ6GRE667JVT2OFPEMP4D2O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:JPDQZ6GRE667JVT2OFPEMP4D2O","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":"928f1ccd736079703ece98eb420d4447eab50e628d41f8f4626723a19a479819","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-10-16T16:14:50Z","title_canon_sha256":"126801c1282638d027e9c889e80dcd95fc8f066412b4ebea50c26fd6d841cc13"},"schema_version":"1.0","source":{"id":"1310.4431","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.4431","created_at":"2026-05-18T01:27:54Z"},{"alias_kind":"arxiv_version","alias_value":"1310.4431v1","created_at":"2026-05-18T01:27:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.4431","created_at":"2026-05-18T01:27:54Z"},{"alias_kind":"pith_short_12","alias_value":"JPDQZ6GRE667","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JPDQZ6GRE667JVT2","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JPDQZ6GR","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:1faa60bdfc6161e84121b6856e2e6f80c513b16f9911ddc6ba45af3081cf77d1","target":"graph","created_at":"2026-05-18T01:27:54Z","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 prove that a weakly ergodic, eventually strong Feller semigroup on the space of measures on a Polish space converges strongly to a projection onto its fixed space.","authors_text":"Moritz Gerlach","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-10-16T16:14:50Z","title":"A Tauberian theorem for strong Feller semigroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.4431","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:ea9cace06f6fbc3c2120fdfae80e0cc016981e3d3c6c82b1fef9337bcf4372d8","target":"record","created_at":"2026-05-18T01:27:54Z","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":"928f1ccd736079703ece98eb420d4447eab50e628d41f8f4626723a19a479819","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-10-16T16:14:50Z","title_canon_sha256":"126801c1282638d027e9c889e80dcd95fc8f066412b4ebea50c26fd6d841cc13"},"schema_version":"1.0","source":{"id":"1310.4431","kind":"arxiv","version":1}},"canonical_sha256":"4bc70cf8d127bdf4d67a715e463f83d3a5c7e67e54d511d11ccbb6dcb6555197","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4bc70cf8d127bdf4d67a715e463f83d3a5c7e67e54d511d11ccbb6dcb6555197","first_computed_at":"2026-05-18T01:27:54.982291Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:27:54.982291Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o7iVflf6PbdZUPjK3MI1lgPb9lGKbX6LMeZOT4uzT/tSv3UdQPd50QPxIApuVeVLllFaBo7F7ZCB6WlZxYp2Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:27:54.983090Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.4431","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ea9cace06f6fbc3c2120fdfae80e0cc016981e3d3c6c82b1fef9337bcf4372d8","sha256:1faa60bdfc6161e84121b6856e2e6f80c513b16f9911ddc6ba45af3081cf77d1"],"state_sha256":"919e41a94a30d9f359334ff2258589a40e98f5e6fb88c188b1f61eea0f2730b2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BIVlMxSDGCRGu1R5TfWNeXD++9UPfHfEopV5/il0MaMwshpB0tZwQPLjZK9o+iBs1mGPVB/dx3KN3gg1oHXwBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T05:02:28.469286Z","bundle_sha256":"0c98d11e62c59ba08bcf3aeb44348ae2f77a0fd87f99d2d4108e677f806614a9"}}