{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:KV6AHLAX6KWB7OSFTCA5FXXOTU","short_pith_number":"pith:KV6AHLAX","canonical_record":{"source":{"id":"1510.00003","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-09-30T19:19:38Z","cross_cats_sorted":["math.CA","math.PR"],"title_canon_sha256":"21a4b0319c50451ab6e61f60567c6f2e02fdfd205d1c2432dcaca821a68818dd","abstract_canon_sha256":"7494b9ad4c45bc23d87861ede73ca512ce766e0c4d4f0c081d752a01214c765c"},"schema_version":"1.0"},"canonical_sha256":"557c03ac17f2ac1fba459881d2deee9d07b0330b5bd446672cf9f35e2adaf847","source":{"kind":"arxiv","id":"1510.00003","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.00003","created_at":"2026-05-18T01:10:18Z"},{"alias_kind":"arxiv_version","alias_value":"1510.00003v2","created_at":"2026-05-18T01:10:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.00003","created_at":"2026-05-18T01:10:18Z"},{"alias_kind":"pith_short_12","alias_value":"KV6AHLAX6KWB","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"KV6AHLAX6KWB7OSF","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"KV6AHLAX","created_at":"2026-05-18T12:29:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:KV6AHLAX6KWB7OSFTCA5FXXOTU","target":"record","payload":{"canonical_record":{"source":{"id":"1510.00003","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-09-30T19:19:38Z","cross_cats_sorted":["math.CA","math.PR"],"title_canon_sha256":"21a4b0319c50451ab6e61f60567c6f2e02fdfd205d1c2432dcaca821a68818dd","abstract_canon_sha256":"7494b9ad4c45bc23d87861ede73ca512ce766e0c4d4f0c081d752a01214c765c"},"schema_version":"1.0"},"canonical_sha256":"557c03ac17f2ac1fba459881d2deee9d07b0330b5bd446672cf9f35e2adaf847","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:18.298686Z","signature_b64":"eXlXRvHv/E2EdAMZ3aYQjZ3T9fe2B5P9M1hQnUGvmJJsUE4/ZhvlTgpguqBHogP0MGzVpJvzN1hkysV77x77DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"557c03ac17f2ac1fba459881d2deee9d07b0330b5bd446672cf9f35e2adaf847","last_reissued_at":"2026-05-18T01:10:18.298007Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:18.298007Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.00003","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:10:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g0tTTvMT/vNA5VNYDFB+IpysLpE8K/wsSYZldBuVTgpjlhuil8EkUtXoYFydCHPtY9TrMHs8C7C2rF/JANBaAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T02:20:47.494384Z"},"content_sha256":"54539ff3579fe109e23f3c7c072f77e218979d1050bcc851c8d54bdcb7d885f5","schema_version":"1.0","event_id":"sha256:54539ff3579fe109e23f3c7c072f77e218979d1050bcc851c8d54bdcb7d885f5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:KV6AHLAX6KWB7OSFTCA5FXXOTU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Hausdorff Continuity of Free L\\`evy Processes and Free Convolution Semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.PR"],"primary_cat":"math.OA","authors_text":"John D. Williams","submitted_at":"2015-09-30T19:19:38Z","abstract_excerpt":"Let $\\mu$ denote a Borel probability measure and let $\\{ \\mu_{t} \\}_{t\\geq 1}$ denote the free additive convolution semigroup of Nica and Speicher. We show that the support of these measures varies continuously in the Hausdorff metric for $t >1$. We utilize complex analytic methods and, in particular, a characterization of the absolutely continuous portion of these supports due to Huang."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.00003","kind":"arxiv","version":2},"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":"2026-05-18T01:10:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KTG9Yk3L77583UlTzmDIuypAFWv9HcRtWqMFGqysDPMXJo0bu7lQIcmwXU6+mHfFjK8O5EZg97TGjxrk1lvtDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T02:20:47.494745Z"},"content_sha256":"b84d4540c7e1e04411869824957f59a4616904d507730bc00bb0631fdf4cc253","schema_version":"1.0","event_id":"sha256:b84d4540c7e1e04411869824957f59a4616904d507730bc00bb0631fdf4cc253"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KV6AHLAX6KWB7OSFTCA5FXXOTU/bundle.json","state_url":"https://pith.science/pith/KV6AHLAX6KWB7OSFTCA5FXXOTU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KV6AHLAX6KWB7OSFTCA5FXXOTU/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":"2026-06-03T02:20:47Z","links":{"resolver":"https://pith.science/pith/KV6AHLAX6KWB7OSFTCA5FXXOTU","bundle":"https://pith.science/pith/KV6AHLAX6KWB7OSFTCA5FXXOTU/bundle.json","state":"https://pith.science/pith/KV6AHLAX6KWB7OSFTCA5FXXOTU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KV6AHLAX6KWB7OSFTCA5FXXOTU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:KV6AHLAX6KWB7OSFTCA5FXXOTU","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":"7494b9ad4c45bc23d87861ede73ca512ce766e0c4d4f0c081d752a01214c765c","cross_cats_sorted":["math.CA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-09-30T19:19:38Z","title_canon_sha256":"21a4b0319c50451ab6e61f60567c6f2e02fdfd205d1c2432dcaca821a68818dd"},"schema_version":"1.0","source":{"id":"1510.00003","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.00003","created_at":"2026-05-18T01:10:18Z"},{"alias_kind":"arxiv_version","alias_value":"1510.00003v2","created_at":"2026-05-18T01:10:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.00003","created_at":"2026-05-18T01:10:18Z"},{"alias_kind":"pith_short_12","alias_value":"KV6AHLAX6KWB","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"KV6AHLAX6KWB7OSF","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"KV6AHLAX","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:b84d4540c7e1e04411869824957f59a4616904d507730bc00bb0631fdf4cc253","target":"graph","created_at":"2026-05-18T01:10:18Z","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":"Let $\\mu$ denote a Borel probability measure and let $\\{ \\mu_{t} \\}_{t\\geq 1}$ denote the free additive convolution semigroup of Nica and Speicher. We show that the support of these measures varies continuously in the Hausdorff metric for $t >1$. We utilize complex analytic methods and, in particular, a characterization of the absolutely continuous portion of these supports due to Huang.","authors_text":"John D. Williams","cross_cats":["math.CA","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-09-30T19:19:38Z","title":"On the Hausdorff Continuity of Free L\\`evy Processes and Free Convolution Semigroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.00003","kind":"arxiv","version":2},"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":"sha256:54539ff3579fe109e23f3c7c072f77e218979d1050bcc851c8d54bdcb7d885f5","target":"record","created_at":"2026-05-18T01:10:18Z","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":"7494b9ad4c45bc23d87861ede73ca512ce766e0c4d4f0c081d752a01214c765c","cross_cats_sorted":["math.CA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-09-30T19:19:38Z","title_canon_sha256":"21a4b0319c50451ab6e61f60567c6f2e02fdfd205d1c2432dcaca821a68818dd"},"schema_version":"1.0","source":{"id":"1510.00003","kind":"arxiv","version":2}},"canonical_sha256":"557c03ac17f2ac1fba459881d2deee9d07b0330b5bd446672cf9f35e2adaf847","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"557c03ac17f2ac1fba459881d2deee9d07b0330b5bd446672cf9f35e2adaf847","first_computed_at":"2026-05-18T01:10:18.298007Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:18.298007Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eXlXRvHv/E2EdAMZ3aYQjZ3T9fe2B5P9M1hQnUGvmJJsUE4/ZhvlTgpguqBHogP0MGzVpJvzN1hkysV77x77DA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:18.298686Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.00003","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:54539ff3579fe109e23f3c7c072f77e218979d1050bcc851c8d54bdcb7d885f5","sha256:b84d4540c7e1e04411869824957f59a4616904d507730bc00bb0631fdf4cc253"],"state_sha256":"763a4149fa6e2c1cdfa814579ef5d2e255591b8cafd48c4d338ff31166d3fa94"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BJJoOHqz0vbTE15FWSiA7dPGS5hn3ofpKpp+AG2w1LbKwW7/6af+FAkOGthRygpJD3WBxonWku0YxtX9ep4nAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T02:20:47.496710Z","bundle_sha256":"16db53d7cedf61e43d43db6903cbcab4235dc7d8233e475e84da89c8d1cdb756"}}