{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:7DNI44P27FZ2YHZHNMCRRGDMOB","short_pith_number":"pith:7DNI44P2","canonical_record":{"source":{"id":"1509.08614","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-29T07:18:32Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"b1922e2928b0e788a0aa9d7e74eb3c4a0d5be324ce82eb2b3f49c02c78362bdb","abstract_canon_sha256":"f9820ddb215023831fd553d82e94673b7b8daf123d24d9f5d38bb3221704cc62"},"schema_version":"1.0"},"canonical_sha256":"f8da8e71faf973ac1f276b0518986c705749835d1ab8b547b051a326fff7325c","source":{"kind":"arxiv","id":"1509.08614","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.08614","created_at":"2026-05-17T23:45:10Z"},{"alias_kind":"arxiv_version","alias_value":"1509.08614v3","created_at":"2026-05-17T23:45:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.08614","created_at":"2026-05-17T23:45:10Z"},{"alias_kind":"pith_short_12","alias_value":"7DNI44P27FZ2","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"7DNI44P27FZ2YHZH","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"7DNI44P2","created_at":"2026-05-18T12:29:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:7DNI44P27FZ2YHZHNMCRRGDMOB","target":"record","payload":{"canonical_record":{"source":{"id":"1509.08614","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-29T07:18:32Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"b1922e2928b0e788a0aa9d7e74eb3c4a0d5be324ce82eb2b3f49c02c78362bdb","abstract_canon_sha256":"f9820ddb215023831fd553d82e94673b7b8daf123d24d9f5d38bb3221704cc62"},"schema_version":"1.0"},"canonical_sha256":"f8da8e71faf973ac1f276b0518986c705749835d1ab8b547b051a326fff7325c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:10.347944Z","signature_b64":"fBtuyMc/lCH/WG7Ch17tBf/OKfSBTPbxMF5WIojYgPxN6y2K8Qh24Q2yD+sSEX/tfiZQhGEh5PnsHaO5yIZaBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f8da8e71faf973ac1f276b0518986c705749835d1ab8b547b051a326fff7325c","last_reissued_at":"2026-05-17T23:45:10.347229Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:10.347229Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.08614","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:45:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wnxe+YQU6g4DMUH47hA7vQDie64I3IZmFi01xYbdWs/BN5coEl9Eeuib+l9Y0bU2r4opsRnDDFYrK/dgH5uXAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T07:31:23.589857Z"},"content_sha256":"be44f09ecd012b0bb56a722b5eabfa35d07d70ffc31d41ca5b60075613b6e361","schema_version":"1.0","event_id":"sha256:be44f09ecd012b0bb56a722b5eabfa35d07d70ffc31d41ca5b60075613b6e361"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:7DNI44P27FZ2YHZHNMCRRGDMOB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Free infinite divisibility for powers of random variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.PR","authors_text":"Takahiro Hasebe","submitted_at":"2015-09-29T07:18:32Z","abstract_excerpt":"We prove that $X^r$ follows an FID distribution if: (1) $X$ follows a free Poisson distribution without an atom at 0 and $r\\in(-\\infty,0]\\cup[1,\\infty)$; (2) $X$ follows a free Poisson distribution with an atom at 0 and $r\\geq1$; (3) $X$ follows a mixture of some HCM distributions and $|r|\\geq1$; (4) $X$ follows some beta distributions and $r$ is taken from some interval. In particular, if $S$ is a standard semicircular element then $|S|^r$ is freely infinitely divisible for $r\\in(-\\infty,0]\\cup[2,\\infty)$. Also we consider the symmetrization of the above probability measures, and in particula"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.08614","kind":"arxiv","version":3},"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":"2026-05-17T23:45:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HedstJTDPDG4JzGDfd+ZEoNrSTCtd7LuJwKBohhex3cxhVgCDzQGUoZ8FuxaGpwdvfMXSlLdr9CDUe5PMu6RAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T07:31:23.590236Z"},"content_sha256":"e1d4bc90914d653f4f20cfbb9db3163cc60629548cbae245b4f44ee0c75b189a","schema_version":"1.0","event_id":"sha256:e1d4bc90914d653f4f20cfbb9db3163cc60629548cbae245b4f44ee0c75b189a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7DNI44P27FZ2YHZHNMCRRGDMOB/bundle.json","state_url":"https://pith.science/pith/7DNI44P27FZ2YHZHNMCRRGDMOB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7DNI44P27FZ2YHZHNMCRRGDMOB/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":"2026-05-31T07:31:23Z","links":{"resolver":"https://pith.science/pith/7DNI44P27FZ2YHZHNMCRRGDMOB","bundle":"https://pith.science/pith/7DNI44P27FZ2YHZHNMCRRGDMOB/bundle.json","state":"https://pith.science/pith/7DNI44P27FZ2YHZHNMCRRGDMOB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7DNI44P27FZ2YHZHNMCRRGDMOB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:7DNI44P27FZ2YHZHNMCRRGDMOB","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":"f9820ddb215023831fd553d82e94673b7b8daf123d24d9f5d38bb3221704cc62","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-29T07:18:32Z","title_canon_sha256":"b1922e2928b0e788a0aa9d7e74eb3c4a0d5be324ce82eb2b3f49c02c78362bdb"},"schema_version":"1.0","source":{"id":"1509.08614","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.08614","created_at":"2026-05-17T23:45:10Z"},{"alias_kind":"arxiv_version","alias_value":"1509.08614v3","created_at":"2026-05-17T23:45:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.08614","created_at":"2026-05-17T23:45:10Z"},{"alias_kind":"pith_short_12","alias_value":"7DNI44P27FZ2","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"7DNI44P27FZ2YHZH","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"7DNI44P2","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:e1d4bc90914d653f4f20cfbb9db3163cc60629548cbae245b4f44ee0c75b189a","target":"graph","created_at":"2026-05-17T23:45:10Z","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 $X^r$ follows an FID distribution if: (1) $X$ follows a free Poisson distribution without an atom at 0 and $r\\in(-\\infty,0]\\cup[1,\\infty)$; (2) $X$ follows a free Poisson distribution with an atom at 0 and $r\\geq1$; (3) $X$ follows a mixture of some HCM distributions and $|r|\\geq1$; (4) $X$ follows some beta distributions and $r$ is taken from some interval. In particular, if $S$ is a standard semicircular element then $|S|^r$ is freely infinitely divisible for $r\\in(-\\infty,0]\\cup[2,\\infty)$. Also we consider the symmetrization of the above probability measures, and in particula","authors_text":"Takahiro Hasebe","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-29T07:18:32Z","title":"Free infinite divisibility for powers of random variables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.08614","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:be44f09ecd012b0bb56a722b5eabfa35d07d70ffc31d41ca5b60075613b6e361","target":"record","created_at":"2026-05-17T23:45:10Z","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":"f9820ddb215023831fd553d82e94673b7b8daf123d24d9f5d38bb3221704cc62","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-29T07:18:32Z","title_canon_sha256":"b1922e2928b0e788a0aa9d7e74eb3c4a0d5be324ce82eb2b3f49c02c78362bdb"},"schema_version":"1.0","source":{"id":"1509.08614","kind":"arxiv","version":3}},"canonical_sha256":"f8da8e71faf973ac1f276b0518986c705749835d1ab8b547b051a326fff7325c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f8da8e71faf973ac1f276b0518986c705749835d1ab8b547b051a326fff7325c","first_computed_at":"2026-05-17T23:45:10.347229Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:10.347229Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fBtuyMc/lCH/WG7Ch17tBf/OKfSBTPbxMF5WIojYgPxN6y2K8Qh24Q2yD+sSEX/tfiZQhGEh5PnsHaO5yIZaBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:10.347944Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.08614","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:be44f09ecd012b0bb56a722b5eabfa35d07d70ffc31d41ca5b60075613b6e361","sha256:e1d4bc90914d653f4f20cfbb9db3163cc60629548cbae245b4f44ee0c75b189a"],"state_sha256":"ec72a8b3073e480deccc74cf60124b69efe38846a805ea719e7cd1b470b1fcce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d0anqWUBVhaTovMjdYLnDBzgQTIi8tSLnSsyrHqy3T7WRXkrvgv/7cKhS7IeiPUnDZwV5Ddw5+ywB1c707qyDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T07:31:23.592688Z","bundle_sha256":"e4eaf6e3b909cc7f6e0552656c4764c11df71681d2abb19d3fc2645dc62f3ff3"}}