{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:2DJNGDMCTY2IIZ3VO653URDT74","short_pith_number":"pith:2DJNGDMC","canonical_record":{"source":{"id":"1510.04182","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-10-14T16:08:54Z","cross_cats_sorted":[],"title_canon_sha256":"2e0aa12613114b2ca056b01f9b43205e5d761d4272a916a5b814962f84a86b9a","abstract_canon_sha256":"a110e5b4c7330b9d30091059e6ce914f85c6ee28f6286fd1194bfdf63f64bcf3"},"schema_version":"1.0"},"canonical_sha256":"d0d2d30d829e3484677577bbba4473ff3a693c6fa9043a831c3a2dd82bd495db","source":{"kind":"arxiv","id":"1510.04182","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.04182","created_at":"2026-05-18T01:30:08Z"},{"alias_kind":"arxiv_version","alias_value":"1510.04182v1","created_at":"2026-05-18T01:30:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.04182","created_at":"2026-05-18T01:30:08Z"},{"alias_kind":"pith_short_12","alias_value":"2DJNGDMCTY2I","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"2DJNGDMCTY2IIZ3V","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"2DJNGDMC","created_at":"2026-05-18T12:28:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:2DJNGDMCTY2IIZ3VO653URDT74","target":"record","payload":{"canonical_record":{"source":{"id":"1510.04182","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-10-14T16:08:54Z","cross_cats_sorted":[],"title_canon_sha256":"2e0aa12613114b2ca056b01f9b43205e5d761d4272a916a5b814962f84a86b9a","abstract_canon_sha256":"a110e5b4c7330b9d30091059e6ce914f85c6ee28f6286fd1194bfdf63f64bcf3"},"schema_version":"1.0"},"canonical_sha256":"d0d2d30d829e3484677577bbba4473ff3a693c6fa9043a831c3a2dd82bd495db","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:08.994681Z","signature_b64":"oI9NnawWiFvU6Zt5yUUhK8igGVVlBBFk8c4MjMfo7MeasiYB8f1DWYDRGrrTbTX0Zt0XXfIcnvuIygqAgDTDCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d0d2d30d829e3484677577bbba4473ff3a693c6fa9043a831c3a2dd82bd495db","last_reissued_at":"2026-05-18T01:30:08.994051Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:08.994051Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.04182","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":"2026-05-18T01:30:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WkJUrCKRg1QaB2r1dnwGTJyM5OXAnDlX0yU3H87po5ry/dMrUA8yVq1zJ/9GHLA6uBN+hGQaphAeEJ5lRuEICA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T23:57:25.808408Z"},"content_sha256":"ee1b9b392b5fe8c9143dd91055985f6cc69574b8b6c37a44fd7fe8100e6ba87c","schema_version":"1.0","event_id":"sha256:ee1b9b392b5fe8c9143dd91055985f6cc69574b8b6c37a44fd7fe8100e6ba87c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:2DJNGDMCTY2IIZ3VO653URDT74","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Vector rearrangement invariant banach spaces of random variables with exponential decreasing tails of distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"E. Ostrovsky, L. Sirota","submitted_at":"2015-10-14T16:08:54Z","abstract_excerpt":"We present in this paper the theory of multivariate Banach spaces of random variables with exponential decreasing tails of distributions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.04182","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":"2026-05-18T01:30:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YBpQpfnGInpN5OyS/iuU9MWPM4vqSYMXj52BHgagK23JgCaOGdqDKtTC3dwIbsdj5qk81woPIv2Pd4sQHXdVCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T23:57:25.808757Z"},"content_sha256":"17ae23aac89143905f2ef11b8021abc9c068ebffc8caaa105659293e1d1e8c97","schema_version":"1.0","event_id":"sha256:17ae23aac89143905f2ef11b8021abc9c068ebffc8caaa105659293e1d1e8c97"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2DJNGDMCTY2IIZ3VO653URDT74/bundle.json","state_url":"https://pith.science/pith/2DJNGDMCTY2IIZ3VO653URDT74/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2DJNGDMCTY2IIZ3VO653URDT74/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":"2026-06-22T23:57:25Z","links":{"resolver":"https://pith.science/pith/2DJNGDMCTY2IIZ3VO653URDT74","bundle":"https://pith.science/pith/2DJNGDMCTY2IIZ3VO653URDT74/bundle.json","state":"https://pith.science/pith/2DJNGDMCTY2IIZ3VO653URDT74/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2DJNGDMCTY2IIZ3VO653URDT74/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:2DJNGDMCTY2IIZ3VO653URDT74","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":"a110e5b4c7330b9d30091059e6ce914f85c6ee28f6286fd1194bfdf63f64bcf3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-10-14T16:08:54Z","title_canon_sha256":"2e0aa12613114b2ca056b01f9b43205e5d761d4272a916a5b814962f84a86b9a"},"schema_version":"1.0","source":{"id":"1510.04182","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.04182","created_at":"2026-05-18T01:30:08Z"},{"alias_kind":"arxiv_version","alias_value":"1510.04182v1","created_at":"2026-05-18T01:30:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.04182","created_at":"2026-05-18T01:30:08Z"},{"alias_kind":"pith_short_12","alias_value":"2DJNGDMCTY2I","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"2DJNGDMCTY2IIZ3V","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"2DJNGDMC","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:17ae23aac89143905f2ef11b8021abc9c068ebffc8caaa105659293e1d1e8c97","target":"graph","created_at":"2026-05-18T01:30:08Z","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 present in this paper the theory of multivariate Banach spaces of random variables with exponential decreasing tails of distributions.","authors_text":"E. Ostrovsky, L. Sirota","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-10-14T16:08:54Z","title":"Vector rearrangement invariant banach spaces of random variables with exponential decreasing tails of distributions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.04182","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:ee1b9b392b5fe8c9143dd91055985f6cc69574b8b6c37a44fd7fe8100e6ba87c","target":"record","created_at":"2026-05-18T01:30:08Z","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":"a110e5b4c7330b9d30091059e6ce914f85c6ee28f6286fd1194bfdf63f64bcf3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-10-14T16:08:54Z","title_canon_sha256":"2e0aa12613114b2ca056b01f9b43205e5d761d4272a916a5b814962f84a86b9a"},"schema_version":"1.0","source":{"id":"1510.04182","kind":"arxiv","version":1}},"canonical_sha256":"d0d2d30d829e3484677577bbba4473ff3a693c6fa9043a831c3a2dd82bd495db","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d0d2d30d829e3484677577bbba4473ff3a693c6fa9043a831c3a2dd82bd495db","first_computed_at":"2026-05-18T01:30:08.994051Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:08.994051Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oI9NnawWiFvU6Zt5yUUhK8igGVVlBBFk8c4MjMfo7MeasiYB8f1DWYDRGrrTbTX0Zt0XXfIcnvuIygqAgDTDCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:08.994681Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.04182","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee1b9b392b5fe8c9143dd91055985f6cc69574b8b6c37a44fd7fe8100e6ba87c","sha256:17ae23aac89143905f2ef11b8021abc9c068ebffc8caaa105659293e1d1e8c97"],"state_sha256":"dfb7acbd51daefee6fd219c0a29357f1e43f944832970f7267e0a15dc2c439b7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P7gMXK6nu0Qg9dlkOD7tVAPufcav8teodMsusyb6dJ1QTzlz4S0yZrvORUFSX2Ldy+BUIGUoXPS23Wt/ptY6Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T23:57:25.810908Z","bundle_sha256":"37f1f701a9de66193d54fa317a4dd58b2e24bac2fd30a049f103a06a979ba592"}}