{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:6EVYITGCP2UEL4CQBTIATHNFMQ","short_pith_number":"pith:6EVYITGC","canonical_record":{"source":{"id":"1501.06188","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-01-25T17:50:43Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"64d99f8919a0c7addf482ed93e82dcdf178abf4e4f90b6d37ddaf845d2840d37","abstract_canon_sha256":"e839182204453380424e6f325a8a3012c3bb4c29232595e0db221cc07707b1fb"},"schema_version":"1.0"},"canonical_sha256":"f12b844cc27ea845f0500cd0099da5641a0ba6c8f61350d3cf6b4f8643cd517c","source":{"kind":"arxiv","id":"1501.06188","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.06188","created_at":"2026-05-18T00:55:17Z"},{"alias_kind":"arxiv_version","alias_value":"1501.06188v4","created_at":"2026-05-18T00:55:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.06188","created_at":"2026-05-18T00:55:17Z"},{"alias_kind":"pith_short_12","alias_value":"6EVYITGCP2UE","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6EVYITGCP2UEL4CQ","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6EVYITGC","created_at":"2026-05-18T12:29:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:6EVYITGCP2UEL4CQBTIATHNFMQ","target":"record","payload":{"canonical_record":{"source":{"id":"1501.06188","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-01-25T17:50:43Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"64d99f8919a0c7addf482ed93e82dcdf178abf4e4f90b6d37ddaf845d2840d37","abstract_canon_sha256":"e839182204453380424e6f325a8a3012c3bb4c29232595e0db221cc07707b1fb"},"schema_version":"1.0"},"canonical_sha256":"f12b844cc27ea845f0500cd0099da5641a0ba6c8f61350d3cf6b4f8643cd517c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:55:17.776065Z","signature_b64":"t5k0jUsXfjrELXU5AyUPrix5DLyTPojjtLXZ6nNeGRfszOGhUK+PGuseZdtYnm5TL9LTfLSOc2WDSffJ38bOAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f12b844cc27ea845f0500cd0099da5641a0ba6c8f61350d3cf6b4f8643cd517c","last_reissued_at":"2026-05-18T00:55:17.775350Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:55:17.775350Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.06188","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:55:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ENFYbtAMrmUQDH9Tonr/BejHI/keY+ClyNMG7u4L39Gb++JKvUCh9St/qjugRTcmJulGtVOKMQTwx9WIhsW6AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T07:36:52.744569Z"},"content_sha256":"02358c57c508c98182085c8cd489ac7a63d611cd9247de0bb1d3ac5d07144448","schema_version":"1.0","event_id":"sha256:02358c57c508c98182085c8cd489ac7a63d611cd9247de0bb1d3ac5d07144448"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:6EVYITGCP2UEL4CQBTIATHNFMQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the extendibility of finitely exchangeable probability measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.PR","authors_text":"Linglong Yuan, Takis Konstantopoulos","submitted_at":"2015-01-25T17:50:43Z","abstract_excerpt":"A length-$n$ random sequence $X_1,\\ldots,X_n$ in a space $S$ is finitely exchangeable if its distribution is invariant under all $n!$ permutations of coordinates. Given $N > n$, we study the extendibility problem: when is it the case that there is a length-$N$ exchangeable random sequence $Y_1,\\ldots, Y_N$ so that $(Y_1,\\ldots,Y_n)$ has the same distribution as $(X_1,\\ldots,X_n)$? In this paper, we give a necessary and sufficient condition so that, for given $n$ and $N$, the extendibility problem admits a solution. This is done by employing functional-analytic and measure-theoretic arguments t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06188","kind":"arxiv","version":4},"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":"2026-05-18T00:55:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KTxaP4UiPanNb3e2D7FIBDamZ0l5kXmMAFEVf6n77eIqodT3GY/0w/qtp5bLxeCogj2eP77TsN71vmu4PnI0AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T07:36:52.745045Z"},"content_sha256":"f0610a3cdfee7ad5da78b498fa82a849cd163f52a0dfcaa6fb3a2ff77a8847a9","schema_version":"1.0","event_id":"sha256:f0610a3cdfee7ad5da78b498fa82a849cd163f52a0dfcaa6fb3a2ff77a8847a9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6EVYITGCP2UEL4CQBTIATHNFMQ/bundle.json","state_url":"https://pith.science/pith/6EVYITGCP2UEL4CQBTIATHNFMQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6EVYITGCP2UEL4CQBTIATHNFMQ/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":"2026-06-25T07:36:52Z","links":{"resolver":"https://pith.science/pith/6EVYITGCP2UEL4CQBTIATHNFMQ","bundle":"https://pith.science/pith/6EVYITGCP2UEL4CQBTIATHNFMQ/bundle.json","state":"https://pith.science/pith/6EVYITGCP2UEL4CQBTIATHNFMQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6EVYITGCP2UEL4CQBTIATHNFMQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:6EVYITGCP2UEL4CQBTIATHNFMQ","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":"e839182204453380424e6f325a8a3012c3bb4c29232595e0db221cc07707b1fb","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-01-25T17:50:43Z","title_canon_sha256":"64d99f8919a0c7addf482ed93e82dcdf178abf4e4f90b6d37ddaf845d2840d37"},"schema_version":"1.0","source":{"id":"1501.06188","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.06188","created_at":"2026-05-18T00:55:17Z"},{"alias_kind":"arxiv_version","alias_value":"1501.06188v4","created_at":"2026-05-18T00:55:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.06188","created_at":"2026-05-18T00:55:17Z"},{"alias_kind":"pith_short_12","alias_value":"6EVYITGCP2UE","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6EVYITGCP2UEL4CQ","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6EVYITGC","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:f0610a3cdfee7ad5da78b498fa82a849cd163f52a0dfcaa6fb3a2ff77a8847a9","target":"graph","created_at":"2026-05-18T00:55:17Z","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":"A length-$n$ random sequence $X_1,\\ldots,X_n$ in a space $S$ is finitely exchangeable if its distribution is invariant under all $n!$ permutations of coordinates. Given $N > n$, we study the extendibility problem: when is it the case that there is a length-$N$ exchangeable random sequence $Y_1,\\ldots, Y_N$ so that $(Y_1,\\ldots,Y_n)$ has the same distribution as $(X_1,\\ldots,X_n)$? In this paper, we give a necessary and sufficient condition so that, for given $n$ and $N$, the extendibility problem admits a solution. This is done by employing functional-analytic and measure-theoretic arguments t","authors_text":"Linglong Yuan, Takis Konstantopoulos","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-01-25T17:50:43Z","title":"On the extendibility of finitely exchangeable probability measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06188","kind":"arxiv","version":4},"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":"sha256:02358c57c508c98182085c8cd489ac7a63d611cd9247de0bb1d3ac5d07144448","target":"record","created_at":"2026-05-18T00:55:17Z","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":"e839182204453380424e6f325a8a3012c3bb4c29232595e0db221cc07707b1fb","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-01-25T17:50:43Z","title_canon_sha256":"64d99f8919a0c7addf482ed93e82dcdf178abf4e4f90b6d37ddaf845d2840d37"},"schema_version":"1.0","source":{"id":"1501.06188","kind":"arxiv","version":4}},"canonical_sha256":"f12b844cc27ea845f0500cd0099da5641a0ba6c8f61350d3cf6b4f8643cd517c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f12b844cc27ea845f0500cd0099da5641a0ba6c8f61350d3cf6b4f8643cd517c","first_computed_at":"2026-05-18T00:55:17.775350Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:17.775350Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t5k0jUsXfjrELXU5AyUPrix5DLyTPojjtLXZ6nNeGRfszOGhUK+PGuseZdtYnm5TL9LTfLSOc2WDSffJ38bOAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:17.776065Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.06188","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:02358c57c508c98182085c8cd489ac7a63d611cd9247de0bb1d3ac5d07144448","sha256:f0610a3cdfee7ad5da78b498fa82a849cd163f52a0dfcaa6fb3a2ff77a8847a9"],"state_sha256":"6a7011e1a2636183f7363fe70e40f13dc679cbc3749050a6fd8dd6a3210cebad"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9/8Ew+0cvMFiUmcuaOZ2YHkVq/1WfLaykAYWug4+CJoIcg7UTWQYmoS/ep9vhrjxmryUQMz7tquxuYebLD7oAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T07:36:52.747623Z","bundle_sha256":"58f0740a8e7dac61d70fa3c1dd504974b1b50f0f36ba1e08c0cc711143b6b69c"}}