{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:D3CVBZ463TX4A3IVC2QSKJWOLY","short_pith_number":"pith:D3CVBZ46","canonical_record":{"source":{"id":"2606.18654","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-17T03:43:07Z","cross_cats_sorted":[],"title_canon_sha256":"7c4d6e9ef818438514e74cfb50fc2e27937373bf88f4243f4dc6cc6834969d29","abstract_canon_sha256":"e4fefe8e3b74c1bbcbe9e87d3fedd47aa7402f33a375a52dd916265896576baf"},"schema_version":"1.0"},"canonical_sha256":"1ec550e79edcefc06d1516a12526ce5e1bb3347b4a891c3e141b98c0564b74ba","source":{"kind":"arxiv","id":"2606.18654","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.18654","created_at":"2026-06-19T16:11:43Z"},{"alias_kind":"arxiv_version","alias_value":"2606.18654v1","created_at":"2026-06-19T16:11:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.18654","created_at":"2026-06-19T16:11:43Z"},{"alias_kind":"pith_short_12","alias_value":"D3CVBZ463TX4","created_at":"2026-06-19T16:11:43Z"},{"alias_kind":"pith_short_16","alias_value":"D3CVBZ463TX4A3IV","created_at":"2026-06-19T16:11:43Z"},{"alias_kind":"pith_short_8","alias_value":"D3CVBZ46","created_at":"2026-06-19T16:11:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:D3CVBZ463TX4A3IVC2QSKJWOLY","target":"record","payload":{"canonical_record":{"source":{"id":"2606.18654","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-17T03:43:07Z","cross_cats_sorted":[],"title_canon_sha256":"7c4d6e9ef818438514e74cfb50fc2e27937373bf88f4243f4dc6cc6834969d29","abstract_canon_sha256":"e4fefe8e3b74c1bbcbe9e87d3fedd47aa7402f33a375a52dd916265896576baf"},"schema_version":"1.0"},"canonical_sha256":"1ec550e79edcefc06d1516a12526ce5e1bb3347b4a891c3e141b98c0564b74ba","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:11:43.724222Z","signature_b64":"kJcKhTEQ8IYH/5dAc3X0PuxlqLAnTtdhHyxTCQEjM2+Cu9tO5hjMehi8q58xGsz4I3KdEsdz2ttQuNFrmSlADw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1ec550e79edcefc06d1516a12526ce5e1bb3347b4a891c3e141b98c0564b74ba","last_reissued_at":"2026-06-19T16:11:43.723887Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:11:43.723887Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.18654","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":"2026-06-19T16:11:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7giD8xsaNQ8kJujW8uarXBvKu3fqHyKcqZpwpNELn9TaWNojffrEsObNcR6O6vAOYFGDAkBMDVC/bhL5s+4iBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T02:22:27.146721Z"},"content_sha256":"f96059077bd37b89c41b8d25b2ac2171914cb25df6f59f9e18af23ecdfb77d14","schema_version":"1.0","event_id":"sha256:f96059077bd37b89c41b8d25b2ac2171914cb25df6f59f9e18af23ecdfb77d14"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:D3CVBZ463TX4A3IVC2QSKJWOLY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rigidity of infinite exchangeable sequences with Gaussian marginals","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Maximillian Newman","submitted_at":"2026-06-17T03:43:07Z","abstract_excerpt":"We study infinite exchangeable sequences with Gaussian one-dimensional marginals. We formulate the conjecture that joint Gaussianity of a single pair of coordinates forces the entire sequence to be a Gaussian process. Although this conjecture remains open, we prove that joint Gaussianity of the first four coordinates is sufficient. We also establish the corresponding two-point criterion under the additional assumption that the directing measure is almost surely infinitely divisible."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.18654","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.18654/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-19T16:11:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wyCiicIT1Enbtz/DkVzZBYpPs14LD4eOS6hbBzMY3sjh3nIx0AXSOx6ReJxstvTmon+j8/OEeVDhckrEcK+ACg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T02:22:27.147087Z"},"content_sha256":"30e4e38f8205d816aa7a87631da6a3682467b6752fe941a693c9952c70d349aa","schema_version":"1.0","event_id":"sha256:30e4e38f8205d816aa7a87631da6a3682467b6752fe941a693c9952c70d349aa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D3CVBZ463TX4A3IVC2QSKJWOLY/bundle.json","state_url":"https://pith.science/pith/D3CVBZ463TX4A3IVC2QSKJWOLY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D3CVBZ463TX4A3IVC2QSKJWOLY/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":"2026-07-03T02:22:27Z","links":{"resolver":"https://pith.science/pith/D3CVBZ463TX4A3IVC2QSKJWOLY","bundle":"https://pith.science/pith/D3CVBZ463TX4A3IVC2QSKJWOLY/bundle.json","state":"https://pith.science/pith/D3CVBZ463TX4A3IVC2QSKJWOLY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D3CVBZ463TX4A3IVC2QSKJWOLY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:D3CVBZ463TX4A3IVC2QSKJWOLY","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":"e4fefe8e3b74c1bbcbe9e87d3fedd47aa7402f33a375a52dd916265896576baf","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-17T03:43:07Z","title_canon_sha256":"7c4d6e9ef818438514e74cfb50fc2e27937373bf88f4243f4dc6cc6834969d29"},"schema_version":"1.0","source":{"id":"2606.18654","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.18654","created_at":"2026-06-19T16:11:43Z"},{"alias_kind":"arxiv_version","alias_value":"2606.18654v1","created_at":"2026-06-19T16:11:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.18654","created_at":"2026-06-19T16:11:43Z"},{"alias_kind":"pith_short_12","alias_value":"D3CVBZ463TX4","created_at":"2026-06-19T16:11:43Z"},{"alias_kind":"pith_short_16","alias_value":"D3CVBZ463TX4A3IV","created_at":"2026-06-19T16:11:43Z"},{"alias_kind":"pith_short_8","alias_value":"D3CVBZ46","created_at":"2026-06-19T16:11:43Z"}],"graph_snapshots":[{"event_id":"sha256:30e4e38f8205d816aa7a87631da6a3682467b6752fe941a693c9952c70d349aa","target":"graph","created_at":"2026-06-19T16:11:43Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.18654/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study infinite exchangeable sequences with Gaussian one-dimensional marginals. We formulate the conjecture that joint Gaussianity of a single pair of coordinates forces the entire sequence to be a Gaussian process. Although this conjecture remains open, we prove that joint Gaussianity of the first four coordinates is sufficient. We also establish the corresponding two-point criterion under the additional assumption that the directing measure is almost surely infinitely divisible.","authors_text":"Maximillian Newman","cross_cats":[],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-17T03:43:07Z","title":"Rigidity of infinite exchangeable sequences with Gaussian marginals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.18654","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:f96059077bd37b89c41b8d25b2ac2171914cb25df6f59f9e18af23ecdfb77d14","target":"record","created_at":"2026-06-19T16:11:43Z","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":"e4fefe8e3b74c1bbcbe9e87d3fedd47aa7402f33a375a52dd916265896576baf","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-17T03:43:07Z","title_canon_sha256":"7c4d6e9ef818438514e74cfb50fc2e27937373bf88f4243f4dc6cc6834969d29"},"schema_version":"1.0","source":{"id":"2606.18654","kind":"arxiv","version":1}},"canonical_sha256":"1ec550e79edcefc06d1516a12526ce5e1bb3347b4a891c3e141b98c0564b74ba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ec550e79edcefc06d1516a12526ce5e1bb3347b4a891c3e141b98c0564b74ba","first_computed_at":"2026-06-19T16:11:43.723887Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:11:43.723887Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kJcKhTEQ8IYH/5dAc3X0PuxlqLAnTtdhHyxTCQEjM2+Cu9tO5hjMehi8q58xGsz4I3KdEsdz2ttQuNFrmSlADw==","signature_status":"signed_v1","signed_at":"2026-06-19T16:11:43.724222Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.18654","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f96059077bd37b89c41b8d25b2ac2171914cb25df6f59f9e18af23ecdfb77d14","sha256:30e4e38f8205d816aa7a87631da6a3682467b6752fe941a693c9952c70d349aa"],"state_sha256":"b9db5d7ddd0ee3c6284730781bb0be2a99fb33238f95cd62d2f6048f06e84bdd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YyTZnotqA/1NPLaMhaC+tlJ/IoxGCjjkorWR3jwwVvM/OI5qssigWwlqch/TZ6OCNRBniEsFb7Qfy5EUDn3zCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T02:22:27.151860Z","bundle_sha256":"138834dd2dc4338a9e7f48232311099f307426dfa517a6afcec06d3b1300063d"}}