{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:FW3PYPIYLPHNVE6V2YP6U7EZQY","short_pith_number":"pith:FW3PYPIY","canonical_record":{"source":{"id":"1509.06733","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-09-22T19:10:15Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"5e327776de1bce6a8b9472a26782748cf3fce211c487fe3bbcd410be838e8a1e","abstract_canon_sha256":"0406d3dedc42dcfda3f2677fdeccd85179988a24b15e7912558e2b260a3804a9"},"schema_version":"1.0"},"canonical_sha256":"2db6fc3d185bceda93d5d61fea7c99862dfddc543ab00658969b608c015e80da","source":{"kind":"arxiv","id":"1509.06733","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.06733","created_at":"2026-05-18T01:31:13Z"},{"alias_kind":"arxiv_version","alias_value":"1509.06733v2","created_at":"2026-05-18T01:31:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.06733","created_at":"2026-05-18T01:31:13Z"},{"alias_kind":"pith_short_12","alias_value":"FW3PYPIYLPHN","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"FW3PYPIYLPHNVE6V","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"FW3PYPIY","created_at":"2026-05-18T12:29:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:FW3PYPIYLPHNVE6V2YP6U7EZQY","target":"record","payload":{"canonical_record":{"source":{"id":"1509.06733","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-09-22T19:10:15Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"5e327776de1bce6a8b9472a26782748cf3fce211c487fe3bbcd410be838e8a1e","abstract_canon_sha256":"0406d3dedc42dcfda3f2677fdeccd85179988a24b15e7912558e2b260a3804a9"},"schema_version":"1.0"},"canonical_sha256":"2db6fc3d185bceda93d5d61fea7c99862dfddc543ab00658969b608c015e80da","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:31:13.304776Z","signature_b64":"vhP/0bZmLw5oVrLD4jC4EUgn43h3gVJU38mKMbJpM05FU6UkaNogrwyNqZVwdvSVFioiUkIVues53EzzBRMsAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2db6fc3d185bceda93d5d61fea7c99862dfddc543ab00658969b608c015e80da","last_reissued_at":"2026-05-18T01:31:13.304029Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:31:13.304029Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.06733","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":"2026-05-18T01:31:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k++93QxZmb51yOQM8jixjJerpTtobaHEOarWp+BmsqXZcSLwOjVESEmrxG5Q7liHRKjCri/DuefHsGQjp3wnDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T07:13:52.183146Z"},"content_sha256":"2cd296955f55e4b7d6f6582fa305563e3c3693f0637e69e7203c10447697bd1d","schema_version":"1.0","event_id":"sha256:2cd296955f55e4b7d6f6582fa305563e3c3693f0637e69e7203c10447697bd1d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:FW3PYPIYLPHNVE6V2YP6U7EZQY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Relatively exchangeable structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.LO","authors_text":"Harry Crane, Henry Towsner","submitted_at":"2015-09-22T19:10:15Z","abstract_excerpt":"We study random relational structures that are \\emph{relatively exchangeable}---that is, whose distributions are invariant under the automorphisms of a reference structure $\\mathfrak{M}$. When $\\mathfrak{M}$ has {\\em trivial definable closure}, every relatively exchangeable structure satisfies a general Aldous--Hoover-type representation. If $\\mathfrak{M}$ satisfies the stronger properties of {\\em ultrahomogeneity} and {\\em $n$-disjoint amalgamation property} ($n$-DAP) for every $n\\geq1$, then relatively exchangeable structures have a more precise description whereby each component depends loc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06733","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":"2026-05-18T01:31:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fwz3ONzFXbu3Eh+8LzDBsmGYILh2kNA48/lAckYFGJrgG8WkfTedXbX3TFFrD2oMrC+E/o5E3yRoDUjUQmJWCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T07:13:52.183543Z"},"content_sha256":"657c627313f502d3263c0b829109a0cb0b7202d18790e9fdf0b7e84fc68e0f18","schema_version":"1.0","event_id":"sha256:657c627313f502d3263c0b829109a0cb0b7202d18790e9fdf0b7e84fc68e0f18"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FW3PYPIYLPHNVE6V2YP6U7EZQY/bundle.json","state_url":"https://pith.science/pith/FW3PYPIYLPHNVE6V2YP6U7EZQY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FW3PYPIYLPHNVE6V2YP6U7EZQY/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":"2026-05-24T07:13:52Z","links":{"resolver":"https://pith.science/pith/FW3PYPIYLPHNVE6V2YP6U7EZQY","bundle":"https://pith.science/pith/FW3PYPIYLPHNVE6V2YP6U7EZQY/bundle.json","state":"https://pith.science/pith/FW3PYPIYLPHNVE6V2YP6U7EZQY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FW3PYPIYLPHNVE6V2YP6U7EZQY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:FW3PYPIYLPHNVE6V2YP6U7EZQY","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":"0406d3dedc42dcfda3f2677fdeccd85179988a24b15e7912558e2b260a3804a9","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-09-22T19:10:15Z","title_canon_sha256":"5e327776de1bce6a8b9472a26782748cf3fce211c487fe3bbcd410be838e8a1e"},"schema_version":"1.0","source":{"id":"1509.06733","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.06733","created_at":"2026-05-18T01:31:13Z"},{"alias_kind":"arxiv_version","alias_value":"1509.06733v2","created_at":"2026-05-18T01:31:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.06733","created_at":"2026-05-18T01:31:13Z"},{"alias_kind":"pith_short_12","alias_value":"FW3PYPIYLPHN","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"FW3PYPIYLPHNVE6V","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"FW3PYPIY","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:657c627313f502d3263c0b829109a0cb0b7202d18790e9fdf0b7e84fc68e0f18","target":"graph","created_at":"2026-05-18T01:31:13Z","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 study random relational structures that are \\emph{relatively exchangeable}---that is, whose distributions are invariant under the automorphisms of a reference structure $\\mathfrak{M}$. When $\\mathfrak{M}$ has {\\em trivial definable closure}, every relatively exchangeable structure satisfies a general Aldous--Hoover-type representation. If $\\mathfrak{M}$ satisfies the stronger properties of {\\em ultrahomogeneity} and {\\em $n$-disjoint amalgamation property} ($n$-DAP) for every $n\\geq1$, then relatively exchangeable structures have a more precise description whereby each component depends loc","authors_text":"Harry Crane, Henry Towsner","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-09-22T19:10:15Z","title":"Relatively exchangeable structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06733","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":"sha256:2cd296955f55e4b7d6f6582fa305563e3c3693f0637e69e7203c10447697bd1d","target":"record","created_at":"2026-05-18T01:31:13Z","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":"0406d3dedc42dcfda3f2677fdeccd85179988a24b15e7912558e2b260a3804a9","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-09-22T19:10:15Z","title_canon_sha256":"5e327776de1bce6a8b9472a26782748cf3fce211c487fe3bbcd410be838e8a1e"},"schema_version":"1.0","source":{"id":"1509.06733","kind":"arxiv","version":2}},"canonical_sha256":"2db6fc3d185bceda93d5d61fea7c99862dfddc543ab00658969b608c015e80da","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2db6fc3d185bceda93d5d61fea7c99862dfddc543ab00658969b608c015e80da","first_computed_at":"2026-05-18T01:31:13.304029Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:31:13.304029Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vhP/0bZmLw5oVrLD4jC4EUgn43h3gVJU38mKMbJpM05FU6UkaNogrwyNqZVwdvSVFioiUkIVues53EzzBRMsAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:31:13.304776Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.06733","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2cd296955f55e4b7d6f6582fa305563e3c3693f0637e69e7203c10447697bd1d","sha256:657c627313f502d3263c0b829109a0cb0b7202d18790e9fdf0b7e84fc68e0f18"],"state_sha256":"410be849cf6db76ef57a3c84d44ecf67772b00a0965fa069b57352c055069b75"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GaNsQOmx+czIm97GsOQkzI/chkBU5lvnzBwQXxlGAGyfKJnmOEA8+bF6bymOw5/yRyNXwCYZwXsiN3lGAhUDAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T07:13:52.186775Z","bundle_sha256":"7951270bb86cbbbff7b35a103a9dd7c088198f04d11a74e8cd9d401805cfd738"}}