{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:CFEENSKVT3A3DZNP2GQ4IZVNNU","short_pith_number":"pith:CFEENSKV","canonical_record":{"source":{"id":"1905.02146","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-05-06T17:00:40Z","cross_cats_sorted":[],"title_canon_sha256":"8b9b2caf57043d05cd8be28f3e9d568d3f36146ac8164c299016549766cb8556","abstract_canon_sha256":"b8d30fbdb1c15b8b340628db135696a819d2f5521618c0e7c2893619c57c0189"},"schema_version":"1.0"},"canonical_sha256":"114846c9559ec1b1e5afd1a1c466ad6d2fc7082d339fb7d3f03aa2369a327bf0","source":{"kind":"arxiv","id":"1905.02146","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.02146","created_at":"2026-07-05T02:10:22Z"},{"alias_kind":"arxiv_version","alias_value":"1905.02146v2","created_at":"2026-07-05T02:10:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.02146","created_at":"2026-07-05T02:10:22Z"},{"alias_kind":"pith_short_12","alias_value":"CFEENSKVT3A3","created_at":"2026-07-05T02:10:22Z"},{"alias_kind":"pith_short_16","alias_value":"CFEENSKVT3A3DZNP","created_at":"2026-07-05T02:10:22Z"},{"alias_kind":"pith_short_8","alias_value":"CFEENSKV","created_at":"2026-07-05T02:10:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:CFEENSKVT3A3DZNP2GQ4IZVNNU","target":"record","payload":{"canonical_record":{"source":{"id":"1905.02146","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-05-06T17:00:40Z","cross_cats_sorted":[],"title_canon_sha256":"8b9b2caf57043d05cd8be28f3e9d568d3f36146ac8164c299016549766cb8556","abstract_canon_sha256":"b8d30fbdb1c15b8b340628db135696a819d2f5521618c0e7c2893619c57c0189"},"schema_version":"1.0"},"canonical_sha256":"114846c9559ec1b1e5afd1a1c466ad6d2fc7082d339fb7d3f03aa2369a327bf0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:10:22.814017Z","signature_b64":"iqQAwcqyVBQf0o13TfupGqg2TQkV4QKfGtMOjTUMiLIwawDlUqCY7OP9ED3fsZ8CNDsodVenyd9J0V12n/dkAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"114846c9559ec1b1e5afd1a1c466ad6d2fc7082d339fb7d3f03aa2369a327bf0","last_reissued_at":"2026-07-05T02:10:22.809288Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:10:22.809288Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1905.02146","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":"2026-07-05T02:10:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n2BEyQy0Dlbt1QoxenaWPs6NOr4NsUrRP2YUE2LYe5OK62aT+HckkPD+8owTkSNq1qZ9TOVEM1RFEWz+ZHzbCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T04:59:00.568656Z"},"content_sha256":"3fce2730c78dc1b8548903d3f871c4505f8ac9ea39d168b5d8468c3af4af8c48","schema_version":"1.0","event_id":"sha256:3fce2730c78dc1b8548903d3f871c4505f8ac9ea39d168b5d8468c3af4af8c48"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:CFEENSKVT3A3DZNP2GQ4IZVNNU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The interchange process on high-dimensional products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jonathan Hermon, Justin Salez","submitted_at":"2019-05-06T17:00:40Z","abstract_excerpt":"We resolve a long-standing conjecture of Wilson (2004), reiterated by Oliveira (2016), asserting that the mixing-time of the unit-rate Interchange Process on the $n$-dimensional hypercube is of order $n$. This follows from a sharp inequality established at the level of Dirichlet forms, from which we also deduce that macroscopic cycles emerge in constant time, and that the log-Sobolev constant of the exclusion process is of order $1$. Beyond the hypercube, our results apply to cartesian products of arbitrary graphs of fixed size, shedding light on a broad conjecture of Oliveira (2013)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.02146","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1905.02146/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":"2026-07-05T02:10:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RpcaGFfNNwXouM9aTgPumQGqYUyZQeFrx9GvnjZIXHE03Xp8nmK3bqFj+lGgZQb8uNsc7jEjJtLoVeDyTlYLCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T04:59:00.569259Z"},"content_sha256":"0e3277c2d96d8fb0aa27591f71d4ae53b866e2412ecfb4ed7d799e60795836f6","schema_version":"1.0","event_id":"sha256:0e3277c2d96d8fb0aa27591f71d4ae53b866e2412ecfb4ed7d799e60795836f6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CFEENSKVT3A3DZNP2GQ4IZVNNU/bundle.json","state_url":"https://pith.science/pith/CFEENSKVT3A3DZNP2GQ4IZVNNU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CFEENSKVT3A3DZNP2GQ4IZVNNU/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":"2026-08-16T04:59:00Z","links":{"resolver":"https://pith.science/pith/CFEENSKVT3A3DZNP2GQ4IZVNNU","bundle":"https://pith.science/pith/CFEENSKVT3A3DZNP2GQ4IZVNNU/bundle.json","state":"https://pith.science/pith/CFEENSKVT3A3DZNP2GQ4IZVNNU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CFEENSKVT3A3DZNP2GQ4IZVNNU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:CFEENSKVT3A3DZNP2GQ4IZVNNU","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":"b8d30fbdb1c15b8b340628db135696a819d2f5521618c0e7c2893619c57c0189","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-05-06T17:00:40Z","title_canon_sha256":"8b9b2caf57043d05cd8be28f3e9d568d3f36146ac8164c299016549766cb8556"},"schema_version":"1.0","source":{"id":"1905.02146","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.02146","created_at":"2026-07-05T02:10:22Z"},{"alias_kind":"arxiv_version","alias_value":"1905.02146v2","created_at":"2026-07-05T02:10:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.02146","created_at":"2026-07-05T02:10:22Z"},{"alias_kind":"pith_short_12","alias_value":"CFEENSKVT3A3","created_at":"2026-07-05T02:10:22Z"},{"alias_kind":"pith_short_16","alias_value":"CFEENSKVT3A3DZNP","created_at":"2026-07-05T02:10:22Z"},{"alias_kind":"pith_short_8","alias_value":"CFEENSKV","created_at":"2026-07-05T02:10:22Z"}],"graph_snapshots":[{"event_id":"sha256:0e3277c2d96d8fb0aa27591f71d4ae53b866e2412ecfb4ed7d799e60795836f6","target":"graph","created_at":"2026-07-05T02:10:22Z","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/1905.02146/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We resolve a long-standing conjecture of Wilson (2004), reiterated by Oliveira (2016), asserting that the mixing-time of the unit-rate Interchange Process on the $n$-dimensional hypercube is of order $n$. This follows from a sharp inequality established at the level of Dirichlet forms, from which we also deduce that macroscopic cycles emerge in constant time, and that the log-Sobolev constant of the exclusion process is of order $1$. Beyond the hypercube, our results apply to cartesian products of arbitrary graphs of fixed size, shedding light on a broad conjecture of Oliveira (2013).","authors_text":"Jonathan Hermon, Justin Salez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-05-06T17:00:40Z","title":"The interchange process on high-dimensional products"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.02146","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":"sha256:3fce2730c78dc1b8548903d3f871c4505f8ac9ea39d168b5d8468c3af4af8c48","target":"record","created_at":"2026-07-05T02:10:22Z","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":"b8d30fbdb1c15b8b340628db135696a819d2f5521618c0e7c2893619c57c0189","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-05-06T17:00:40Z","title_canon_sha256":"8b9b2caf57043d05cd8be28f3e9d568d3f36146ac8164c299016549766cb8556"},"schema_version":"1.0","source":{"id":"1905.02146","kind":"arxiv","version":2}},"canonical_sha256":"114846c9559ec1b1e5afd1a1c466ad6d2fc7082d339fb7d3f03aa2369a327bf0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"114846c9559ec1b1e5afd1a1c466ad6d2fc7082d339fb7d3f03aa2369a327bf0","first_computed_at":"2026-07-05T02:10:22.809288Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:10:22.809288Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iqQAwcqyVBQf0o13TfupGqg2TQkV4QKfGtMOjTUMiLIwawDlUqCY7OP9ED3fsZ8CNDsodVenyd9J0V12n/dkAw==","signature_status":"signed_v1","signed_at":"2026-07-05T02:10:22.814017Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.02146","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3fce2730c78dc1b8548903d3f871c4505f8ac9ea39d168b5d8468c3af4af8c48","sha256:0e3277c2d96d8fb0aa27591f71d4ae53b866e2412ecfb4ed7d799e60795836f6"],"state_sha256":"838ba9c5841532b953b339b0b1c22e3cdab0d2a033c81b3607d4c544b3deaed8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PsRRr85q3mOmpqDO0TaWc5km9GecFvP7YCq5e7gmUQFiq2OXqwmkfaK5YUvmseZhZObeBKvHOAx57Z5qDMoiCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T04:59:00.579253Z","bundle_sha256":"3ad48a82b5c0d6290c229d1565f4e55f81161c851e92b86b0a1a5da46ded46e4"}}