{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:ULP3SYADX3VLO5H7UZTBFHHE43","short_pith_number":"pith:ULP3SYAD","canonical_record":{"source":{"id":"2605.19084","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-05-18T20:17:46Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"b35cd3732eb06a36654ccd3a0c13b006a8b397a08dfceb27062da847903ba1cb","abstract_canon_sha256":"684be40afee8c9bb0e5efc0b8368d0423a102984b5b420e8cfdb3b1806572ca5"},"schema_version":"1.0"},"canonical_sha256":"a2dfb96003beeab774ffa666129ce4e6d086ed7692a74d70a1ccdf6d608c3886","source":{"kind":"arxiv","id":"2605.19084","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.19084","created_at":"2026-05-20T01:05:26Z"},{"alias_kind":"arxiv_version","alias_value":"2605.19084v1","created_at":"2026-05-20T01:05:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.19084","created_at":"2026-05-20T01:05:26Z"},{"alias_kind":"pith_short_12","alias_value":"ULP3SYADX3VL","created_at":"2026-05-20T01:05:26Z"},{"alias_kind":"pith_short_16","alias_value":"ULP3SYADX3VLO5H7","created_at":"2026-05-20T01:05:26Z"},{"alias_kind":"pith_short_8","alias_value":"ULP3SYAD","created_at":"2026-05-20T01:05:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:ULP3SYADX3VLO5H7UZTBFHHE43","target":"record","payload":{"canonical_record":{"source":{"id":"2605.19084","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-05-18T20:17:46Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"b35cd3732eb06a36654ccd3a0c13b006a8b397a08dfceb27062da847903ba1cb","abstract_canon_sha256":"684be40afee8c9bb0e5efc0b8368d0423a102984b5b420e8cfdb3b1806572ca5"},"schema_version":"1.0"},"canonical_sha256":"a2dfb96003beeab774ffa666129ce4e6d086ed7692a74d70a1ccdf6d608c3886","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T01:05:26.560577Z","signature_b64":"Sdl5O4WHYcyi2EhVuT92eSlvqyngZDkxsX56y1cVElOp/baAy7NjZO77ZpRFn2UKAuTb5wylhLLavX7PndN5AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a2dfb96003beeab774ffa666129ce4e6d086ed7692a74d70a1ccdf6d608c3886","last_reissued_at":"2026-05-20T01:05:26.559903Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T01:05:26.559903Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.19084","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":"2026-05-20T01:05:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J9fj29CAv15X1A+DSOoM2EBPnZ2+CkyKcSElIofbYuNyp2TYTGUsxkMyjd2PpvPoM/5oZK24PYv3IDp3mg4+AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T10:40:25.849746Z"},"content_sha256":"4eba4f222953ece90a49da1ed214ca5b316bca6ae75c8ce281d504b1a9eeb610","schema_version":"1.0","event_id":"sha256:4eba4f222953ece90a49da1ed214ca5b316bca6ae75c8ce281d504b1a9eeb610"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:ULP3SYADX3VLO5H7UZTBFHHE43","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Limit Profiles for Separation Distance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Evita Nestoridi, Peter E. Francis","submitted_at":"2026-05-18T20:17:46Z","abstract_excerpt":"This paper studies limit profiles for the separation distance. A limit profile records the limiting shape of the distance to stationarity inside the cutoff window, at times of the form $t_n+cw_n$. We start with two famous card shuffles, a general setup for inverse riffle shuffles and random transpositions, and we determine their separation distance limit profiles. We then develop a spectral comparison technique and study continuity properties in the style of [Nes24; Nes25], adapted to separation distance. The comparison method is illustrated through random transpositions, as well as random wal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.19084","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/2605.19084/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":"2026-05-20T01:05:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J5B4JZx+MTClFz8elcb5MryswWfhkdE+mdCxFwdY11kKi9JXq26ZqmurrxfMVwOt6ckHuu7AiHtPtGZORL1+DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T10:40:25.850453Z"},"content_sha256":"1ba8f1f626fa4afad0b676cb2d99c892ed0b8f98d5426c95a54e356244259b97","schema_version":"1.0","event_id":"sha256:1ba8f1f626fa4afad0b676cb2d99c892ed0b8f98d5426c95a54e356244259b97"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ULP3SYADX3VLO5H7UZTBFHHE43/bundle.json","state_url":"https://pith.science/pith/ULP3SYADX3VLO5H7UZTBFHHE43/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ULP3SYADX3VLO5H7UZTBFHHE43/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":"2026-05-27T10:40:25Z","links":{"resolver":"https://pith.science/pith/ULP3SYADX3VLO5H7UZTBFHHE43","bundle":"https://pith.science/pith/ULP3SYADX3VLO5H7UZTBFHHE43/bundle.json","state":"https://pith.science/pith/ULP3SYADX3VLO5H7UZTBFHHE43/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ULP3SYADX3VLO5H7UZTBFHHE43/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:ULP3SYADX3VLO5H7UZTBFHHE43","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":"684be40afee8c9bb0e5efc0b8368d0423a102984b5b420e8cfdb3b1806572ca5","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-05-18T20:17:46Z","title_canon_sha256":"b35cd3732eb06a36654ccd3a0c13b006a8b397a08dfceb27062da847903ba1cb"},"schema_version":"1.0","source":{"id":"2605.19084","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.19084","created_at":"2026-05-20T01:05:26Z"},{"alias_kind":"arxiv_version","alias_value":"2605.19084v1","created_at":"2026-05-20T01:05:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.19084","created_at":"2026-05-20T01:05:26Z"},{"alias_kind":"pith_short_12","alias_value":"ULP3SYADX3VL","created_at":"2026-05-20T01:05:26Z"},{"alias_kind":"pith_short_16","alias_value":"ULP3SYADX3VLO5H7","created_at":"2026-05-20T01:05:26Z"},{"alias_kind":"pith_short_8","alias_value":"ULP3SYAD","created_at":"2026-05-20T01:05:26Z"}],"graph_snapshots":[{"event_id":"sha256:1ba8f1f626fa4afad0b676cb2d99c892ed0b8f98d5426c95a54e356244259b97","target":"graph","created_at":"2026-05-20T01:05:26Z","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/2605.19084/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper studies limit profiles for the separation distance. A limit profile records the limiting shape of the distance to stationarity inside the cutoff window, at times of the form $t_n+cw_n$. We start with two famous card shuffles, a general setup for inverse riffle shuffles and random transpositions, and we determine their separation distance limit profiles. We then develop a spectral comparison technique and study continuity properties in the style of [Nes24; Nes25], adapted to separation distance. The comparison method is illustrated through random transpositions, as well as random wal","authors_text":"Evita Nestoridi, Peter E. Francis","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-05-18T20:17:46Z","title":"Limit Profiles for Separation Distance"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.19084","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":"sha256:4eba4f222953ece90a49da1ed214ca5b316bca6ae75c8ce281d504b1a9eeb610","target":"record","created_at":"2026-05-20T01:05:26Z","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":"684be40afee8c9bb0e5efc0b8368d0423a102984b5b420e8cfdb3b1806572ca5","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-05-18T20:17:46Z","title_canon_sha256":"b35cd3732eb06a36654ccd3a0c13b006a8b397a08dfceb27062da847903ba1cb"},"schema_version":"1.0","source":{"id":"2605.19084","kind":"arxiv","version":1}},"canonical_sha256":"a2dfb96003beeab774ffa666129ce4e6d086ed7692a74d70a1ccdf6d608c3886","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a2dfb96003beeab774ffa666129ce4e6d086ed7692a74d70a1ccdf6d608c3886","first_computed_at":"2026-05-20T01:05:26.559903Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T01:05:26.559903Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Sdl5O4WHYcyi2EhVuT92eSlvqyngZDkxsX56y1cVElOp/baAy7NjZO77ZpRFn2UKAuTb5wylhLLavX7PndN5AQ==","signature_status":"signed_v1","signed_at":"2026-05-20T01:05:26.560577Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.19084","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4eba4f222953ece90a49da1ed214ca5b316bca6ae75c8ce281d504b1a9eeb610","sha256:1ba8f1f626fa4afad0b676cb2d99c892ed0b8f98d5426c95a54e356244259b97"],"state_sha256":"86e7b099bfb3623d11645b987e10b161cbbbb50e5755266a2a168edc22b43bee"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gZMxXQj3tC1AfJ03byB7khpj1bG3UYv9y8qGtIUTQoux7eEMRhgZLO+h7HZC2w5TkuKA6jpPH2AMMHC5w8CqBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T10:40:25.854060Z","bundle_sha256":"09503ac7d81ac92b3be64afdd2103d5b415635a223ba30ac09e5ed949b4f4fcb"}}