{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:V4PE6U36HOE7WEGP5UUL5MBR3N","short_pith_number":"pith:V4PE6U36","canonical_record":{"source":{"id":"1812.11939","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-12-31T18:22:45Z","cross_cats_sorted":[],"title_canon_sha256":"c4d0388defa892ea1e6c594b69dfff08a6178c31b0f49ecf2a02e28e17740e0a","abstract_canon_sha256":"1c72ae25fa376fea9879c8ca702834b233aeebbe80a8f0cdda65dd3b120f7c71"},"schema_version":"1.0"},"canonical_sha256":"af1e4f537e3b89fb10cfed28beb031db7b21131828d6306219da8c67e6389358","source":{"kind":"arxiv","id":"1812.11939","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.11939","created_at":"2026-05-17T23:42:58Z"},{"alias_kind":"arxiv_version","alias_value":"1812.11939v2","created_at":"2026-05-17T23:42:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.11939","created_at":"2026-05-17T23:42:58Z"},{"alias_kind":"pith_short_12","alias_value":"V4PE6U36HOE7","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"V4PE6U36HOE7WEGP","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"V4PE6U36","created_at":"2026-05-18T12:32:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:V4PE6U36HOE7WEGP5UUL5MBR3N","target":"record","payload":{"canonical_record":{"source":{"id":"1812.11939","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-12-31T18:22:45Z","cross_cats_sorted":[],"title_canon_sha256":"c4d0388defa892ea1e6c594b69dfff08a6178c31b0f49ecf2a02e28e17740e0a","abstract_canon_sha256":"1c72ae25fa376fea9879c8ca702834b233aeebbe80a8f0cdda65dd3b120f7c71"},"schema_version":"1.0"},"canonical_sha256":"af1e4f537e3b89fb10cfed28beb031db7b21131828d6306219da8c67e6389358","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:58.526830Z","signature_b64":"DK+8IQgC7el4f/6vVXE4Ma1iCly6/5qWfM/IMwa5UwnTSNHA2QMinzh7WAAiZmZYn1fwf+zwc720TahAcxNzBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af1e4f537e3b89fb10cfed28beb031db7b21131828d6306219da8c67e6389358","last_reissued_at":"2026-05-17T23:42:58.526233Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:58.526233Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.11939","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":"2026-05-17T23:42:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M/PHracYLdX/NUoBc1gRWHGwamIM0tnMcSinJ8Kz0Pn1x/OmMI/4V5kzFBQbpURk9k1YLv6UJ4L2WKC0nHb2BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T10:07:40.384414Z"},"content_sha256":"ef7a86857a72580f94b282ad2ccb63f858eff90187a1d1f6210c512afe979a32","schema_version":"1.0","event_id":"sha256:ef7a86857a72580f94b282ad2ccb63f858eff90187a1d1f6210c512afe979a32"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:V4PE6U36HOE7WEGP5UUL5MBR3N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cutoff and discrete Product Structure in ASEP","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Peter Nejjar","submitted_at":"2018-12-31T18:22:45Z","abstract_excerpt":"We consider the asymmetric simple exclusion process (ASEP) on $\\mathbb{Z}$ with an initial data such that in the large time particle density $\\rho(\\cdot)$ a discontinuity at the origin is created, where the value of $\\rho$ jumps from zero to one, but $\\rho(-\\varepsilon),1-\\rho(\\varepsilon) >0 $ for any $\\varepsilon>0$. We consider the position of a particle $x_{M}$ macroscopically located at the discontinuity, and show that its limit law has a cutoff under $t^{1/2}$ scaling. Inside the discontinuity region, we show that a discrete product limit law arises, which bounds from above the limiting "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.11939","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":"2026-05-17T23:42:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hEfOwc8WAnZdVYg2zA8HSr7ofE3p1hc7WtRoUXzK8ro80NawjImxLkGuHpSKHDAYg9RwOCGdsXlLFLsd1BsFDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T10:07:40.384760Z"},"content_sha256":"683b7fe566e237b4ca84428de6a5df1152ec80f2c6a1563dd31cf6b0cfec9ecc","schema_version":"1.0","event_id":"sha256:683b7fe566e237b4ca84428de6a5df1152ec80f2c6a1563dd31cf6b0cfec9ecc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V4PE6U36HOE7WEGP5UUL5MBR3N/bundle.json","state_url":"https://pith.science/pith/V4PE6U36HOE7WEGP5UUL5MBR3N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V4PE6U36HOE7WEGP5UUL5MBR3N/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":"2026-06-23T10:07:40Z","links":{"resolver":"https://pith.science/pith/V4PE6U36HOE7WEGP5UUL5MBR3N","bundle":"https://pith.science/pith/V4PE6U36HOE7WEGP5UUL5MBR3N/bundle.json","state":"https://pith.science/pith/V4PE6U36HOE7WEGP5UUL5MBR3N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V4PE6U36HOE7WEGP5UUL5MBR3N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:V4PE6U36HOE7WEGP5UUL5MBR3N","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":"1c72ae25fa376fea9879c8ca702834b233aeebbe80a8f0cdda65dd3b120f7c71","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-12-31T18:22:45Z","title_canon_sha256":"c4d0388defa892ea1e6c594b69dfff08a6178c31b0f49ecf2a02e28e17740e0a"},"schema_version":"1.0","source":{"id":"1812.11939","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.11939","created_at":"2026-05-17T23:42:58Z"},{"alias_kind":"arxiv_version","alias_value":"1812.11939v2","created_at":"2026-05-17T23:42:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.11939","created_at":"2026-05-17T23:42:58Z"},{"alias_kind":"pith_short_12","alias_value":"V4PE6U36HOE7","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"V4PE6U36HOE7WEGP","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"V4PE6U36","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:683b7fe566e237b4ca84428de6a5df1152ec80f2c6a1563dd31cf6b0cfec9ecc","target":"graph","created_at":"2026-05-17T23:42:58Z","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 consider the asymmetric simple exclusion process (ASEP) on $\\mathbb{Z}$ with an initial data such that in the large time particle density $\\rho(\\cdot)$ a discontinuity at the origin is created, where the value of $\\rho$ jumps from zero to one, but $\\rho(-\\varepsilon),1-\\rho(\\varepsilon) >0 $ for any $\\varepsilon>0$. We consider the position of a particle $x_{M}$ macroscopically located at the discontinuity, and show that its limit law has a cutoff under $t^{1/2}$ scaling. Inside the discontinuity region, we show that a discrete product limit law arises, which bounds from above the limiting ","authors_text":"Peter Nejjar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-12-31T18:22:45Z","title":"Cutoff and discrete Product Structure in ASEP"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.11939","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:ef7a86857a72580f94b282ad2ccb63f858eff90187a1d1f6210c512afe979a32","target":"record","created_at":"2026-05-17T23:42:58Z","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":"1c72ae25fa376fea9879c8ca702834b233aeebbe80a8f0cdda65dd3b120f7c71","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-12-31T18:22:45Z","title_canon_sha256":"c4d0388defa892ea1e6c594b69dfff08a6178c31b0f49ecf2a02e28e17740e0a"},"schema_version":"1.0","source":{"id":"1812.11939","kind":"arxiv","version":2}},"canonical_sha256":"af1e4f537e3b89fb10cfed28beb031db7b21131828d6306219da8c67e6389358","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"af1e4f537e3b89fb10cfed28beb031db7b21131828d6306219da8c67e6389358","first_computed_at":"2026-05-17T23:42:58.526233Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:58.526233Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DK+8IQgC7el4f/6vVXE4Ma1iCly6/5qWfM/IMwa5UwnTSNHA2QMinzh7WAAiZmZYn1fwf+zwc720TahAcxNzBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:58.526830Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.11939","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ef7a86857a72580f94b282ad2ccb63f858eff90187a1d1f6210c512afe979a32","sha256:683b7fe566e237b4ca84428de6a5df1152ec80f2c6a1563dd31cf6b0cfec9ecc"],"state_sha256":"df66afd0543cc22ecdaaac6d68099b8669945a962aa09ddaf5276a9d7161571a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fICD/p1s0B0OpMDOIJS3xTMmSV4R6uWHllbYo5mvHH+9wUILBLQ1zBpFOdZAa74afDMAt8xsSQUWUbCx3X3cDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T10:07:40.386709Z","bundle_sha256":"b8b64fee715ae7cf71059bb4289c1fef11b62ce5a215d1030fc337d76d540daa"}}