{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:VF3K3WPRJB56FF7CGQ6SUVY7ZU","short_pith_number":"pith:VF3K3WPR","canonical_record":{"source":{"id":"1808.08407","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-08-25T10:57:26Z","cross_cats_sorted":[],"title_canon_sha256":"7bc6e55b930acd2fa40aaabffb449d6cadac975db92a1e0c0ba7aace47715f7b","abstract_canon_sha256":"814249d1e6cc5a67c57c52c2ba46569ef5fae3d1772804753515998818a62057"},"schema_version":"1.0"},"canonical_sha256":"a976add9f1487be297e2343d2a571fcd3ca50b7ef70e0f9a78219484d31786bc","source":{"kind":"arxiv","id":"1808.08407","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.08407","created_at":"2026-05-18T00:07:16Z"},{"alias_kind":"arxiv_version","alias_value":"1808.08407v1","created_at":"2026-05-18T00:07:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.08407","created_at":"2026-05-18T00:07:16Z"},{"alias_kind":"pith_short_12","alias_value":"VF3K3WPRJB56","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VF3K3WPRJB56FF7C","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VF3K3WPR","created_at":"2026-05-18T12:32:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:VF3K3WPRJB56FF7CGQ6SUVY7ZU","target":"record","payload":{"canonical_record":{"source":{"id":"1808.08407","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-08-25T10:57:26Z","cross_cats_sorted":[],"title_canon_sha256":"7bc6e55b930acd2fa40aaabffb449d6cadac975db92a1e0c0ba7aace47715f7b","abstract_canon_sha256":"814249d1e6cc5a67c57c52c2ba46569ef5fae3d1772804753515998818a62057"},"schema_version":"1.0"},"canonical_sha256":"a976add9f1487be297e2343d2a571fcd3ca50b7ef70e0f9a78219484d31786bc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:16.583879Z","signature_b64":"f6gxL/mLSh4G6iu8CGljYsBoFwQvKdignWmJ+49YGu+nfWzuzijl6LDWXx0QTPgCn7GpnJqwNZD4SnPik0l5Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a976add9f1487be297e2343d2a571fcd3ca50b7ef70e0f9a78219484d31786bc","last_reissued_at":"2026-05-18T00:07:16.583227Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:16.583227Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.08407","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":"2026-05-18T00:07:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o+XxOp2RfAA3u6nvDUFEN2RRVbIqybxulmox3n/P97sg0fce+NLcRkjVfKy0dapeSu9TYavYRWaVI738tYUDDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T20:42:49.396118Z"},"content_sha256":"2c3af0c75422847290cfe258794b8d998d811606c92c09c523387341b745669b","schema_version":"1.0","event_id":"sha256:2c3af0c75422847290cfe258794b8d998d811606c92c09c523387341b745669b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:VF3K3WPRJB56FF7CGQ6SUVY7ZU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Longest increasing path within the critical strip","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Mathew Joseph, Partha Dey, Ron Peled","submitted_at":"2018-08-25T10:57:26Z","abstract_excerpt":"A Poisson point process of unit intensity is placed in the square $[0,n]^2$. An increasing path is a curve connecting $(0,0)$ with $(n,n)$ which is non-decreasing in each coordinate. Its length is the number of points of the Poisson process which it passes through. Baik, Deift and Johansson proved that the maximal length of an increasing path has expectation $2n-n^{1/3}(c_1+o(1))$, variance $n^{2/3}(c_2+o(1))$ and that it converges to the Tracy-Widom distribution after suitable scaling. Johansson further showed that all maximal paths have a displacement of $n^{\\frac23+o(1)}$ from the diagonal "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.08407","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":""},"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":"2026-05-18T00:07:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MzPA3UwdB8mB+1hWgcrTDhBAaqj6Vt9OYtSDAL4npomUO6o2HkSpYbx0wny7c/nxxMnt/LyPSJzSS2goNAZXDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T20:42:49.396772Z"},"content_sha256":"66ef82f35652834929ad11fd7e3f333488f13ce16beb3f02594d38ee4423d2ec","schema_version":"1.0","event_id":"sha256:66ef82f35652834929ad11fd7e3f333488f13ce16beb3f02594d38ee4423d2ec"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VF3K3WPRJB56FF7CGQ6SUVY7ZU/bundle.json","state_url":"https://pith.science/pith/VF3K3WPRJB56FF7CGQ6SUVY7ZU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VF3K3WPRJB56FF7CGQ6SUVY7ZU/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":"2026-05-26T20:42:49Z","links":{"resolver":"https://pith.science/pith/VF3K3WPRJB56FF7CGQ6SUVY7ZU","bundle":"https://pith.science/pith/VF3K3WPRJB56FF7CGQ6SUVY7ZU/bundle.json","state":"https://pith.science/pith/VF3K3WPRJB56FF7CGQ6SUVY7ZU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VF3K3WPRJB56FF7CGQ6SUVY7ZU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:VF3K3WPRJB56FF7CGQ6SUVY7ZU","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":"814249d1e6cc5a67c57c52c2ba46569ef5fae3d1772804753515998818a62057","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-08-25T10:57:26Z","title_canon_sha256":"7bc6e55b930acd2fa40aaabffb449d6cadac975db92a1e0c0ba7aace47715f7b"},"schema_version":"1.0","source":{"id":"1808.08407","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.08407","created_at":"2026-05-18T00:07:16Z"},{"alias_kind":"arxiv_version","alias_value":"1808.08407v1","created_at":"2026-05-18T00:07:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.08407","created_at":"2026-05-18T00:07:16Z"},{"alias_kind":"pith_short_12","alias_value":"VF3K3WPRJB56","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VF3K3WPRJB56FF7C","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VF3K3WPR","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:66ef82f35652834929ad11fd7e3f333488f13ce16beb3f02594d38ee4423d2ec","target":"graph","created_at":"2026-05-18T00:07:16Z","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":"A Poisson point process of unit intensity is placed in the square $[0,n]^2$. An increasing path is a curve connecting $(0,0)$ with $(n,n)$ which is non-decreasing in each coordinate. Its length is the number of points of the Poisson process which it passes through. Baik, Deift and Johansson proved that the maximal length of an increasing path has expectation $2n-n^{1/3}(c_1+o(1))$, variance $n^{2/3}(c_2+o(1))$ and that it converges to the Tracy-Widom distribution after suitable scaling. Johansson further showed that all maximal paths have a displacement of $n^{\\frac23+o(1)}$ from the diagonal ","authors_text":"Mathew Joseph, Partha Dey, Ron Peled","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-08-25T10:57:26Z","title":"Longest increasing path within the critical strip"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.08407","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":"sha256:2c3af0c75422847290cfe258794b8d998d811606c92c09c523387341b745669b","target":"record","created_at":"2026-05-18T00:07:16Z","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":"814249d1e6cc5a67c57c52c2ba46569ef5fae3d1772804753515998818a62057","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-08-25T10:57:26Z","title_canon_sha256":"7bc6e55b930acd2fa40aaabffb449d6cadac975db92a1e0c0ba7aace47715f7b"},"schema_version":"1.0","source":{"id":"1808.08407","kind":"arxiv","version":1}},"canonical_sha256":"a976add9f1487be297e2343d2a571fcd3ca50b7ef70e0f9a78219484d31786bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a976add9f1487be297e2343d2a571fcd3ca50b7ef70e0f9a78219484d31786bc","first_computed_at":"2026-05-18T00:07:16.583227Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:16.583227Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f6gxL/mLSh4G6iu8CGljYsBoFwQvKdignWmJ+49YGu+nfWzuzijl6LDWXx0QTPgCn7GpnJqwNZD4SnPik0l5Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:16.583879Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.08407","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2c3af0c75422847290cfe258794b8d998d811606c92c09c523387341b745669b","sha256:66ef82f35652834929ad11fd7e3f333488f13ce16beb3f02594d38ee4423d2ec"],"state_sha256":"7ce30a727dcc1c7a23d54a5df4a11c17d7422349ceb24685eefb3aa4bedd130d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SG1I4l39zTv/67jccXvgfEs+IkTuOve0VpPssV1PNMw0x191rbNNJBTRwjyoGGQmVv53Xoox42SM5KVqzdOlAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T20:42:49.400966Z","bundle_sha256":"2747e8debd16e504f6061de3a0e97bd075685219468a94a5d899ca8e70566ace"}}