{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:7YDI2EFHVTHY2MR7B4SIW3PYYP","short_pith_number":"pith:7YDI2EFH","canonical_record":{"source":{"id":"1302.3770","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-02-15T15:24:18Z","cross_cats_sorted":[],"title_canon_sha256":"823f8f1cffadea6121aff2eac7c6ee24ddfce7eda891bc5942852b24d12019d0","abstract_canon_sha256":"cb131f640b91191ba3467bf0cde4566be34f87e4a596736b5e6e5913ac5f9456"},"schema_version":"1.0"},"canonical_sha256":"fe068d10a7accf8d323f0f248b6df8c3c1828f244afa29a0df3ec4f49b508a28","source":{"kind":"arxiv","id":"1302.3770","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.3770","created_at":"2026-05-18T03:33:35Z"},{"alias_kind":"arxiv_version","alias_value":"1302.3770v1","created_at":"2026-05-18T03:33:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.3770","created_at":"2026-05-18T03:33:35Z"},{"alias_kind":"pith_short_12","alias_value":"7YDI2EFHVTHY","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"7YDI2EFHVTHY2MR7","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"7YDI2EFH","created_at":"2026-05-18T12:27:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:7YDI2EFHVTHY2MR7B4SIW3PYYP","target":"record","payload":{"canonical_record":{"source":{"id":"1302.3770","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-02-15T15:24:18Z","cross_cats_sorted":[],"title_canon_sha256":"823f8f1cffadea6121aff2eac7c6ee24ddfce7eda891bc5942852b24d12019d0","abstract_canon_sha256":"cb131f640b91191ba3467bf0cde4566be34f87e4a596736b5e6e5913ac5f9456"},"schema_version":"1.0"},"canonical_sha256":"fe068d10a7accf8d323f0f248b6df8c3c1828f244afa29a0df3ec4f49b508a28","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:33:35.799184Z","signature_b64":"/TEdhXF2NiwqP/waw8mT5vYpt1tVDUQZ9UW+OuTIi/wtm6VMdq98qSHbxKXnXICf3HUogemnFVhu8q6FNMBDCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe068d10a7accf8d323f0f248b6df8c3c1828f244afa29a0df3ec4f49b508a28","last_reissued_at":"2026-05-18T03:33:35.798354Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:33:35.798354Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.3770","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":"2026-05-18T03:33:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5H1vKrP2TDwrSBQPLsH2UO3JzZChls/XycgP63dZgLCDEW96iG8xJyA4pf+EuTGxImCXAYNy/evN9w+5/HOUAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T02:10:36.663010Z"},"content_sha256":"a85a2d4248935f058aeffeae9beb9408264642709ca2b050acd5bb9c9d892fe5","schema_version":"1.0","event_id":"sha256:a85a2d4248935f058aeffeae9beb9408264642709ca2b050acd5bb9c9d892fe5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:7YDI2EFHVTHY2MR7B4SIW3PYYP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Quicksort Process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Mahmoud Ragab, Uwe Roesler","submitted_at":"2013-02-15T15:24:18Z","abstract_excerpt":"Quicksort on the fly returns the input of $n$ reals in increasing natural order during the sorting process. Correctly normalized the running time up to returning the l-th smallest out of n seen as a process in l converges weakly to a limiting process with path in the space of cadlag functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.3770","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":"2026-05-18T03:33:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0TaKNDRXoUZr58r2h6Q72EJjtIKvJLrdRsYiWglMGP1Waxr72oNFygt5wjp61mO6L04qaAutSZtRFm2PsLvhBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T02:10:36.663360Z"},"content_sha256":"472ac5825dce3fa25064ae6829d074ad90b0cb77910d9fb01011dab2539d99c9","schema_version":"1.0","event_id":"sha256:472ac5825dce3fa25064ae6829d074ad90b0cb77910d9fb01011dab2539d99c9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7YDI2EFHVTHY2MR7B4SIW3PYYP/bundle.json","state_url":"https://pith.science/pith/7YDI2EFHVTHY2MR7B4SIW3PYYP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7YDI2EFHVTHY2MR7B4SIW3PYYP/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":"2026-06-23T02:10:36Z","links":{"resolver":"https://pith.science/pith/7YDI2EFHVTHY2MR7B4SIW3PYYP","bundle":"https://pith.science/pith/7YDI2EFHVTHY2MR7B4SIW3PYYP/bundle.json","state":"https://pith.science/pith/7YDI2EFHVTHY2MR7B4SIW3PYYP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7YDI2EFHVTHY2MR7B4SIW3PYYP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:7YDI2EFHVTHY2MR7B4SIW3PYYP","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":"cb131f640b91191ba3467bf0cde4566be34f87e4a596736b5e6e5913ac5f9456","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-02-15T15:24:18Z","title_canon_sha256":"823f8f1cffadea6121aff2eac7c6ee24ddfce7eda891bc5942852b24d12019d0"},"schema_version":"1.0","source":{"id":"1302.3770","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.3770","created_at":"2026-05-18T03:33:35Z"},{"alias_kind":"arxiv_version","alias_value":"1302.3770v1","created_at":"2026-05-18T03:33:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.3770","created_at":"2026-05-18T03:33:35Z"},{"alias_kind":"pith_short_12","alias_value":"7YDI2EFHVTHY","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"7YDI2EFHVTHY2MR7","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"7YDI2EFH","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:472ac5825dce3fa25064ae6829d074ad90b0cb77910d9fb01011dab2539d99c9","target":"graph","created_at":"2026-05-18T03:33:35Z","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":"Quicksort on the fly returns the input of $n$ reals in increasing natural order during the sorting process. Correctly normalized the running time up to returning the l-th smallest out of n seen as a process in l converges weakly to a limiting process with path in the space of cadlag functions.","authors_text":"Mahmoud Ragab, Uwe Roesler","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-02-15T15:24:18Z","title":"The Quicksort Process"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.3770","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:a85a2d4248935f058aeffeae9beb9408264642709ca2b050acd5bb9c9d892fe5","target":"record","created_at":"2026-05-18T03:33:35Z","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":"cb131f640b91191ba3467bf0cde4566be34f87e4a596736b5e6e5913ac5f9456","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-02-15T15:24:18Z","title_canon_sha256":"823f8f1cffadea6121aff2eac7c6ee24ddfce7eda891bc5942852b24d12019d0"},"schema_version":"1.0","source":{"id":"1302.3770","kind":"arxiv","version":1}},"canonical_sha256":"fe068d10a7accf8d323f0f248b6df8c3c1828f244afa29a0df3ec4f49b508a28","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fe068d10a7accf8d323f0f248b6df8c3c1828f244afa29a0df3ec4f49b508a28","first_computed_at":"2026-05-18T03:33:35.798354Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:33:35.798354Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/TEdhXF2NiwqP/waw8mT5vYpt1tVDUQZ9UW+OuTIi/wtm6VMdq98qSHbxKXnXICf3HUogemnFVhu8q6FNMBDCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:33:35.799184Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.3770","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a85a2d4248935f058aeffeae9beb9408264642709ca2b050acd5bb9c9d892fe5","sha256:472ac5825dce3fa25064ae6829d074ad90b0cb77910d9fb01011dab2539d99c9"],"state_sha256":"1842e8fd7b645a1ed811a837519a12a058ee7a7120e5404029574b190696dc9d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WZnUUcbI576+tojfqaRFYHyDWgt45D+9PyzooJpGTgzITiHOABpFwmJZDjdtXaMZMVi60rg1vNuxSZH6ovfFAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T02:10:36.665246Z","bundle_sha256":"d32f76384fd5ca8f8902df85d35afae9d8684d24880a4b0ee3258c993467a67b"}}