{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:CKYHKHTYY3FXCEX37FX4MXAA7U","short_pith_number":"pith:CKYHKHTY","canonical_record":{"source":{"id":"2607.01273","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-06-30T21:17:45Z","cross_cats_sorted":[],"title_canon_sha256":"7f1e44bec24b3b794e0c897ad81f1437431ef499ca76143b3c0d409828427483","abstract_canon_sha256":"5d8ad25f37bbc1b153615a0f9046e3e43e5e19d0f9903dce4eb0d8646f652912"},"schema_version":"1.0"},"canonical_sha256":"12b0751e78c6cb7112fbf96fc65c00fd027ba2152cfa47b1c13d029b491fe99b","source":{"kind":"arxiv","id":"2607.01273","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.01273","created_at":"2026-07-03T00:16:55Z"},{"alias_kind":"arxiv_version","alias_value":"2607.01273v1","created_at":"2026-07-03T00:16:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.01273","created_at":"2026-07-03T00:16:55Z"},{"alias_kind":"pith_short_12","alias_value":"CKYHKHTYY3FX","created_at":"2026-07-03T00:16:55Z"},{"alias_kind":"pith_short_16","alias_value":"CKYHKHTYY3FXCEX3","created_at":"2026-07-03T00:16:55Z"},{"alias_kind":"pith_short_8","alias_value":"CKYHKHTY","created_at":"2026-07-03T00:16:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:CKYHKHTYY3FXCEX37FX4MXAA7U","target":"record","payload":{"canonical_record":{"source":{"id":"2607.01273","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-06-30T21:17:45Z","cross_cats_sorted":[],"title_canon_sha256":"7f1e44bec24b3b794e0c897ad81f1437431ef499ca76143b3c0d409828427483","abstract_canon_sha256":"5d8ad25f37bbc1b153615a0f9046e3e43e5e19d0f9903dce4eb0d8646f652912"},"schema_version":"1.0"},"canonical_sha256":"12b0751e78c6cb7112fbf96fc65c00fd027ba2152cfa47b1c13d029b491fe99b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-03T00:16:55.996870Z","signature_b64":"wFoQr6ysB04k7UO9ufI3H94KX+59Vj+4ovDbLxwWFNRsd8589EvvylAU2nziYz8gamahjCng0DXFvg6LKtygCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"12b0751e78c6cb7112fbf96fc65c00fd027ba2152cfa47b1c13d029b491fe99b","last_reissued_at":"2026-07-03T00:16:55.996458Z","signature_status":"signed_v1","first_computed_at":"2026-07-03T00:16:55.996458Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.01273","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":"2026-07-03T00:16:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ErbG43o6osrNwbdFpE6eO38izV8TH1cgIP8bwPQZtuW0KNbXQ2kbgwN/IdKq0IT0vaHsWfJJgxVIGI91ucqcCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T12:18:04.691002Z"},"content_sha256":"fed437a41db4a33481998af085e8df6e85f483e2b83a8e888f5f5db41c92c594","schema_version":"1.0","event_id":"sha256:fed437a41db4a33481998af085e8df6e85f483e2b83a8e888f5f5db41c92c594"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:CKYHKHTYY3FXCEX37FX4MXAA7U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Deranged Unit-Interval Parking Functions and the Deranged Bell Numbers","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Yahia Djemmada","submitted_at":"2026-06-30T21:17:45Z","abstract_excerpt":"Unit-interval parking functions of length $n$ are enumerated by the Fubini numbers $F_n$ and are in explicit bijection with the ordered set partitions of $[n]$. We use this bijection to single out the unit-interval parking functions whose associated ordered set partition is \\emph{deranged} in the sense of Belbachir, Djemmada, and N\\'emeth -- no block occupies the position indexed by its minimum element -- and call them the \\emph{deranged unit-interval parking functions} $\\DUPF_n$. Since the bijection restricts to the deranged objects, $|\\DUPF_n| = \\tilde F_n$, the $n$-th deranged Bell number. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.01273","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/2607.01273/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":"2026-07-03T00:16:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0EIqg7k8ZExJ94fnnmIlFVBMV898HtXs+3dCJyMABNxV6Ut0ToNzxD5bMG0NDxcw4jzqNLexkjIf/QJqvySjDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T12:18:04.691652Z"},"content_sha256":"c23ad8ab23caaa2ada07900eff2acad866a27c50a60e32b6539d6efba801ccfc","schema_version":"1.0","event_id":"sha256:c23ad8ab23caaa2ada07900eff2acad866a27c50a60e32b6539d6efba801ccfc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CKYHKHTYY3FXCEX37FX4MXAA7U/bundle.json","state_url":"https://pith.science/pith/CKYHKHTYY3FXCEX37FX4MXAA7U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CKYHKHTYY3FXCEX37FX4MXAA7U/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":"2026-08-07T12:18:04Z","links":{"resolver":"https://pith.science/pith/CKYHKHTYY3FXCEX37FX4MXAA7U","bundle":"https://pith.science/pith/CKYHKHTYY3FXCEX37FX4MXAA7U/bundle.json","state":"https://pith.science/pith/CKYHKHTYY3FXCEX37FX4MXAA7U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CKYHKHTYY3FXCEX37FX4MXAA7U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:CKYHKHTYY3FXCEX37FX4MXAA7U","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":"5d8ad25f37bbc1b153615a0f9046e3e43e5e19d0f9903dce4eb0d8646f652912","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-06-30T21:17:45Z","title_canon_sha256":"7f1e44bec24b3b794e0c897ad81f1437431ef499ca76143b3c0d409828427483"},"schema_version":"1.0","source":{"id":"2607.01273","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.01273","created_at":"2026-07-03T00:16:55Z"},{"alias_kind":"arxiv_version","alias_value":"2607.01273v1","created_at":"2026-07-03T00:16:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.01273","created_at":"2026-07-03T00:16:55Z"},{"alias_kind":"pith_short_12","alias_value":"CKYHKHTYY3FX","created_at":"2026-07-03T00:16:55Z"},{"alias_kind":"pith_short_16","alias_value":"CKYHKHTYY3FXCEX3","created_at":"2026-07-03T00:16:55Z"},{"alias_kind":"pith_short_8","alias_value":"CKYHKHTY","created_at":"2026-07-03T00:16:55Z"}],"graph_snapshots":[{"event_id":"sha256:c23ad8ab23caaa2ada07900eff2acad866a27c50a60e32b6539d6efba801ccfc","target":"graph","created_at":"2026-07-03T00:16:55Z","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/2607.01273/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Unit-interval parking functions of length $n$ are enumerated by the Fubini numbers $F_n$ and are in explicit bijection with the ordered set partitions of $[n]$. We use this bijection to single out the unit-interval parking functions whose associated ordered set partition is \\emph{deranged} in the sense of Belbachir, Djemmada, and N\\'emeth -- no block occupies the position indexed by its minimum element -- and call them the \\emph{deranged unit-interval parking functions} $\\DUPF_n$. Since the bijection restricts to the deranged objects, $|\\DUPF_n| = \\tilde F_n$, the $n$-th deranged Bell number. ","authors_text":"Yahia Djemmada","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-06-30T21:17:45Z","title":"On Deranged Unit-Interval Parking Functions and the Deranged Bell Numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.01273","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:fed437a41db4a33481998af085e8df6e85f483e2b83a8e888f5f5db41c92c594","target":"record","created_at":"2026-07-03T00:16:55Z","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":"5d8ad25f37bbc1b153615a0f9046e3e43e5e19d0f9903dce4eb0d8646f652912","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-06-30T21:17:45Z","title_canon_sha256":"7f1e44bec24b3b794e0c897ad81f1437431ef499ca76143b3c0d409828427483"},"schema_version":"1.0","source":{"id":"2607.01273","kind":"arxiv","version":1}},"canonical_sha256":"12b0751e78c6cb7112fbf96fc65c00fd027ba2152cfa47b1c13d029b491fe99b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"12b0751e78c6cb7112fbf96fc65c00fd027ba2152cfa47b1c13d029b491fe99b","first_computed_at":"2026-07-03T00:16:55.996458Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-03T00:16:55.996458Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wFoQr6ysB04k7UO9ufI3H94KX+59Vj+4ovDbLxwWFNRsd8589EvvylAU2nziYz8gamahjCng0DXFvg6LKtygCA==","signature_status":"signed_v1","signed_at":"2026-07-03T00:16:55.996870Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.01273","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fed437a41db4a33481998af085e8df6e85f483e2b83a8e888f5f5db41c92c594","sha256:c23ad8ab23caaa2ada07900eff2acad866a27c50a60e32b6539d6efba801ccfc"],"state_sha256":"a51fb580f246736942c9e5dbf9ddbf366b72f85f4d0bb26fe7f6979d38fc3cdd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sP8HzOmfTV00tO37NLSHWJRaIUzhF/6wv+CAW4Zv3wFDj7VuKooKcj3NbbtzvU3E//sHWbPURTy6LkHDQDQVBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T12:18:04.696543Z","bundle_sha256":"0deed9048942499903cbf565c4599d551758615d18cef16076008324d062233b"}}