{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:4ZCADAR2XYAO674RXYPLWD6ZYP","short_pith_number":"pith:4ZCADAR2","schema_version":"1.0","canonical_sha256":"e64401823abe00ef7f91be1ebb0fd9c3e75f08a7895ce7ad0912b9decc1c73be","source":{"kind":"arxiv","id":"2406.06359","version":1},"attestation_state":"computed","paper":{"title":"A bijection for the evolution of $B$-trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.PR"],"primary_cat":"math.CO","authors_text":"Fabian Burghart, Stephan Wagner","submitted_at":"2024-06-10T15:20:18Z","abstract_excerpt":"A $B$-tree is a type of search tree where every node (except possibly for the root) contains between $m$ and $2m$ keys for some positive integer $m$, and all leaves have the same distance to the root. We study sequences of $B$-trees that can arise from successively inserting keys, and in particular present a bijection between such sequences (which we call histories) and a special type of increasing trees. We describe the set of permutations for the keys that belong to a given history, and also show how to use this bijection to analyse statistics associated with $B$-trees."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2406.06359","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-06-10T15:20:18Z","cross_cats_sorted":["cs.DS","math.PR"],"title_canon_sha256":"521929465455ac7c3cf933f3d4982518acb077008b5ec4a8b9db2fdf25a2ac06","abstract_canon_sha256":"0dcebd04c434e5dc1b06837da1b134584c176c4d8df9f7f5e4e74e8272424357"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:29:41.307064Z","signature_b64":"UypcnowC1YXmmQV9DA2cO6O9LQdsu5YlXKPsfT+JxUAYVkjXoqDlbzgGs/r2auJjT7WeFTcSAMfciVwYTgprBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e64401823abe00ef7f91be1ebb0fd9c3e75f08a7895ce7ad0912b9decc1c73be","last_reissued_at":"2026-07-05T08:29:41.306441Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:29:41.306441Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A bijection for the evolution of $B$-trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.PR"],"primary_cat":"math.CO","authors_text":"Fabian Burghart, Stephan Wagner","submitted_at":"2024-06-10T15:20:18Z","abstract_excerpt":"A $B$-tree is a type of search tree where every node (except possibly for the root) contains between $m$ and $2m$ keys for some positive integer $m$, and all leaves have the same distance to the root. We study sequences of $B$-trees that can arise from successively inserting keys, and in particular present a bijection between such sequences (which we call histories) and a special type of increasing trees. We describe the set of permutations for the keys that belong to a given history, and also show how to use this bijection to analyse statistics associated with $B$-trees."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.06359","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/2406.06359/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2406.06359","created_at":"2026-07-05T08:29:41.306516+00:00"},{"alias_kind":"arxiv_version","alias_value":"2406.06359v1","created_at":"2026-07-05T08:29:41.306516+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.06359","created_at":"2026-07-05T08:29:41.306516+00:00"},{"alias_kind":"pith_short_12","alias_value":"4ZCADAR2XYAO","created_at":"2026-07-05T08:29:41.306516+00:00"},{"alias_kind":"pith_short_16","alias_value":"4ZCADAR2XYAO674R","created_at":"2026-07-05T08:29:41.306516+00:00"},{"alias_kind":"pith_short_8","alias_value":"4ZCADAR2","created_at":"2026-07-05T08:29:41.306516+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4ZCADAR2XYAO674RXYPLWD6ZYP","json":"https://pith.science/pith/4ZCADAR2XYAO674RXYPLWD6ZYP.json","graph_json":"https://pith.science/api/pith-number/4ZCADAR2XYAO674RXYPLWD6ZYP/graph.json","events_json":"https://pith.science/api/pith-number/4ZCADAR2XYAO674RXYPLWD6ZYP/events.json","paper":"https://pith.science/paper/4ZCADAR2"},"agent_actions":{"view_html":"https://pith.science/pith/4ZCADAR2XYAO674RXYPLWD6ZYP","download_json":"https://pith.science/pith/4ZCADAR2XYAO674RXYPLWD6ZYP.json","view_paper":"https://pith.science/paper/4ZCADAR2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2406.06359&json=true","fetch_graph":"https://pith.science/api/pith-number/4ZCADAR2XYAO674RXYPLWD6ZYP/graph.json","fetch_events":"https://pith.science/api/pith-number/4ZCADAR2XYAO674RXYPLWD6ZYP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4ZCADAR2XYAO674RXYPLWD6ZYP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4ZCADAR2XYAO674RXYPLWD6ZYP/action/storage_attestation","attest_author":"https://pith.science/pith/4ZCADAR2XYAO674RXYPLWD6ZYP/action/author_attestation","sign_citation":"https://pith.science/pith/4ZCADAR2XYAO674RXYPLWD6ZYP/action/citation_signature","submit_replication":"https://pith.science/pith/4ZCADAR2XYAO674RXYPLWD6ZYP/action/replication_record"}},"created_at":"2026-07-05T08:29:41.306516+00:00","updated_at":"2026-07-05T08:29:41.306516+00:00"}