{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:53ODDFKJC6ZXSO57OPNAXLQDTW","short_pith_number":"pith:53ODDFKJ","canonical_record":{"source":{"id":"2407.03666","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2024-07-04T06:17:23Z","cross_cats_sorted":[],"title_canon_sha256":"f0ac406cd5b875d0b677385a5ec285541c320b6eaa62242cc5e1e19d90809bc7","abstract_canon_sha256":"b1c8e2fb6155e8e9174c1abd6db6707d55e0fe49bea5b53bb6fe90c0d8820625"},"schema_version":"1.0"},"canonical_sha256":"eedc31954917b3793bbf73da0bae039dbe6e7e6b7cd60fc33a6d30fb727eeb90","source":{"kind":"arxiv","id":"2407.03666","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.03666","created_at":"2026-07-05T11:50:27Z"},{"alias_kind":"arxiv_version","alias_value":"2407.03666v2","created_at":"2026-07-05T11:50:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.03666","created_at":"2026-07-05T11:50:27Z"},{"alias_kind":"pith_short_12","alias_value":"53ODDFKJC6ZX","created_at":"2026-07-05T11:50:27Z"},{"alias_kind":"pith_short_16","alias_value":"53ODDFKJC6ZXSO57","created_at":"2026-07-05T11:50:27Z"},{"alias_kind":"pith_short_8","alias_value":"53ODDFKJ","created_at":"2026-07-05T11:50:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:53ODDFKJC6ZXSO57OPNAXLQDTW","target":"record","payload":{"canonical_record":{"source":{"id":"2407.03666","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2024-07-04T06:17:23Z","cross_cats_sorted":[],"title_canon_sha256":"f0ac406cd5b875d0b677385a5ec285541c320b6eaa62242cc5e1e19d90809bc7","abstract_canon_sha256":"b1c8e2fb6155e8e9174c1abd6db6707d55e0fe49bea5b53bb6fe90c0d8820625"},"schema_version":"1.0"},"canonical_sha256":"eedc31954917b3793bbf73da0bae039dbe6e7e6b7cd60fc33a6d30fb727eeb90","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:50:27.416338Z","signature_b64":"O2Vx5CPKUlKdecw3wChgHIEqkK5TmTnQlP/xKr0VRJ8Trb+vTxLXKyEo0POFwti7K3cGQdaDiHRPJAG3KOJ5Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eedc31954917b3793bbf73da0bae039dbe6e7e6b7cd60fc33a6d30fb727eeb90","last_reissued_at":"2026-07-05T11:50:27.415833Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:50:27.415833Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2407.03666","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":"2026-07-05T11:50:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/Jeb+rWL9e/bex3o5aeFDoY9VJih7L48e59k83/vCqKqaT7yLCnyrFjnbSkvoY15v9DDQYtKl9w480dM3xfzAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T09:13:52.218257Z"},"content_sha256":"ba48fabb726fe20194fd86ea14e46497205f12d345ec8418320b0e9ab948921f","schema_version":"1.0","event_id":"sha256:ba48fabb726fe20194fd86ea14e46497205f12d345ec8418320b0e9ab948921f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:53ODDFKJC6ZXSO57OPNAXLQDTW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Greedy BST on Permutation Initial Tree","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Akash Pareek","submitted_at":"2024-07-04T06:17:23Z","abstract_excerpt":"The Greedy binary search tree (BST) algorithm, like the Splay tree, is a prominent candidate for the \\emph{dynamic optimality conjecture}. While Greedy satisfies many desirable properties of BST, its cost and analysis to execute a search sequence $S$ is known to depend heavily on the choice of the \\emph{initial tree} configuration. Most prior analyses assume a flat (empty) initial tree, under which several tight bounds are established.\n  In this work, we introduce the notion of a \\emph{permutation initial tree}, a specific class of non-flat initial tree and prove that for any permutation searc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.03666","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2407.03666/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":"2026-07-05T11:50:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oKUF1vrotVy/tEtaDBXsYkPO25ismTiPH6vmW48CskPQwfY5GkKZCusxL2nWG78aoBWZBKzHMmKFSvsKO0sJBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T09:13:52.218746Z"},"content_sha256":"124ceda31de730d045b64b8fa7a2e955c801bdf866a2bd23a078d70401d2afeb","schema_version":"1.0","event_id":"sha256:124ceda31de730d045b64b8fa7a2e955c801bdf866a2bd23a078d70401d2afeb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/53ODDFKJC6ZXSO57OPNAXLQDTW/bundle.json","state_url":"https://pith.science/pith/53ODDFKJC6ZXSO57OPNAXLQDTW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/53ODDFKJC6ZXSO57OPNAXLQDTW/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":"2026-08-04T09:13:52Z","links":{"resolver":"https://pith.science/pith/53ODDFKJC6ZXSO57OPNAXLQDTW","bundle":"https://pith.science/pith/53ODDFKJC6ZXSO57OPNAXLQDTW/bundle.json","state":"https://pith.science/pith/53ODDFKJC6ZXSO57OPNAXLQDTW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/53ODDFKJC6ZXSO57OPNAXLQDTW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:53ODDFKJC6ZXSO57OPNAXLQDTW","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":"b1c8e2fb6155e8e9174c1abd6db6707d55e0fe49bea5b53bb6fe90c0d8820625","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2024-07-04T06:17:23Z","title_canon_sha256":"f0ac406cd5b875d0b677385a5ec285541c320b6eaa62242cc5e1e19d90809bc7"},"schema_version":"1.0","source":{"id":"2407.03666","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.03666","created_at":"2026-07-05T11:50:27Z"},{"alias_kind":"arxiv_version","alias_value":"2407.03666v2","created_at":"2026-07-05T11:50:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.03666","created_at":"2026-07-05T11:50:27Z"},{"alias_kind":"pith_short_12","alias_value":"53ODDFKJC6ZX","created_at":"2026-07-05T11:50:27Z"},{"alias_kind":"pith_short_16","alias_value":"53ODDFKJC6ZXSO57","created_at":"2026-07-05T11:50:27Z"},{"alias_kind":"pith_short_8","alias_value":"53ODDFKJ","created_at":"2026-07-05T11:50:27Z"}],"graph_snapshots":[{"event_id":"sha256:124ceda31de730d045b64b8fa7a2e955c801bdf866a2bd23a078d70401d2afeb","target":"graph","created_at":"2026-07-05T11:50:27Z","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/2407.03666/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Greedy binary search tree (BST) algorithm, like the Splay tree, is a prominent candidate for the \\emph{dynamic optimality conjecture}. While Greedy satisfies many desirable properties of BST, its cost and analysis to execute a search sequence $S$ is known to depend heavily on the choice of the \\emph{initial tree} configuration. Most prior analyses assume a flat (empty) initial tree, under which several tight bounds are established.\n  In this work, we introduce the notion of a \\emph{permutation initial tree}, a specific class of non-flat initial tree and prove that for any permutation searc","authors_text":"Akash Pareek","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2024-07-04T06:17:23Z","title":"Greedy BST on Permutation Initial Tree"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.03666","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:ba48fabb726fe20194fd86ea14e46497205f12d345ec8418320b0e9ab948921f","target":"record","created_at":"2026-07-05T11:50:27Z","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":"b1c8e2fb6155e8e9174c1abd6db6707d55e0fe49bea5b53bb6fe90c0d8820625","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2024-07-04T06:17:23Z","title_canon_sha256":"f0ac406cd5b875d0b677385a5ec285541c320b6eaa62242cc5e1e19d90809bc7"},"schema_version":"1.0","source":{"id":"2407.03666","kind":"arxiv","version":2}},"canonical_sha256":"eedc31954917b3793bbf73da0bae039dbe6e7e6b7cd60fc33a6d30fb727eeb90","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eedc31954917b3793bbf73da0bae039dbe6e7e6b7cd60fc33a6d30fb727eeb90","first_computed_at":"2026-07-05T11:50:27.415833Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:50:27.415833Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O2Vx5CPKUlKdecw3wChgHIEqkK5TmTnQlP/xKr0VRJ8Trb+vTxLXKyEo0POFwti7K3cGQdaDiHRPJAG3KOJ5Ag==","signature_status":"signed_v1","signed_at":"2026-07-05T11:50:27.416338Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.03666","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba48fabb726fe20194fd86ea14e46497205f12d345ec8418320b0e9ab948921f","sha256:124ceda31de730d045b64b8fa7a2e955c801bdf866a2bd23a078d70401d2afeb"],"state_sha256":"4a06ee644f1a52b2cad87635ff86fa5aa881dc6a2588ca4987b765b147857f3f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lGy8l52MNjQpfHHAchSoWSIjZvGIFsUhqV0qK282d+5iFmutGT6o4Av2U3nNK0QdbUjab5FxcHrQdrnBrF4RCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T09:13:52.222258Z","bundle_sha256":"c5f7620f5550ebb523d9d7e61f47b6d8be8c83bd2a7232a12bf28acc639361ae"}}