{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:TGGL6HJKF3USH5ABR6HCGYYWQU","short_pith_number":"pith:TGGL6HJK","canonical_record":{"source":{"id":"0905.0768","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2009-05-06T07:56:38Z","cross_cats_sorted":[],"title_canon_sha256":"f66c72eb0244bd9195fb8f2118441a2d42426bfcbe8589ab4a04fb88a7b504fa","abstract_canon_sha256":"d197e5b732d9f29e684318888cf764aa2f684c75d59ea35e8e62e7336eebdb0c"},"schema_version":"1.0"},"canonical_sha256":"998cbf1d2a2ee923f4018f8e23631685277de8985714f6dadea1cd28560d0d45","source":{"kind":"arxiv","id":"0905.0768","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0905.0768","created_at":"2026-05-18T04:40:21Z"},{"alias_kind":"arxiv_version","alias_value":"0905.0768v5","created_at":"2026-05-18T04:40:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.0768","created_at":"2026-05-18T04:40:21Z"},{"alias_kind":"pith_short_12","alias_value":"TGGL6HJKF3US","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"TGGL6HJKF3USH5AB","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"TGGL6HJK","created_at":"2026-05-18T12:26:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:TGGL6HJKF3USH5ABR6HCGYYWQU","target":"record","payload":{"canonical_record":{"source":{"id":"0905.0768","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2009-05-06T07:56:38Z","cross_cats_sorted":[],"title_canon_sha256":"f66c72eb0244bd9195fb8f2118441a2d42426bfcbe8589ab4a04fb88a7b504fa","abstract_canon_sha256":"d197e5b732d9f29e684318888cf764aa2f684c75d59ea35e8e62e7336eebdb0c"},"schema_version":"1.0"},"canonical_sha256":"998cbf1d2a2ee923f4018f8e23631685277de8985714f6dadea1cd28560d0d45","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:40:21.777337Z","signature_b64":"4MonchyQbcE34BiLugSf2ahkGtCCFUYk7DKh+7jdIFwXAkVITPJOhPMEIBspvjHzGba4OoeBxjruynmSeNoDDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"998cbf1d2a2ee923f4018f8e23631685277de8985714f6dadea1cd28560d0d45","last_reissued_at":"2026-05-18T04:40:21.776843Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:40:21.776843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0905.0768","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:40:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JotgNk5761iDXDaLaUEiEbfIexO1x1aUlyNpF1MidrdTCwp13TT8td6wzpgUUjXHvOFDqMmoG4zYKDnumVgLAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T07:36:45.723765Z"},"content_sha256":"ae5085dfdb1ad68374689f1963b4a39ccdd8563f47e2db4204fdebe6fc29da19","schema_version":"1.0","event_id":"sha256:ae5085dfdb1ad68374689f1963b4a39ccdd8563f47e2db4204fdebe6fc29da19"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:TGGL6HJKF3USH5ABR6HCGYYWQU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fully-Functional Static and Dynamic Succinct Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Gonzalo Navarro, Kunihiko Sadakane","submitted_at":"2009-05-06T07:56:38Z","abstract_excerpt":"We propose new succinct representations of ordinal trees, which have been studied extensively. It is known that any $n$-node static tree can be represented in $2n + o(n)$ bits and a number of operations on the tree can be supported in constant time under the word-RAM model. However the data structures are complicated and difficult to dynamize. We propose a simple and flexible data structure, called the range min-max tree, that reduces the large number of relevant tree operations considered in the literature to a few primitives that are carried out in constant time on sufficiently small trees. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.0768","kind":"arxiv","version":5},"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":"2026-05-18T04:40:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+rd0TOcmmzO1/JViH1PNUdJIQA0wmcED88YiLPb49q2tyV6LrYE9YpOIsgeCQhff8r3jH7oqCERCcqWTIWySCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T07:36:45.724505Z"},"content_sha256":"c286ae21eb00ca2c6d110f566f8c6e2b8ca3937676f430ae9e6327c087e64d2b","schema_version":"1.0","event_id":"sha256:c286ae21eb00ca2c6d110f566f8c6e2b8ca3937676f430ae9e6327c087e64d2b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TGGL6HJKF3USH5ABR6HCGYYWQU/bundle.json","state_url":"https://pith.science/pith/TGGL6HJKF3USH5ABR6HCGYYWQU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TGGL6HJKF3USH5ABR6HCGYYWQU/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":"2026-06-09T07:36:45Z","links":{"resolver":"https://pith.science/pith/TGGL6HJKF3USH5ABR6HCGYYWQU","bundle":"https://pith.science/pith/TGGL6HJKF3USH5ABR6HCGYYWQU/bundle.json","state":"https://pith.science/pith/TGGL6HJKF3USH5ABR6HCGYYWQU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TGGL6HJKF3USH5ABR6HCGYYWQU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:TGGL6HJKF3USH5ABR6HCGYYWQU","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":"d197e5b732d9f29e684318888cf764aa2f684c75d59ea35e8e62e7336eebdb0c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2009-05-06T07:56:38Z","title_canon_sha256":"f66c72eb0244bd9195fb8f2118441a2d42426bfcbe8589ab4a04fb88a7b504fa"},"schema_version":"1.0","source":{"id":"0905.0768","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0905.0768","created_at":"2026-05-18T04:40:21Z"},{"alias_kind":"arxiv_version","alias_value":"0905.0768v5","created_at":"2026-05-18T04:40:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.0768","created_at":"2026-05-18T04:40:21Z"},{"alias_kind":"pith_short_12","alias_value":"TGGL6HJKF3US","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"TGGL6HJKF3USH5AB","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"TGGL6HJK","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:c286ae21eb00ca2c6d110f566f8c6e2b8ca3937676f430ae9e6327c087e64d2b","target":"graph","created_at":"2026-05-18T04:40:21Z","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":"We propose new succinct representations of ordinal trees, which have been studied extensively. It is known that any $n$-node static tree can be represented in $2n + o(n)$ bits and a number of operations on the tree can be supported in constant time under the word-RAM model. However the data structures are complicated and difficult to dynamize. We propose a simple and flexible data structure, called the range min-max tree, that reduces the large number of relevant tree operations considered in the literature to a few primitives that are carried out in constant time on sufficiently small trees. ","authors_text":"Gonzalo Navarro, Kunihiko Sadakane","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2009-05-06T07:56:38Z","title":"Fully-Functional Static and Dynamic Succinct Trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.0768","kind":"arxiv","version":5},"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:ae5085dfdb1ad68374689f1963b4a39ccdd8563f47e2db4204fdebe6fc29da19","target":"record","created_at":"2026-05-18T04:40:21Z","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":"d197e5b732d9f29e684318888cf764aa2f684c75d59ea35e8e62e7336eebdb0c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2009-05-06T07:56:38Z","title_canon_sha256":"f66c72eb0244bd9195fb8f2118441a2d42426bfcbe8589ab4a04fb88a7b504fa"},"schema_version":"1.0","source":{"id":"0905.0768","kind":"arxiv","version":5}},"canonical_sha256":"998cbf1d2a2ee923f4018f8e23631685277de8985714f6dadea1cd28560d0d45","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"998cbf1d2a2ee923f4018f8e23631685277de8985714f6dadea1cd28560d0d45","first_computed_at":"2026-05-18T04:40:21.776843Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:40:21.776843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4MonchyQbcE34BiLugSf2ahkGtCCFUYk7DKh+7jdIFwXAkVITPJOhPMEIBspvjHzGba4OoeBxjruynmSeNoDDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:40:21.777337Z","signed_message":"canonical_sha256_bytes"},"source_id":"0905.0768","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae5085dfdb1ad68374689f1963b4a39ccdd8563f47e2db4204fdebe6fc29da19","sha256:c286ae21eb00ca2c6d110f566f8c6e2b8ca3937676f430ae9e6327c087e64d2b"],"state_sha256":"4f9f015c937ba159ffc3eb926bd5e4527e1936238734ac0bfde1449c36689b71"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bXG/NjUTN/H4ypDvtlLW6W8DeGmqgU6XtLurVoZGKimg42HtvJaEFwe9kkAA9t2IpVX0XLxQlVA/kWWWABxjBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T07:36:45.728408Z","bundle_sha256":"743ae2bc39bb08b0f57ffb220275309538aaf7e4a1447f177ca685ced27b9b6c"}}