{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:QHODHTYE3NE5WNRRD77ZZXMMM2","short_pith_number":"pith:QHODHTYE","canonical_record":{"source":{"id":"math/0401089","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.CO","submitted_at":"2004-01-09T10:18:43Z","cross_cats_sorted":[],"title_canon_sha256":"df03bc2fcc130da548186c5499bd81b06f30f2b759ceb4010bef5e2598f041e1","abstract_canon_sha256":"81378c225b08151986e1fed094bc09e97a7d92dcc2add3a67efb92a3550e7b77"},"schema_version":"1.0"},"canonical_sha256":"81dc33cf04db49db36311fff9cdd8c669d233823360fbc108c6785b16c65f51f","source":{"kind":"arxiv","id":"math/0401089","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0401089","created_at":"2026-05-18T03:34:00Z"},{"alias_kind":"arxiv_version","alias_value":"math/0401089v2","created_at":"2026-05-18T03:34:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0401089","created_at":"2026-05-18T03:34:00Z"},{"alias_kind":"pith_short_12","alias_value":"QHODHTYE3NE5","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"QHODHTYE3NE5WNRR","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"QHODHTYE","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:QHODHTYE3NE5WNRRD77ZZXMMM2","target":"record","payload":{"canonical_record":{"source":{"id":"math/0401089","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.CO","submitted_at":"2004-01-09T10:18:43Z","cross_cats_sorted":[],"title_canon_sha256":"df03bc2fcc130da548186c5499bd81b06f30f2b759ceb4010bef5e2598f041e1","abstract_canon_sha256":"81378c225b08151986e1fed094bc09e97a7d92dcc2add3a67efb92a3550e7b77"},"schema_version":"1.0"},"canonical_sha256":"81dc33cf04db49db36311fff9cdd8c669d233823360fbc108c6785b16c65f51f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:34:00.538124Z","signature_b64":"Lwsimil3eA8AMQhnae+zzCnbMoMdGy2cCAs+oTVG8OCr/BZRhbBkUhzKxQvgSw9UaPv2LxMj/+UwCpTy/V9oDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"81dc33cf04db49db36311fff9cdd8c669d233823360fbc108c6785b16c65f51f","last_reissued_at":"2026-05-18T03:34:00.537347Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:34:00.537347Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0401089","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":"2026-05-18T03:34:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9NmiqnzIm3KYBamzSXnDCSOKW6ZidF/b8k9qM7H6Z1VyCOKU/EyaX9pBHMhGcOheaKk2kXvx6Q/Z5RzIy4/rCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T22:28:41.036355Z"},"content_sha256":"7305dd4f3dde6b753e008eb103bc9bc896b16222a620086647cef8daa325679f","schema_version":"1.0","event_id":"sha256:7305dd4f3dde6b753e008eb103bc9bc896b16222a620086647cef8daa325679f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:QHODHTYE3NE5WNRRD77ZZXMMM2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Algebra of Binary Search Trees","license":"","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"F. Hivert, J.-C. Novelli, J.-Y. Thibon","submitted_at":"2004-01-09T10:18:43Z","abstract_excerpt":"We introduce a monoid structure on the set of binary search trees, by a process very similar to the construction of the plactic monoid, the Robinson-Schensted insertion being replaced by the binary search tree insertion. This leads to a new construction of the algebra of Planar Binary Trees of Loday-Ronco, defining it in the same way as Non-Commutative Symmetric Functions and Free Symmetric Functions. We briefly explain how the main known properties of the Loday-Ronco algebra can be described and proved with this combinatorial point of view, and then discuss it from a representation theoretica"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0401089","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":""},"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":"2026-05-18T03:34:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yx7ecfXouOumF5qZUYUXHLN3+HOIIydOz2bxZ11WEy/uKS4G5jPBdnqtUafs1zTIvklB/7EZD4OHfUicG05XDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T22:28:41.036724Z"},"content_sha256":"e9454e5cedcf1c079acaaca10fdb5505383aa01149a7ddb1132822407771e3db","schema_version":"1.0","event_id":"sha256:e9454e5cedcf1c079acaaca10fdb5505383aa01149a7ddb1132822407771e3db"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QHODHTYE3NE5WNRRD77ZZXMMM2/bundle.json","state_url":"https://pith.science/pith/QHODHTYE3NE5WNRRD77ZZXMMM2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QHODHTYE3NE5WNRRD77ZZXMMM2/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":"2026-05-28T22:28:41Z","links":{"resolver":"https://pith.science/pith/QHODHTYE3NE5WNRRD77ZZXMMM2","bundle":"https://pith.science/pith/QHODHTYE3NE5WNRRD77ZZXMMM2/bundle.json","state":"https://pith.science/pith/QHODHTYE3NE5WNRRD77ZZXMMM2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QHODHTYE3NE5WNRRD77ZZXMMM2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:QHODHTYE3NE5WNRRD77ZZXMMM2","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":"81378c225b08151986e1fed094bc09e97a7d92dcc2add3a67efb92a3550e7b77","cross_cats_sorted":[],"license":"","primary_cat":"math.CO","submitted_at":"2004-01-09T10:18:43Z","title_canon_sha256":"df03bc2fcc130da548186c5499bd81b06f30f2b759ceb4010bef5e2598f041e1"},"schema_version":"1.0","source":{"id":"math/0401089","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0401089","created_at":"2026-05-18T03:34:00Z"},{"alias_kind":"arxiv_version","alias_value":"math/0401089v2","created_at":"2026-05-18T03:34:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0401089","created_at":"2026-05-18T03:34:00Z"},{"alias_kind":"pith_short_12","alias_value":"QHODHTYE3NE5","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"QHODHTYE3NE5WNRR","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"QHODHTYE","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:e9454e5cedcf1c079acaaca10fdb5505383aa01149a7ddb1132822407771e3db","target":"graph","created_at":"2026-05-18T03:34:00Z","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 introduce a monoid structure on the set of binary search trees, by a process very similar to the construction of the plactic monoid, the Robinson-Schensted insertion being replaced by the binary search tree insertion. This leads to a new construction of the algebra of Planar Binary Trees of Loday-Ronco, defining it in the same way as Non-Commutative Symmetric Functions and Free Symmetric Functions. We briefly explain how the main known properties of the Loday-Ronco algebra can be described and proved with this combinatorial point of view, and then discuss it from a representation theoretica","authors_text":"F. Hivert, J.-C. Novelli, J.-Y. Thibon","cross_cats":[],"headline":"","license":"","primary_cat":"math.CO","submitted_at":"2004-01-09T10:18:43Z","title":"The Algebra of Binary Search Trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0401089","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":"sha256:7305dd4f3dde6b753e008eb103bc9bc896b16222a620086647cef8daa325679f","target":"record","created_at":"2026-05-18T03:34:00Z","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":"81378c225b08151986e1fed094bc09e97a7d92dcc2add3a67efb92a3550e7b77","cross_cats_sorted":[],"license":"","primary_cat":"math.CO","submitted_at":"2004-01-09T10:18:43Z","title_canon_sha256":"df03bc2fcc130da548186c5499bd81b06f30f2b759ceb4010bef5e2598f041e1"},"schema_version":"1.0","source":{"id":"math/0401089","kind":"arxiv","version":2}},"canonical_sha256":"81dc33cf04db49db36311fff9cdd8c669d233823360fbc108c6785b16c65f51f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"81dc33cf04db49db36311fff9cdd8c669d233823360fbc108c6785b16c65f51f","first_computed_at":"2026-05-18T03:34:00.537347Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:34:00.537347Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Lwsimil3eA8AMQhnae+zzCnbMoMdGy2cCAs+oTVG8OCr/BZRhbBkUhzKxQvgSw9UaPv2LxMj/+UwCpTy/V9oDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:34:00.538124Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0401089","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7305dd4f3dde6b753e008eb103bc9bc896b16222a620086647cef8daa325679f","sha256:e9454e5cedcf1c079acaaca10fdb5505383aa01149a7ddb1132822407771e3db"],"state_sha256":"221b3e91800692dc284820c4cd6bc989f24a36b06e21081f31e0df69766020ab"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xClDKCKPB8V/tRJKJf7IW30iUlFHjEJ+bZuqGDIrvak1Ax5J9tnOrGYv8yNTekktFEbhMYVZKEb4Nn87+ERGAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T22:28:41.038938Z","bundle_sha256":"fe2245c9a962edf1c42b9ff8061f423b4087a847b3d9e361a9a798eca888387f"}}