{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:YXORRUTJPU74KRBWOEI6D37TDU","short_pith_number":"pith:YXORRUTJ","canonical_record":{"source":{"id":"1707.03976","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.RO","submitted_at":"2017-07-13T04:30:34Z","cross_cats_sorted":[],"title_canon_sha256":"4fd180cd65e07309e2375773362370b5da92f44a23eb6b7b871cb735dd5ad812","abstract_canon_sha256":"a86c0567ec0a629ec7aee8a504ef1591519f72667c2609cffd0cf83a80f26ab2"},"schema_version":"1.0"},"canonical_sha256":"c5dd18d2697d3fc544367111e1eff31d08cdcf3f1165c7c7a2f3caa324d70359","source":{"kind":"arxiv","id":"1707.03976","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.03976","created_at":"2026-05-18T00:40:22Z"},{"alias_kind":"arxiv_version","alias_value":"1707.03976v1","created_at":"2026-05-18T00:40:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.03976","created_at":"2026-05-18T00:40:22Z"},{"alias_kind":"pith_short_12","alias_value":"YXORRUTJPU74","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"YXORRUTJPU74KRBW","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"YXORRUTJ","created_at":"2026-05-18T12:31:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:YXORRUTJPU74KRBWOEI6D37TDU","target":"record","payload":{"canonical_record":{"source":{"id":"1707.03976","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.RO","submitted_at":"2017-07-13T04:30:34Z","cross_cats_sorted":[],"title_canon_sha256":"4fd180cd65e07309e2375773362370b5da92f44a23eb6b7b871cb735dd5ad812","abstract_canon_sha256":"a86c0567ec0a629ec7aee8a504ef1591519f72667c2609cffd0cf83a80f26ab2"},"schema_version":"1.0"},"canonical_sha256":"c5dd18d2697d3fc544367111e1eff31d08cdcf3f1165c7c7a2f3caa324d70359","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:22.955976Z","signature_b64":"GDhB0uvd2G5ERiwWeKyGEhlrJMmn+DfmvNO59/9m19TEJ5oTdKdZRgqQ0t1yxIG2NtXEN1hhAsb8znPr9GESAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5dd18d2697d3fc544367111e1eff31d08cdcf3f1165c7c7a2f3caa324d70359","last_reissued_at":"2026-05-18T00:40:22.955221Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:22.955221Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.03976","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":"2026-05-18T00:40:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WpIZ2x0usGzt6hZCFOBSKjtvkq22B/6duPhrS8+Sxmd7zlJHOCmXRxFrW35KvDgU6Aw99LXqwWYK2t1oN2cYDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T06:22:37.210898Z"},"content_sha256":"603c7ac13eef24841f51633ead53850677d955b19db45955f1a56232b590529d","schema_version":"1.0","event_id":"sha256:603c7ac13eef24841f51633ead53850677d955b19db45955f1a56232b590529d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:YXORRUTJPU74KRBWOEI6D37TDU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic Optimality of Rapidly Exploring Random Tree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.RO","authors_text":"Debasish Ghose, Sundaram Suresh, Titas Bera","submitted_at":"2017-07-13T04:30:34Z","abstract_excerpt":"In this paper we investigate the asymptotic optimality property of a randomized sampling based motion planner, namely RRT. We prove that a RRT planner is not an asymptotically optimal motion planner. Our result, while being consistent with similar results which exist in the literature, however, brings out an important characteristics of a RRT planner. We show that the degree distribution of the tree vertices follows a power law in an asymptotic sense. A simulation result is presented to support the theoretical claim. Based on these results we also try to establish a simple necessary condition "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.03976","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":""},"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":"2026-05-18T00:40:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R4fYfivLO9KoDzC2tqZ4MH+TEdRMrc3MnqfnLKThcF/FIxDP9vq8pmniLEzW5cFP3PgR32zy7Dt0zDddY8Z9BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T06:22:37.211239Z"},"content_sha256":"d8bd56a695da711c41c32a862117c7fb34ecc6e81c4dfe7cfffad0012bce55d4","schema_version":"1.0","event_id":"sha256:d8bd56a695da711c41c32a862117c7fb34ecc6e81c4dfe7cfffad0012bce55d4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YXORRUTJPU74KRBWOEI6D37TDU/bundle.json","state_url":"https://pith.science/pith/YXORRUTJPU74KRBWOEI6D37TDU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YXORRUTJPU74KRBWOEI6D37TDU/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":"2026-05-28T06:22:37Z","links":{"resolver":"https://pith.science/pith/YXORRUTJPU74KRBWOEI6D37TDU","bundle":"https://pith.science/pith/YXORRUTJPU74KRBWOEI6D37TDU/bundle.json","state":"https://pith.science/pith/YXORRUTJPU74KRBWOEI6D37TDU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YXORRUTJPU74KRBWOEI6D37TDU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:YXORRUTJPU74KRBWOEI6D37TDU","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":"a86c0567ec0a629ec7aee8a504ef1591519f72667c2609cffd0cf83a80f26ab2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.RO","submitted_at":"2017-07-13T04:30:34Z","title_canon_sha256":"4fd180cd65e07309e2375773362370b5da92f44a23eb6b7b871cb735dd5ad812"},"schema_version":"1.0","source":{"id":"1707.03976","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.03976","created_at":"2026-05-18T00:40:22Z"},{"alias_kind":"arxiv_version","alias_value":"1707.03976v1","created_at":"2026-05-18T00:40:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.03976","created_at":"2026-05-18T00:40:22Z"},{"alias_kind":"pith_short_12","alias_value":"YXORRUTJPU74","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"YXORRUTJPU74KRBW","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"YXORRUTJ","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:d8bd56a695da711c41c32a862117c7fb34ecc6e81c4dfe7cfffad0012bce55d4","target":"graph","created_at":"2026-05-18T00:40:22Z","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":"In this paper we investigate the asymptotic optimality property of a randomized sampling based motion planner, namely RRT. We prove that a RRT planner is not an asymptotically optimal motion planner. Our result, while being consistent with similar results which exist in the literature, however, brings out an important characteristics of a RRT planner. We show that the degree distribution of the tree vertices follows a power law in an asymptotic sense. A simulation result is presented to support the theoretical claim. Based on these results we also try to establish a simple necessary condition ","authors_text":"Debasish Ghose, Sundaram Suresh, Titas Bera","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.RO","submitted_at":"2017-07-13T04:30:34Z","title":"Asymptotic Optimality of Rapidly Exploring Random Tree"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.03976","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":"sha256:603c7ac13eef24841f51633ead53850677d955b19db45955f1a56232b590529d","target":"record","created_at":"2026-05-18T00:40:22Z","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":"a86c0567ec0a629ec7aee8a504ef1591519f72667c2609cffd0cf83a80f26ab2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.RO","submitted_at":"2017-07-13T04:30:34Z","title_canon_sha256":"4fd180cd65e07309e2375773362370b5da92f44a23eb6b7b871cb735dd5ad812"},"schema_version":"1.0","source":{"id":"1707.03976","kind":"arxiv","version":1}},"canonical_sha256":"c5dd18d2697d3fc544367111e1eff31d08cdcf3f1165c7c7a2f3caa324d70359","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5dd18d2697d3fc544367111e1eff31d08cdcf3f1165c7c7a2f3caa324d70359","first_computed_at":"2026-05-18T00:40:22.955221Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:22.955221Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GDhB0uvd2G5ERiwWeKyGEhlrJMmn+DfmvNO59/9m19TEJ5oTdKdZRgqQ0t1yxIG2NtXEN1hhAsb8znPr9GESAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:22.955976Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.03976","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:603c7ac13eef24841f51633ead53850677d955b19db45955f1a56232b590529d","sha256:d8bd56a695da711c41c32a862117c7fb34ecc6e81c4dfe7cfffad0012bce55d4"],"state_sha256":"98f34c6a7e3c69b66adcfa5fc3503d809f3333b437968aed6fcf6095b58188f2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5iF+rZtSd9yfHW9GoC8SxOYTseGZqPXSIHyww0mZngNaufbIlPuGibS1CKd8cnenWnBzY0V5wvlMGc/+joXEBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T06:22:37.213177Z","bundle_sha256":"4c5cb363daf112592557ca2e982a4b438727c9fa2c957ef3c88f002fb47b95a7"}}