{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:ULN6OJX64QKGQSPP4B6E4CLQOL","short_pith_number":"pith:ULN6OJX6","schema_version":"1.0","canonical_sha256":"a2dbe726fee4146849efe07c4e097072d290621e4979770b6b58436cc2b0de8b","source":{"kind":"arxiv","id":"2501.18229","version":1},"attestation_state":"computed","paper":{"title":"GPD: Guided Polynomial Diffusion for Motion Planning","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.RO","authors_text":"Ajit Srikanth, Arun Singh, Brojeshwar Bhowmick, Kallol Saha, Madhava Krishna, Parth Mahanjan, Pawan Wadhwani, Pranjal Paul, Vishal Mandadi","submitted_at":"2025-01-30T09:35:17Z","abstract_excerpt":"Diffusion-based motion planners are becoming popular due to their well-established performance improvements, stemming from sample diversity and the ease of incorporating new constraints directly during inference. However, a primary limitation of the diffusion process is the requirement for a substantial number of denoising steps, especially when the denoising process is coupled with gradient-based guidance. In this paper, we introduce, diffusion in the parametric space of trajectories, where the parameters are represented as Bernstein coefficients. We show that this representation greatly impr"},"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":"2501.18229","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.RO","submitted_at":"2025-01-30T09:35:17Z","cross_cats_sorted":[],"title_canon_sha256":"5f03f4eafa0d20b679f5f0b4f7a510f4a993c9bf5a8dedfa66cd3a0407468225","abstract_canon_sha256":"e5de35adaf35a3e84ed904b408dfbcac4c2da82e2b4c8216ff28b0e3e6bec69f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:07:31.339404Z","signature_b64":"jJRH1THZzHAUUB+aiUjYJbJp+NJnPzYnEU/dzy6KHTqdhPJaF1PSK0tq8jiSBbZeS1oJANg44/WU9XAHYl6wAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a2dbe726fee4146849efe07c4e097072d290621e4979770b6b58436cc2b0de8b","last_reissued_at":"2026-07-05T10:07:31.338754Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:07:31.338754Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"GPD: Guided Polynomial Diffusion for Motion Planning","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.RO","authors_text":"Ajit Srikanth, Arun Singh, Brojeshwar Bhowmick, Kallol Saha, Madhava Krishna, Parth Mahanjan, Pawan Wadhwani, Pranjal Paul, Vishal Mandadi","submitted_at":"2025-01-30T09:35:17Z","abstract_excerpt":"Diffusion-based motion planners are becoming popular due to their well-established performance improvements, stemming from sample diversity and the ease of incorporating new constraints directly during inference. However, a primary limitation of the diffusion process is the requirement for a substantial number of denoising steps, especially when the denoising process is coupled with gradient-based guidance. In this paper, we introduce, diffusion in the parametric space of trajectories, where the parameters are represented as Bernstein coefficients. We show that this representation greatly impr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.18229","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/2501.18229/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":"2501.18229","created_at":"2026-07-05T10:07:31.338815+00:00"},{"alias_kind":"arxiv_version","alias_value":"2501.18229v1","created_at":"2026-07-05T10:07:31.338815+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.18229","created_at":"2026-07-05T10:07:31.338815+00:00"},{"alias_kind":"pith_short_12","alias_value":"ULN6OJX64QKG","created_at":"2026-07-05T10:07:31.338815+00:00"},{"alias_kind":"pith_short_16","alias_value":"ULN6OJX64QKGQSPP","created_at":"2026-07-05T10:07:31.338815+00:00"},{"alias_kind":"pith_short_8","alias_value":"ULN6OJX6","created_at":"2026-07-05T10:07:31.338815+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/ULN6OJX64QKGQSPP4B6E4CLQOL","json":"https://pith.science/pith/ULN6OJX64QKGQSPP4B6E4CLQOL.json","graph_json":"https://pith.science/api/pith-number/ULN6OJX64QKGQSPP4B6E4CLQOL/graph.json","events_json":"https://pith.science/api/pith-number/ULN6OJX64QKGQSPP4B6E4CLQOL/events.json","paper":"https://pith.science/paper/ULN6OJX6"},"agent_actions":{"view_html":"https://pith.science/pith/ULN6OJX64QKGQSPP4B6E4CLQOL","download_json":"https://pith.science/pith/ULN6OJX64QKGQSPP4B6E4CLQOL.json","view_paper":"https://pith.science/paper/ULN6OJX6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2501.18229&json=true","fetch_graph":"https://pith.science/api/pith-number/ULN6OJX64QKGQSPP4B6E4CLQOL/graph.json","fetch_events":"https://pith.science/api/pith-number/ULN6OJX64QKGQSPP4B6E4CLQOL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ULN6OJX64QKGQSPP4B6E4CLQOL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ULN6OJX64QKGQSPP4B6E4CLQOL/action/storage_attestation","attest_author":"https://pith.science/pith/ULN6OJX64QKGQSPP4B6E4CLQOL/action/author_attestation","sign_citation":"https://pith.science/pith/ULN6OJX64QKGQSPP4B6E4CLQOL/action/citation_signature","submit_replication":"https://pith.science/pith/ULN6OJX64QKGQSPP4B6E4CLQOL/action/replication_record"}},"created_at":"2026-07-05T10:07:31.338815+00:00","updated_at":"2026-07-05T10:07:31.338815+00:00"}