{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:OSBUOVR5HBSQUSS6A6VXR6ERJ3","short_pith_number":"pith:OSBUOVR5","canonical_record":{"source":{"id":"2203.03961","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2022-03-08T09:35:01Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"9e8b0aa647147bdb155398f3b61ee5eef0f66f74cbda0b292838648dc00be0dc","abstract_canon_sha256":"9856b6214597ea7aea27c007f20f210256bf69f3911af7131c279421c2261529"},"schema_version":"1.0"},"canonical_sha256":"748347563d38650a4a5e07ab78f8914ec847fdf85cef041e0fac1c568aca8f0b","source":{"kind":"arxiv","id":"2203.03961","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.03961","created_at":"2026-07-05T06:18:15Z"},{"alias_kind":"arxiv_version","alias_value":"2203.03961v2","created_at":"2026-07-05T06:18:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.03961","created_at":"2026-07-05T06:18:15Z"},{"alias_kind":"pith_short_12","alias_value":"OSBUOVR5HBSQ","created_at":"2026-07-05T06:18:15Z"},{"alias_kind":"pith_short_16","alias_value":"OSBUOVR5HBSQUSS6","created_at":"2026-07-05T06:18:15Z"},{"alias_kind":"pith_short_8","alias_value":"OSBUOVR5","created_at":"2026-07-05T06:18:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:OSBUOVR5HBSQUSS6A6VXR6ERJ3","target":"record","payload":{"canonical_record":{"source":{"id":"2203.03961","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2022-03-08T09:35:01Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"9e8b0aa647147bdb155398f3b61ee5eef0f66f74cbda0b292838648dc00be0dc","abstract_canon_sha256":"9856b6214597ea7aea27c007f20f210256bf69f3911af7131c279421c2261529"},"schema_version":"1.0"},"canonical_sha256":"748347563d38650a4a5e07ab78f8914ec847fdf85cef041e0fac1c568aca8f0b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:18:15.820401Z","signature_b64":"kCydgLIGNYXOxSZvr3xpK2vQF2WUyaM68mFDAFspG1W7kNAuR1h/vZSdOFtvxDMIQe73L5VyOj/j4juhmCL5DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"748347563d38650a4a5e07ab78f8914ec847fdf85cef041e0fac1c568aca8f0b","last_reissued_at":"2026-07-05T06:18:15.819899Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:18:15.819899Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2203.03961","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":"2026-07-05T06:18:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a1BIdH+doHCFtPGTt3xCjidwWGV2B2Q3m0OzifEBCqnuetfC9mcgiVqLYpCxJB+DKBcqLIRkV01diRM7Zj7zCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T18:52:25.918198Z"},"content_sha256":"20ebf9159cc2ef2988d9aa77e50c77b81237fcef56560ac546b6b470e1637131","schema_version":"1.0","event_id":"sha256:20ebf9159cc2ef2988d9aa77e50c77b81237fcef56560ac546b6b470e1637131"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:OSBUOVR5HBSQUSS6A6VXR6ERJ3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Computing roadmaps in unbounded smooth real algebraic sets I: connectivity results","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"cs.SC","authors_text":"\\'Eric Schost, Mohab Safey El Din (PolSys), R\\'emi Pr\\'ebet (PolSys)","submitted_at":"2022-03-08T09:35:01Z","abstract_excerpt":"Answering connectivity queries in real algebraic sets is a fundamental problem in effective real algebraic geometry that finds many applications in e.g. robotics where motion planning issues are topical. This computational problem is tackled through the computation of so-called roadmaps which are real algebraic subsets of the set V under study, of dimension at most one, and which have a connected intersection with all semi-algebraically connected components of V. Algorithms for computing roadmaps rely on statements establishing connectivity properties of some well-chosen subsets of V , assumin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.03961","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/2203.03961/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":"2026-07-05T06:18:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nxT99uKoInxC4yTeL1tsY23zHYQKBYNGt8pkwmmUOik1vzBbwUZ7Ek/EHF8d6PpuGgzSWEUhqRGwwBqAi5UnDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T18:52:25.919120Z"},"content_sha256":"132cf2305c84c456625df1c08dcc834436b1cce18929123ab98e5fa117dafeef","schema_version":"1.0","event_id":"sha256:132cf2305c84c456625df1c08dcc834436b1cce18929123ab98e5fa117dafeef"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OSBUOVR5HBSQUSS6A6VXR6ERJ3/bundle.json","state_url":"https://pith.science/pith/OSBUOVR5HBSQUSS6A6VXR6ERJ3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OSBUOVR5HBSQUSS6A6VXR6ERJ3/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":"2026-08-18T18:52:25Z","links":{"resolver":"https://pith.science/pith/OSBUOVR5HBSQUSS6A6VXR6ERJ3","bundle":"https://pith.science/pith/OSBUOVR5HBSQUSS6A6VXR6ERJ3/bundle.json","state":"https://pith.science/pith/OSBUOVR5HBSQUSS6A6VXR6ERJ3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OSBUOVR5HBSQUSS6A6VXR6ERJ3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:OSBUOVR5HBSQUSS6A6VXR6ERJ3","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":"9856b6214597ea7aea27c007f20f210256bf69f3911af7131c279421c2261529","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2022-03-08T09:35:01Z","title_canon_sha256":"9e8b0aa647147bdb155398f3b61ee5eef0f66f74cbda0b292838648dc00be0dc"},"schema_version":"1.0","source":{"id":"2203.03961","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.03961","created_at":"2026-07-05T06:18:15Z"},{"alias_kind":"arxiv_version","alias_value":"2203.03961v2","created_at":"2026-07-05T06:18:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.03961","created_at":"2026-07-05T06:18:15Z"},{"alias_kind":"pith_short_12","alias_value":"OSBUOVR5HBSQ","created_at":"2026-07-05T06:18:15Z"},{"alias_kind":"pith_short_16","alias_value":"OSBUOVR5HBSQUSS6","created_at":"2026-07-05T06:18:15Z"},{"alias_kind":"pith_short_8","alias_value":"OSBUOVR5","created_at":"2026-07-05T06:18:15Z"}],"graph_snapshots":[{"event_id":"sha256:132cf2305c84c456625df1c08dcc834436b1cce18929123ab98e5fa117dafeef","target":"graph","created_at":"2026-07-05T06:18:15Z","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/2203.03961/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Answering connectivity queries in real algebraic sets is a fundamental problem in effective real algebraic geometry that finds many applications in e.g. robotics where motion planning issues are topical. This computational problem is tackled through the computation of so-called roadmaps which are real algebraic subsets of the set V under study, of dimension at most one, and which have a connected intersection with all semi-algebraically connected components of V. Algorithms for computing roadmaps rely on statements establishing connectivity properties of some well-chosen subsets of V , assumin","authors_text":"\\'Eric Schost, Mohab Safey El Din (PolSys), R\\'emi Pr\\'ebet (PolSys)","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2022-03-08T09:35:01Z","title":"Computing roadmaps in unbounded smooth real algebraic sets I: connectivity results"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.03961","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":"sha256:20ebf9159cc2ef2988d9aa77e50c77b81237fcef56560ac546b6b470e1637131","target":"record","created_at":"2026-07-05T06:18:15Z","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":"9856b6214597ea7aea27c007f20f210256bf69f3911af7131c279421c2261529","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2022-03-08T09:35:01Z","title_canon_sha256":"9e8b0aa647147bdb155398f3b61ee5eef0f66f74cbda0b292838648dc00be0dc"},"schema_version":"1.0","source":{"id":"2203.03961","kind":"arxiv","version":2}},"canonical_sha256":"748347563d38650a4a5e07ab78f8914ec847fdf85cef041e0fac1c568aca8f0b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"748347563d38650a4a5e07ab78f8914ec847fdf85cef041e0fac1c568aca8f0b","first_computed_at":"2026-07-05T06:18:15.819899Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:18:15.819899Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kCydgLIGNYXOxSZvr3xpK2vQF2WUyaM68mFDAFspG1W7kNAuR1h/vZSdOFtvxDMIQe73L5VyOj/j4juhmCL5DQ==","signature_status":"signed_v1","signed_at":"2026-07-05T06:18:15.820401Z","signed_message":"canonical_sha256_bytes"},"source_id":"2203.03961","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:20ebf9159cc2ef2988d9aa77e50c77b81237fcef56560ac546b6b470e1637131","sha256:132cf2305c84c456625df1c08dcc834436b1cce18929123ab98e5fa117dafeef"],"state_sha256":"772fba37aae2b19521db3b9d032f184de888e7d35afdc0d48a05a597291ea557"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ndoIDDLJF5lO5w7F8ljN2OC2rttD1NDIJu4y9eGbvjlAiVQKr8L8J2+M2bxDYFH6lism6gwO52wzOeZvUp7sCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T18:52:25.923649Z","bundle_sha256":"72cf402fd4ffb9f191d610c381b2567113744bcbfe6639e0943a9a73fdd26041"}}