{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:WTMI2PD35O35O5ZWSNKEANCWTM","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":"7603c9533509a543c0c457b2564219ccbf93099f6fa8c70fcbe1c95ba9cf3c12","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2009-09-16T14:17:11Z","title_canon_sha256":"3cc8637137ed3ac03c2ac37a87e48d4b8bcb5e246b4fa33373d27607f2ebc2c8"},"schema_version":"1.0","source":{"id":"0909.3023","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.3023","created_at":"2026-05-18T02:41:51Z"},{"alias_kind":"arxiv_version","alias_value":"0909.3023v1","created_at":"2026-05-18T02:41:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.3023","created_at":"2026-05-18T02:41:51Z"},{"alias_kind":"pith_short_12","alias_value":"WTMI2PD35O35","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"WTMI2PD35O35O5ZW","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"WTMI2PD3","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:3774be6a94c39efa1297db5f970c6732d0fdb69422110b2ce90b04ca46159ab9","target":"graph","created_at":"2026-05-18T02:41:51Z","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 study topology of configuration spaces of planar linkages having one leg of variable length. Such telescopic legs are common in modern robotics where they are used for shock absorbtion and serve a variety of other purposes. Using a Morse theoretic technique, we compute explicitly, in terms of the metric data, the Betti numbers of configuration spaces of these mechanisms.","authors_text":"Michael Farber, Viktor Fromm","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2009-09-16T14:17:11Z","title":"Homology of planar telescopic linkages"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.3023","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:c7f403945c731096d6a13e21a6141d29ed37769c6ae639515fd961daaca6f72c","target":"record","created_at":"2026-05-18T02:41:51Z","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":"7603c9533509a543c0c457b2564219ccbf93099f6fa8c70fcbe1c95ba9cf3c12","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2009-09-16T14:17:11Z","title_canon_sha256":"3cc8637137ed3ac03c2ac37a87e48d4b8bcb5e246b4fa33373d27607f2ebc2c8"},"schema_version":"1.0","source":{"id":"0909.3023","kind":"arxiv","version":1}},"canonical_sha256":"b4d88d3c7bebb7d7773693544034569b244ba5da4efadedd92d92f9989292612","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b4d88d3c7bebb7d7773693544034569b244ba5da4efadedd92d92f9989292612","first_computed_at":"2026-05-18T02:41:51.163582Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:51.163582Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+eJY3fgCQnaQW6e2RtSowauihEwn/CoKTXrYJ/Qfv4XwvDfqXqsDKQZMBKlmXDO/f7h36ztQVuQBBKI4wePCBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:51.164046Z","signed_message":"canonical_sha256_bytes"},"source_id":"0909.3023","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c7f403945c731096d6a13e21a6141d29ed37769c6ae639515fd961daaca6f72c","sha256:3774be6a94c39efa1297db5f970c6732d0fdb69422110b2ce90b04ca46159ab9"],"state_sha256":"f52d43a9ec48221ea45c3cf7b450d682acea19f92875b4390a5020bf67750b41"}