{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:EZQGZAOLGAJ43Q3KRU5JIUAE2Y","short_pith_number":"pith:EZQGZAOL","schema_version":"1.0","canonical_sha256":"26606c81cb3013cdc36a8d3a945004d60a7e2e76699f60387d360875735958d6","source":{"kind":"arxiv","id":"1407.4993","version":1},"attestation_state":"computed","paper":{"title":"Intersection homology of linkage spaces in odd dimensional Euclidean space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Dirk Schuetz","submitted_at":"2014-07-18T13:41:52Z","abstract_excerpt":"We consider the moduli spaces $\\mathcal{M}_d(\\ell)$ of a closed linkage with $n$ links and prescribed lengths $\\ell\\in \\mathbb{R}^n$ in $d$-dimensional Euclidean space. For $d>3$ these spaces are no longer manifolds generically, but they have the structure of a pseudomanifold.\n  We use intersection homology to assign a ring to these spaces that can be used to distinguish the homeomorphism types of $\\mathcal{M}_d(\\ell)$ for a large class of length vectors. These rings behave rather differently depending on whether $d$ is even or odd, with the even case having been treated in an earlier paper. T"},"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":"1407.4993","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-07-18T13:41:52Z","cross_cats_sorted":[],"title_canon_sha256":"8a992085f5078cd0a330c5868e17acc595c94e4341417cab9c6c2f0d64304d4d","abstract_canon_sha256":"4aa9d889e2b28d99d070a4012f2d6d1a24121874d74edbef2c46d0b04a37f61e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:30.751423Z","signature_b64":"34XdtmF5P6/DLSwCI5NMBsfxm4G+msXhJELVF37fL7W9NpW4xKq1SepwSgZnw1BzdECaxCT5MD6w/zWve3PiDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"26606c81cb3013cdc36a8d3a945004d60a7e2e76699f60387d360875735958d6","last_reissued_at":"2026-05-18T01:19:30.750944Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:30.750944Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Intersection homology of linkage spaces in odd dimensional Euclidean space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Dirk Schuetz","submitted_at":"2014-07-18T13:41:52Z","abstract_excerpt":"We consider the moduli spaces $\\mathcal{M}_d(\\ell)$ of a closed linkage with $n$ links and prescribed lengths $\\ell\\in \\mathbb{R}^n$ in $d$-dimensional Euclidean space. For $d>3$ these spaces are no longer manifolds generically, but they have the structure of a pseudomanifold.\n  We use intersection homology to assign a ring to these spaces that can be used to distinguish the homeomorphism types of $\\mathcal{M}_d(\\ell)$ for a large class of length vectors. These rings behave rather differently depending on whether $d$ is even or odd, with the even case having been treated in an earlier paper. T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4993","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1407.4993","created_at":"2026-05-18T01:19:30.751013+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.4993v1","created_at":"2026-05-18T01:19:30.751013+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.4993","created_at":"2026-05-18T01:19:30.751013+00:00"},{"alias_kind":"pith_short_12","alias_value":"EZQGZAOLGAJ4","created_at":"2026-05-18T12:28:28.263976+00:00"},{"alias_kind":"pith_short_16","alias_value":"EZQGZAOLGAJ43Q3K","created_at":"2026-05-18T12:28:28.263976+00:00"},{"alias_kind":"pith_short_8","alias_value":"EZQGZAOL","created_at":"2026-05-18T12:28:28.263976+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/EZQGZAOLGAJ43Q3KRU5JIUAE2Y","json":"https://pith.science/pith/EZQGZAOLGAJ43Q3KRU5JIUAE2Y.json","graph_json":"https://pith.science/api/pith-number/EZQGZAOLGAJ43Q3KRU5JIUAE2Y/graph.json","events_json":"https://pith.science/api/pith-number/EZQGZAOLGAJ43Q3KRU5JIUAE2Y/events.json","paper":"https://pith.science/paper/EZQGZAOL"},"agent_actions":{"view_html":"https://pith.science/pith/EZQGZAOLGAJ43Q3KRU5JIUAE2Y","download_json":"https://pith.science/pith/EZQGZAOLGAJ43Q3KRU5JIUAE2Y.json","view_paper":"https://pith.science/paper/EZQGZAOL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.4993&json=true","fetch_graph":"https://pith.science/api/pith-number/EZQGZAOLGAJ43Q3KRU5JIUAE2Y/graph.json","fetch_events":"https://pith.science/api/pith-number/EZQGZAOLGAJ43Q3KRU5JIUAE2Y/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EZQGZAOLGAJ43Q3KRU5JIUAE2Y/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EZQGZAOLGAJ43Q3KRU5JIUAE2Y/action/storage_attestation","attest_author":"https://pith.science/pith/EZQGZAOLGAJ43Q3KRU5JIUAE2Y/action/author_attestation","sign_citation":"https://pith.science/pith/EZQGZAOLGAJ43Q3KRU5JIUAE2Y/action/citation_signature","submit_replication":"https://pith.science/pith/EZQGZAOLGAJ43Q3KRU5JIUAE2Y/action/replication_record"}},"created_at":"2026-05-18T01:19:30.751013+00:00","updated_at":"2026-05-18T01:19:30.751013+00:00"}