{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:EWKJTXZAIOOVWMWKHJYMLP4MNU","short_pith_number":"pith:EWKJTXZA","schema_version":"1.0","canonical_sha256":"259499df20439d5b32ca3a70c5bf8c6d3d0eb0797a7a8dd0bc644ce1dc4859b3","source":{"kind":"arxiv","id":"1603.04109","version":1},"attestation_state":"computed","paper":{"title":"Combinatorial rigidity of Incidence systems and Application to Dictionary learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Meera Sitharam, Menghan Wang, Mohamad Tarifi","submitted_at":"2016-03-14T01:40:40Z","abstract_excerpt":"Given a hypergraph $H$ with $m$ hyperedges and a set $Q$ of $m$ \\emph{pinning subspaces}, i.e.\\ globally fixed subspaces in Euclidean space $\\mathbb{R}^d$, a \\emph{pinned subspace-incidence system} is the pair $(H, Q)$, with the constraint that each pinning subspace in $Q$ is contained in the subspace spanned by the point realizations in $\\mathbb{R}^d$ of vertices of the corresponding hyperedge of $H$. This paper provides a combinatorial characterization of pinned subspace-incidence systems that are \\emph{minimally rigid}, i.e.\\ those systems that are guaranteed to generically yield a locally "},"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":"1603.04109","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2016-03-14T01:40:40Z","cross_cats_sorted":[],"title_canon_sha256":"41e0d16ce509fde62d2ff677429a9cfb7cfcb8a0584a545e191be53a446103a4","abstract_canon_sha256":"93a5d78d2593f895517cccebe8ac62fb043f91f429ca9ca287d8fe198687fcb7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:09.413916Z","signature_b64":"AWFNgfv194y3bGwJu0QGe9aB/Wlp8YYf3ZD5XrrciZcYMJuEundT8as65CtcawdP3QHXag3D9NAscWx4ecasCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"259499df20439d5b32ca3a70c5bf8c6d3d0eb0797a7a8dd0bc644ce1dc4859b3","last_reissued_at":"2026-05-18T01:19:09.413376Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:09.413376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Combinatorial rigidity of Incidence systems and Application to Dictionary learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Meera Sitharam, Menghan Wang, Mohamad Tarifi","submitted_at":"2016-03-14T01:40:40Z","abstract_excerpt":"Given a hypergraph $H$ with $m$ hyperedges and a set $Q$ of $m$ \\emph{pinning subspaces}, i.e.\\ globally fixed subspaces in Euclidean space $\\mathbb{R}^d$, a \\emph{pinned subspace-incidence system} is the pair $(H, Q)$, with the constraint that each pinning subspace in $Q$ is contained in the subspace spanned by the point realizations in $\\mathbb{R}^d$ of vertices of the corresponding hyperedge of $H$. This paper provides a combinatorial characterization of pinned subspace-incidence systems that are \\emph{minimally rigid}, i.e.\\ those systems that are guaranteed to generically yield a locally "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04109","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":"1603.04109","created_at":"2026-05-18T01:19:09.413447+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.04109v1","created_at":"2026-05-18T01:19:09.413447+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.04109","created_at":"2026-05-18T01:19:09.413447+00:00"},{"alias_kind":"pith_short_12","alias_value":"EWKJTXZAIOOV","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_16","alias_value":"EWKJTXZAIOOVWMWK","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_8","alias_value":"EWKJTXZA","created_at":"2026-05-18T12:30:15.759754+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/EWKJTXZAIOOVWMWKHJYMLP4MNU","json":"https://pith.science/pith/EWKJTXZAIOOVWMWKHJYMLP4MNU.json","graph_json":"https://pith.science/api/pith-number/EWKJTXZAIOOVWMWKHJYMLP4MNU/graph.json","events_json":"https://pith.science/api/pith-number/EWKJTXZAIOOVWMWKHJYMLP4MNU/events.json","paper":"https://pith.science/paper/EWKJTXZA"},"agent_actions":{"view_html":"https://pith.science/pith/EWKJTXZAIOOVWMWKHJYMLP4MNU","download_json":"https://pith.science/pith/EWKJTXZAIOOVWMWKHJYMLP4MNU.json","view_paper":"https://pith.science/paper/EWKJTXZA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.04109&json=true","fetch_graph":"https://pith.science/api/pith-number/EWKJTXZAIOOVWMWKHJYMLP4MNU/graph.json","fetch_events":"https://pith.science/api/pith-number/EWKJTXZAIOOVWMWKHJYMLP4MNU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EWKJTXZAIOOVWMWKHJYMLP4MNU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EWKJTXZAIOOVWMWKHJYMLP4MNU/action/storage_attestation","attest_author":"https://pith.science/pith/EWKJTXZAIOOVWMWKHJYMLP4MNU/action/author_attestation","sign_citation":"https://pith.science/pith/EWKJTXZAIOOVWMWKHJYMLP4MNU/action/citation_signature","submit_replication":"https://pith.science/pith/EWKJTXZAIOOVWMWKHJYMLP4MNU/action/replication_record"}},"created_at":"2026-05-18T01:19:09.413447+00:00","updated_at":"2026-05-18T01:19:09.413447+00:00"}