{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:K6A5RMC2UTQGSTBNBWABZ2JMQI","short_pith_number":"pith:K6A5RMC2","schema_version":"1.0","canonical_sha256":"5781d8b05aa4e0694c2d0d801ce92c823dce32ae55e43df8291a1f778c55942a","source":{"kind":"arxiv","id":"1903.10386","version":1},"attestation_state":"computed","paper":{"title":"Lipschitz property for systems of linear mappings and bilinear forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Abdullah Alazemi, Carlos M. da Fonseca, Milica An{\\dj}eli\\'c, Vladimir V. Sergeichuk","submitted_at":"2019-03-25T15:08:20Z","abstract_excerpt":"Let G be a graph with undirected and directed edges. Its representation is given by assigning a vector space to each vertex, a bilinear form on the corresponding vector spaces to each directed edge, and a linear map to each directed edge. Two representations A and A' of G are called isomorphic if there is a system of linear bijections between the vector spaces corresponding to the same vertices that transforms A to A'. We prove that if two representations are isomorphic and close to each other, then their isomorphism can be chosen close to the identity."},"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":"1903.10386","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-03-25T15:08:20Z","cross_cats_sorted":[],"title_canon_sha256":"e5aab8bca91bc50b6691b30f87dacdb5b6ec0dc2fe18a5b74c61b7ad96488c5e","abstract_canon_sha256":"8d8b2d83e6a9a5aa1391103a82b0347f5d6e1fb41e2ab3cc27f9eb9714b13a52"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:29.620247Z","signature_b64":"Ac1AWC3uiMwDTRPG0tvIPUqMVn5eykC/2zcgE54rfwYRetEEKNYZQobsdDXcA1s0b7SubNOu/oKdpxBmTtrVBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5781d8b05aa4e0694c2d0d801ce92c823dce32ae55e43df8291a1f778c55942a","last_reissued_at":"2026-05-17T23:50:29.619641Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:29.619641Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lipschitz property for systems of linear mappings and bilinear forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Abdullah Alazemi, Carlos M. da Fonseca, Milica An{\\dj}eli\\'c, Vladimir V. Sergeichuk","submitted_at":"2019-03-25T15:08:20Z","abstract_excerpt":"Let G be a graph with undirected and directed edges. Its representation is given by assigning a vector space to each vertex, a bilinear form on the corresponding vector spaces to each directed edge, and a linear map to each directed edge. Two representations A and A' of G are called isomorphic if there is a system of linear bijections between the vector spaces corresponding to the same vertices that transforms A to A'. We prove that if two representations are isomorphic and close to each other, then their isomorphism can be chosen close to the identity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.10386","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":"1903.10386","created_at":"2026-05-17T23:50:29.619714+00:00"},{"alias_kind":"arxiv_version","alias_value":"1903.10386v1","created_at":"2026-05-17T23:50:29.619714+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.10386","created_at":"2026-05-17T23:50:29.619714+00:00"},{"alias_kind":"pith_short_12","alias_value":"K6A5RMC2UTQG","created_at":"2026-05-18T12:33:21.387695+00:00"},{"alias_kind":"pith_short_16","alias_value":"K6A5RMC2UTQGSTBN","created_at":"2026-05-18T12:33:21.387695+00:00"},{"alias_kind":"pith_short_8","alias_value":"K6A5RMC2","created_at":"2026-05-18T12:33:21.387695+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/K6A5RMC2UTQGSTBNBWABZ2JMQI","json":"https://pith.science/pith/K6A5RMC2UTQGSTBNBWABZ2JMQI.json","graph_json":"https://pith.science/api/pith-number/K6A5RMC2UTQGSTBNBWABZ2JMQI/graph.json","events_json":"https://pith.science/api/pith-number/K6A5RMC2UTQGSTBNBWABZ2JMQI/events.json","paper":"https://pith.science/paper/K6A5RMC2"},"agent_actions":{"view_html":"https://pith.science/pith/K6A5RMC2UTQGSTBNBWABZ2JMQI","download_json":"https://pith.science/pith/K6A5RMC2UTQGSTBNBWABZ2JMQI.json","view_paper":"https://pith.science/paper/K6A5RMC2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1903.10386&json=true","fetch_graph":"https://pith.science/api/pith-number/K6A5RMC2UTQGSTBNBWABZ2JMQI/graph.json","fetch_events":"https://pith.science/api/pith-number/K6A5RMC2UTQGSTBNBWABZ2JMQI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/K6A5RMC2UTQGSTBNBWABZ2JMQI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/K6A5RMC2UTQGSTBNBWABZ2JMQI/action/storage_attestation","attest_author":"https://pith.science/pith/K6A5RMC2UTQGSTBNBWABZ2JMQI/action/author_attestation","sign_citation":"https://pith.science/pith/K6A5RMC2UTQGSTBNBWABZ2JMQI/action/citation_signature","submit_replication":"https://pith.science/pith/K6A5RMC2UTQGSTBNBWABZ2JMQI/action/replication_record"}},"created_at":"2026-05-17T23:50:29.619714+00:00","updated_at":"2026-05-17T23:50:29.619714+00:00"}