{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:7VGK7BGLLNSL3YL3K7DOK6PMC5","short_pith_number":"pith:7VGK7BGL","schema_version":"1.0","canonical_sha256":"fd4caf84cb5b64bde17b57c6e579ec17424a808d0169a549767d09aa9a73ae41","source":{"kind":"arxiv","id":"1210.5829","version":1},"attestation_state":"computed","paper":{"title":"N-step energy of maps and fixed-point property of random groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.DG","authors_text":"Hiroyasu Izeki, Shin Nayatani, Takefumi Kondo","submitted_at":"2012-10-22T08:18:23Z","abstract_excerpt":"We prove that a random group of the graph model associated with a sequence of expanders has fixed-point property for a certain class of CAT(0) spaces. We use Gromov's criterion for fixed-point property in terms of the growth of n-step energy of equivariant maps from a finitely generated group into a CAT(0) space, to which we give a detailed proof. We estimate a relevant geometric invariant of the tangent cones of the Euclidean buildings associated with the groups PGL(m,Q_r), and deduce from the general result above that the same random group has fixed-point property for all of these Euclidean "},"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":"1210.5829","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-10-22T08:18:23Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"c847abdbd6786cc3d22535ff8f25159f6da725337ee13f2e8def686eb83d5e02","abstract_canon_sha256":"74655d7dcdfb4d32aa62f7193d4f3a35ee3228965995e7b60ec4dc74608ecf6e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:42:35.014670Z","signature_b64":"1FbZXk6jbCt1JO1fYE73W7PYJoYMie677O9ZzNKURJ/j8n1ISxZRBsfr6RilQyMxZNuunTaPcdeJo34jIbc8BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fd4caf84cb5b64bde17b57c6e579ec17424a808d0169a549767d09aa9a73ae41","last_reissued_at":"2026-05-18T03:42:35.013809Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:42:35.013809Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"N-step energy of maps and fixed-point property of random groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.DG","authors_text":"Hiroyasu Izeki, Shin Nayatani, Takefumi Kondo","submitted_at":"2012-10-22T08:18:23Z","abstract_excerpt":"We prove that a random group of the graph model associated with a sequence of expanders has fixed-point property for a certain class of CAT(0) spaces. We use Gromov's criterion for fixed-point property in terms of the growth of n-step energy of equivariant maps from a finitely generated group into a CAT(0) space, to which we give a detailed proof. We estimate a relevant geometric invariant of the tangent cones of the Euclidean buildings associated with the groups PGL(m,Q_r), and deduce from the general result above that the same random group has fixed-point property for all of these Euclidean "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5829","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":"1210.5829","created_at":"2026-05-18T03:42:35.013921+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.5829v1","created_at":"2026-05-18T03:42:35.013921+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.5829","created_at":"2026-05-18T03:42:35.013921+00:00"},{"alias_kind":"pith_short_12","alias_value":"7VGK7BGLLNSL","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_16","alias_value":"7VGK7BGLLNSL3YL3","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_8","alias_value":"7VGK7BGL","created_at":"2026-05-18T12:26:58.693483+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/7VGK7BGLLNSL3YL3K7DOK6PMC5","json":"https://pith.science/pith/7VGK7BGLLNSL3YL3K7DOK6PMC5.json","graph_json":"https://pith.science/api/pith-number/7VGK7BGLLNSL3YL3K7DOK6PMC5/graph.json","events_json":"https://pith.science/api/pith-number/7VGK7BGLLNSL3YL3K7DOK6PMC5/events.json","paper":"https://pith.science/paper/7VGK7BGL"},"agent_actions":{"view_html":"https://pith.science/pith/7VGK7BGLLNSL3YL3K7DOK6PMC5","download_json":"https://pith.science/pith/7VGK7BGLLNSL3YL3K7DOK6PMC5.json","view_paper":"https://pith.science/paper/7VGK7BGL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.5829&json=true","fetch_graph":"https://pith.science/api/pith-number/7VGK7BGLLNSL3YL3K7DOK6PMC5/graph.json","fetch_events":"https://pith.science/api/pith-number/7VGK7BGLLNSL3YL3K7DOK6PMC5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7VGK7BGLLNSL3YL3K7DOK6PMC5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7VGK7BGLLNSL3YL3K7DOK6PMC5/action/storage_attestation","attest_author":"https://pith.science/pith/7VGK7BGLLNSL3YL3K7DOK6PMC5/action/author_attestation","sign_citation":"https://pith.science/pith/7VGK7BGLLNSL3YL3K7DOK6PMC5/action/citation_signature","submit_replication":"https://pith.science/pith/7VGK7BGLLNSL3YL3K7DOK6PMC5/action/replication_record"}},"created_at":"2026-05-18T03:42:35.013921+00:00","updated_at":"2026-05-18T03:42:35.013921+00:00"}