{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:U5G6RFNSRPFHM2UVUNVMCBUZXG","short_pith_number":"pith:U5G6RFNS","schema_version":"1.0","canonical_sha256":"a74de895b28bca766a95a36ac10699b9a2c3b195bc567f1c189f4c83cb9bfd82","source":{"kind":"arxiv","id":"1604.07462","version":1},"attestation_state":"computed","paper":{"title":"Volumes for ${\\rm SL}_N(\\mathbb R)$, the Selberg integral and random lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Peter J. Forrester","submitted_at":"2016-04-25T22:20:03Z","abstract_excerpt":"There is a natural left and right invariant Haar measure associated with the matrix groups GL${}_N(\\mathbb R)$ and SL${}_N(\\mathbb R)$ due to Siegel. For the associated volume to be finite it is necessary to truncate the groups by imposing a bound on the norm, or in the case of SL${}_N(\\mathbb R)$, by restricting to a fundamental domain. We compute the asymptotic volumes associated with the Haar measure for GL${}_N(\\mathbb R)$ and SL${}_N(\\mathbb R)$ matrices in the case of that the operator norm lies between $R_1$ and $1/R_2$ in the former, and this norm, or alternatively the 2-norm, is bound"},"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":"1604.07462","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-04-25T22:20:03Z","cross_cats_sorted":["math.MP","math.PR"],"title_canon_sha256":"970df5a79a08987a2e200e1b5e543d7cbfe4822b921d3ef497e4e524fd42826f","abstract_canon_sha256":"1d6323bc78ac7c5b526b776f57cc5f1910d29467d1358ebae48706f7a7fa9c7f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:19.727811Z","signature_b64":"iYbC1+MxqmSGjBr1VKbwwL8sL4v+lkiMu/OW9PT5oL5qZ40q27kgmgI6Mi9VJEPPYHLT6Q1ioVX5rUpS/9dZDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a74de895b28bca766a95a36ac10699b9a2c3b195bc567f1c189f4c83cb9bfd82","last_reissued_at":"2026-05-18T01:16:19.727231Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:19.727231Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Volumes for ${\\rm SL}_N(\\mathbb R)$, the Selberg integral and random lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Peter J. Forrester","submitted_at":"2016-04-25T22:20:03Z","abstract_excerpt":"There is a natural left and right invariant Haar measure associated with the matrix groups GL${}_N(\\mathbb R)$ and SL${}_N(\\mathbb R)$ due to Siegel. For the associated volume to be finite it is necessary to truncate the groups by imposing a bound on the norm, or in the case of SL${}_N(\\mathbb R)$, by restricting to a fundamental domain. We compute the asymptotic volumes associated with the Haar measure for GL${}_N(\\mathbb R)$ and SL${}_N(\\mathbb R)$ matrices in the case of that the operator norm lies between $R_1$ and $1/R_2$ in the former, and this norm, or alternatively the 2-norm, is bound"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.07462","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":"1604.07462","created_at":"2026-05-18T01:16:19.727334+00:00"},{"alias_kind":"arxiv_version","alias_value":"1604.07462v1","created_at":"2026-05-18T01:16:19.727334+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.07462","created_at":"2026-05-18T01:16:19.727334+00:00"},{"alias_kind":"pith_short_12","alias_value":"U5G6RFNSRPFH","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_16","alias_value":"U5G6RFNSRPFHM2UV","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_8","alias_value":"U5G6RFNS","created_at":"2026-05-18T12:30:46.583412+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/U5G6RFNSRPFHM2UVUNVMCBUZXG","json":"https://pith.science/pith/U5G6RFNSRPFHM2UVUNVMCBUZXG.json","graph_json":"https://pith.science/api/pith-number/U5G6RFNSRPFHM2UVUNVMCBUZXG/graph.json","events_json":"https://pith.science/api/pith-number/U5G6RFNSRPFHM2UVUNVMCBUZXG/events.json","paper":"https://pith.science/paper/U5G6RFNS"},"agent_actions":{"view_html":"https://pith.science/pith/U5G6RFNSRPFHM2UVUNVMCBUZXG","download_json":"https://pith.science/pith/U5G6RFNSRPFHM2UVUNVMCBUZXG.json","view_paper":"https://pith.science/paper/U5G6RFNS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1604.07462&json=true","fetch_graph":"https://pith.science/api/pith-number/U5G6RFNSRPFHM2UVUNVMCBUZXG/graph.json","fetch_events":"https://pith.science/api/pith-number/U5G6RFNSRPFHM2UVUNVMCBUZXG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/U5G6RFNSRPFHM2UVUNVMCBUZXG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/U5G6RFNSRPFHM2UVUNVMCBUZXG/action/storage_attestation","attest_author":"https://pith.science/pith/U5G6RFNSRPFHM2UVUNVMCBUZXG/action/author_attestation","sign_citation":"https://pith.science/pith/U5G6RFNSRPFHM2UVUNVMCBUZXG/action/citation_signature","submit_replication":"https://pith.science/pith/U5G6RFNSRPFHM2UVUNVMCBUZXG/action/replication_record"}},"created_at":"2026-05-18T01:16:19.727334+00:00","updated_at":"2026-05-18T01:16:19.727334+00:00"}