{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:MXIMTA6FTSA73UEZK43P23C6MH","short_pith_number":"pith:MXIMTA6F","schema_version":"1.0","canonical_sha256":"65d0c983c59c81fdd0995736fd6c5e61ee2207fed174bc5a101f6f7d717c194f","source":{"kind":"arxiv","id":"1512.03698","version":1},"attestation_state":"computed","paper":{"title":"On the homotopy theory of $\\mathbf{G}$ - spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.GN"],"primary_cat":"math.CT","authors_text":"Amit Sharma","submitted_at":"2015-12-11T16:42:57Z","abstract_excerpt":"The aim of this paper is to show that the most elementary homotopy theory of $\\mathbf{G}$-spaces is equivalent to a homotopy theory of simplicial sets over $\\mathbf{BG}$, where $\\mathbf{G}$ is a fixed group. Both homotopy theories are presented as Relative categories. We establish the equivalence by constructing a strict homotopy equivalence between the two relative categories. No Model category structure is assumed on either Relative Category."},"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":"1512.03698","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2015-12-11T16:42:57Z","cross_cats_sorted":["math.AT","math.GN"],"title_canon_sha256":"b2a69873536763794b4a1e4916878eb4cced54f5e77153397c857adda55042a3","abstract_canon_sha256":"14b2c9107b74ac152beb7659cc34d79e074156215de6590d5abab0d9a2e77351"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:54:43.811644Z","signature_b64":"LsYjI5JffUQmJNIhDGB7sfCYJRdnA4c0IV2ABlb6sLTbJ3TbnPS96jImDlHpd0F5E+XEYv2RDTaP93S1ORCJDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65d0c983c59c81fdd0995736fd6c5e61ee2207fed174bc5a101f6f7d717c194f","last_reissued_at":"2026-07-05T00:54:43.811254Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:54:43.811254Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the homotopy theory of $\\mathbf{G}$ - spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.GN"],"primary_cat":"math.CT","authors_text":"Amit Sharma","submitted_at":"2015-12-11T16:42:57Z","abstract_excerpt":"The aim of this paper is to show that the most elementary homotopy theory of $\\mathbf{G}$-spaces is equivalent to a homotopy theory of simplicial sets over $\\mathbf{BG}$, where $\\mathbf{G}$ is a fixed group. Both homotopy theories are presented as Relative categories. We establish the equivalence by constructing a strict homotopy equivalence between the two relative categories. No Model category structure is assumed on either Relative Category."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.03698","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1512.03698/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1512.03698","created_at":"2026-07-05T00:54:43.811312+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.03698v1","created_at":"2026-07-05T00:54:43.811312+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.03698","created_at":"2026-07-05T00:54:43.811312+00:00"},{"alias_kind":"pith_short_12","alias_value":"MXIMTA6FTSA7","created_at":"2026-07-05T00:54:43.811312+00:00"},{"alias_kind":"pith_short_16","alias_value":"MXIMTA6FTSA73UEZ","created_at":"2026-07-05T00:54:43.811312+00:00"},{"alias_kind":"pith_short_8","alias_value":"MXIMTA6F","created_at":"2026-07-05T00:54:43.811312+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.05668","citing_title":"A homotopy theory of coherently commutative monoidal quasi-categories","ref_index":24,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MXIMTA6FTSA73UEZK43P23C6MH","json":"https://pith.science/pith/MXIMTA6FTSA73UEZK43P23C6MH.json","graph_json":"https://pith.science/api/pith-number/MXIMTA6FTSA73UEZK43P23C6MH/graph.json","events_json":"https://pith.science/api/pith-number/MXIMTA6FTSA73UEZK43P23C6MH/events.json","paper":"https://pith.science/paper/MXIMTA6F"},"agent_actions":{"view_html":"https://pith.science/pith/MXIMTA6FTSA73UEZK43P23C6MH","download_json":"https://pith.science/pith/MXIMTA6FTSA73UEZK43P23C6MH.json","view_paper":"https://pith.science/paper/MXIMTA6F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.03698&json=true","fetch_graph":"https://pith.science/api/pith-number/MXIMTA6FTSA73UEZK43P23C6MH/graph.json","fetch_events":"https://pith.science/api/pith-number/MXIMTA6FTSA73UEZK43P23C6MH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MXIMTA6FTSA73UEZK43P23C6MH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MXIMTA6FTSA73UEZK43P23C6MH/action/storage_attestation","attest_author":"https://pith.science/pith/MXIMTA6FTSA73UEZK43P23C6MH/action/author_attestation","sign_citation":"https://pith.science/pith/MXIMTA6FTSA73UEZK43P23C6MH/action/citation_signature","submit_replication":"https://pith.science/pith/MXIMTA6FTSA73UEZK43P23C6MH/action/replication_record"}},"created_at":"2026-07-05T00:54:43.811312+00:00","updated_at":"2026-07-05T00:54:43.811312+00:00"}