{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:QPZYLJVW6Q7QFU2JOQXSRP7VJI","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"3ba5d5686c69f8bf2d89637a683a2b5cdc9bfdf1d6ecdb4cd87f1d2422d7d07e","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-10-02T10:11:05Z","title_canon_sha256":"7bf1b022991523e6bb4977c5c87c43be74662a02ad56a2010256a4891af5e5fa"},"schema_version":"1.0","source":{"id":"1210.0723","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.0723","created_at":"2026-05-18T01:26:11Z"},{"alias_kind":"arxiv_version","alias_value":"1210.0723v5","created_at":"2026-05-18T01:26:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.0723","created_at":"2026-05-18T01:26:11Z"},{"alias_kind":"pith_short_12","alias_value":"QPZYLJVW6Q7Q","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QPZYLJVW6Q7QFU2J","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QPZYLJVW","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:328d6b14e78860c68bd59c765f5ca211897fc67d015fffe85e6586a4438e01ce","target":"graph","created_at":"2026-05-18T01:26:11Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The homotopy theory of small functors is a useful tool for studying various questions in homotopy theory. In this paper, we develop the homotopy theory of small functors from spectra to spectra, and study its interplay with Spanier-Whitehead duality and enriched representability in the dual category of spectra.\n  We note that the Spanier-Whitehead duality functor $D\\colon \\mathrm{Sp}\\rightarrow \\mathrm{Sp}^{\\mathrm{op}}$ factors through the category of small functors from spectra to spectra and construct a new model structure on the category of small functors, which is Quillen equivalent to $\\","authors_text":"Boris Chorny, Georg Biedermann","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-10-02T10:11:05Z","title":"Duality and small functors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.0723","kind":"arxiv","version":5},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:23eea1274bacb44316bb140b5b3d5bff1f529f9d659cfcfd199461cdba18fdd0","target":"record","created_at":"2026-05-18T01:26:11Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"3ba5d5686c69f8bf2d89637a683a2b5cdc9bfdf1d6ecdb4cd87f1d2422d7d07e","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-10-02T10:11:05Z","title_canon_sha256":"7bf1b022991523e6bb4977c5c87c43be74662a02ad56a2010256a4891af5e5fa"},"schema_version":"1.0","source":{"id":"1210.0723","kind":"arxiv","version":5}},"canonical_sha256":"83f385a6b6f43f02d349742f28bff54a2c571d9bef9ddf87b772a0d64edb01d9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"83f385a6b6f43f02d349742f28bff54a2c571d9bef9ddf87b772a0d64edb01d9","first_computed_at":"2026-05-18T01:26:11.234646Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:26:11.234646Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Dl6l7GV9FlomgRvitUrdqdHtqKxKTC/aQvB49trb9l7RS1qj3wLjyOvMgGHyG9JwO07YmWbnk7vwFBMwh28GCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:26:11.235168Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.0723","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:23eea1274bacb44316bb140b5b3d5bff1f529f9d659cfcfd199461cdba18fdd0","sha256:328d6b14e78860c68bd59c765f5ca211897fc67d015fffe85e6586a4438e01ce"],"state_sha256":"e9a6d6d8f52dcb988a3fd6853fd95f06006e523045a17cc66409a43d3928cb5a"}