{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:EEL7BSEGVJHX2XRQR2LU2WDYXM","short_pith_number":"pith:EEL7BSEG","schema_version":"1.0","canonical_sha256":"2117f0c886aa4f7d5e308e974d5878bb218dcab72112361ba5334c2af89053d0","source":{"kind":"arxiv","id":"1606.07032","version":2},"attestation_state":"computed","paper":{"title":"Stable Postnikov data of Picard 2-categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.KT"],"primary_cat":"math.AT","authors_text":"Ang\\'elica M. Osorno, Marc Stephan, Nick Gurski, Niles Johnson","submitted_at":"2016-06-22T18:16:38Z","abstract_excerpt":"Picard 2-categories are symmetric monoidal 2-categories with invertible 0-, 1-, and 2-cells. The classifying space of a Picard 2-category $\\mathcal{D}$ is an infinite loop space, the zeroth space of the $K$-theory spectrum $K\\mathcal{D}$. This spectrum has stable homotopy groups concentrated in levels 0, 1, and 2. In this paper, we describe part of the Postnikov data of $K\\mathcal{D}$ in terms of categorical structure. We use this to show that there is no strict skeletal Picard 2-category whose $K$-theory realizes the 2-truncation of the sphere spectrum. As part of the proof, we construct a ca"},"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":"1606.07032","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-06-22T18:16:38Z","cross_cats_sorted":["math.CT","math.KT"],"title_canon_sha256":"479e2d12af3c4f1149e42a715ea348b46177d47a14333ffd155eda0d723a3468","abstract_canon_sha256":"d3d361fba0eacf9948108bbabe75b516f5fc19c9392ba437067f413eb37da296"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:05.885916Z","signature_b64":"QXlPfodhSSPIXEZy1zfzWsgewCjKLb3QMLBVBYJ6nvA/w7tvvNlIHupEyLVNCqK4EqoxVls2Z3TDaKensvZrDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2117f0c886aa4f7d5e308e974d5878bb218dcab72112361ba5334c2af89053d0","last_reissued_at":"2026-05-18T00:29:05.885481Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:05.885481Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stable Postnikov data of Picard 2-categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.KT"],"primary_cat":"math.AT","authors_text":"Ang\\'elica M. Osorno, Marc Stephan, Nick Gurski, Niles Johnson","submitted_at":"2016-06-22T18:16:38Z","abstract_excerpt":"Picard 2-categories are symmetric monoidal 2-categories with invertible 0-, 1-, and 2-cells. The classifying space of a Picard 2-category $\\mathcal{D}$ is an infinite loop space, the zeroth space of the $K$-theory spectrum $K\\mathcal{D}$. This spectrum has stable homotopy groups concentrated in levels 0, 1, and 2. In this paper, we describe part of the Postnikov data of $K\\mathcal{D}$ in terms of categorical structure. We use this to show that there is no strict skeletal Picard 2-category whose $K$-theory realizes the 2-truncation of the sphere spectrum. As part of the proof, we construct a ca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.07032","kind":"arxiv","version":2},"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":"1606.07032","created_at":"2026-05-18T00:29:05.885547+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.07032v2","created_at":"2026-05-18T00:29:05.885547+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.07032","created_at":"2026-05-18T00:29:05.885547+00:00"},{"alias_kind":"pith_short_12","alias_value":"EEL7BSEGVJHX","created_at":"2026-05-18T12:30:12.583610+00:00"},{"alias_kind":"pith_short_16","alias_value":"EEL7BSEGVJHX2XRQ","created_at":"2026-05-18T12:30:12.583610+00:00"},{"alias_kind":"pith_short_8","alias_value":"EEL7BSEG","created_at":"2026-05-18T12:30:12.583610+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/EEL7BSEGVJHX2XRQR2LU2WDYXM","json":"https://pith.science/pith/EEL7BSEGVJHX2XRQR2LU2WDYXM.json","graph_json":"https://pith.science/api/pith-number/EEL7BSEGVJHX2XRQR2LU2WDYXM/graph.json","events_json":"https://pith.science/api/pith-number/EEL7BSEGVJHX2XRQR2LU2WDYXM/events.json","paper":"https://pith.science/paper/EEL7BSEG"},"agent_actions":{"view_html":"https://pith.science/pith/EEL7BSEGVJHX2XRQR2LU2WDYXM","download_json":"https://pith.science/pith/EEL7BSEGVJHX2XRQR2LU2WDYXM.json","view_paper":"https://pith.science/paper/EEL7BSEG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.07032&json=true","fetch_graph":"https://pith.science/api/pith-number/EEL7BSEGVJHX2XRQR2LU2WDYXM/graph.json","fetch_events":"https://pith.science/api/pith-number/EEL7BSEGVJHX2XRQR2LU2WDYXM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EEL7BSEGVJHX2XRQR2LU2WDYXM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EEL7BSEGVJHX2XRQR2LU2WDYXM/action/storage_attestation","attest_author":"https://pith.science/pith/EEL7BSEGVJHX2XRQR2LU2WDYXM/action/author_attestation","sign_citation":"https://pith.science/pith/EEL7BSEGVJHX2XRQR2LU2WDYXM/action/citation_signature","submit_replication":"https://pith.science/pith/EEL7BSEGVJHX2XRQR2LU2WDYXM/action/replication_record"}},"created_at":"2026-05-18T00:29:05.885547+00:00","updated_at":"2026-05-18T00:29:05.885547+00:00"}