{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:GLC3XMG6YFGKNO7XDCGJZ57A7A","short_pith_number":"pith:GLC3XMG6","schema_version":"1.0","canonical_sha256":"32c5bbb0dec14ca6bbf7188c9cf7e0f82f2779a2b38ca69a36e2a8d91350b049","source":{"kind":"arxiv","id":"1812.10242","version":1},"attestation_state":"computed","paper":{"title":"The representation theory of the increasing monoid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.CO"],"primary_cat":"math.RT","authors_text":"Andrew Snowden, Sema G\\\"unt\\\"urk\\\"un","submitted_at":"2018-12-26T06:38:05Z","abstract_excerpt":"We study the representation theory of the increasing monoid. Our results provide a fairly comprehensive picture of the representation category: for example, we describe the Grothendieck group (including the effective cone), classify injective objects, establish properties of injective and projective resolutions, construct a derived auto-duality, and so on. Our work is motivated by numerous connections of this theory to other areas, such as representation stability, commutative algebra, simplicial theory, and shuffle algebras."},"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":"1812.10242","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-12-26T06:38:05Z","cross_cats_sorted":["math.AC","math.CO"],"title_canon_sha256":"8656c0107a6a486d6ef5a2e3edda492a8bd0911d56967499deafe57880c51c40","abstract_canon_sha256":"60b03e0dbb28da4671471fb4afaca8b7c2070c9ccc2faadabef87e44a62f0779"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:24.686108Z","signature_b64":"TWlTM7Z0ZYLIP4aq9L/F3iw+D5PDJkC0mVqzYgWA7C+UAu/iYrnpt6pOgWI0sVQwZylGH1NI+z6giLxm/LjeAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"32c5bbb0dec14ca6bbf7188c9cf7e0f82f2779a2b38ca69a36e2a8d91350b049","last_reissued_at":"2026-05-17T23:57:24.685546Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:24.685546Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The representation theory of the increasing monoid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.CO"],"primary_cat":"math.RT","authors_text":"Andrew Snowden, Sema G\\\"unt\\\"urk\\\"un","submitted_at":"2018-12-26T06:38:05Z","abstract_excerpt":"We study the representation theory of the increasing monoid. Our results provide a fairly comprehensive picture of the representation category: for example, we describe the Grothendieck group (including the effective cone), classify injective objects, establish properties of injective and projective resolutions, construct a derived auto-duality, and so on. Our work is motivated by numerous connections of this theory to other areas, such as representation stability, commutative algebra, simplicial theory, and shuffle algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.10242","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":"1812.10242","created_at":"2026-05-17T23:57:24.685606+00:00"},{"alias_kind":"arxiv_version","alias_value":"1812.10242v1","created_at":"2026-05-17T23:57:24.685606+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.10242","created_at":"2026-05-17T23:57:24.685606+00:00"},{"alias_kind":"pith_short_12","alias_value":"GLC3XMG6YFGK","created_at":"2026-05-18T12:32:25.280505+00:00"},{"alias_kind":"pith_short_16","alias_value":"GLC3XMG6YFGKNO7X","created_at":"2026-05-18T12:32:25.280505+00:00"},{"alias_kind":"pith_short_8","alias_value":"GLC3XMG6","created_at":"2026-05-18T12:32:25.280505+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2608.00982","citing_title":"GL-algebras in positive characteristic III: the divided power algebra","ref_index":16,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GLC3XMG6YFGKNO7XDCGJZ57A7A","json":"https://pith.science/pith/GLC3XMG6YFGKNO7XDCGJZ57A7A.json","graph_json":"https://pith.science/api/pith-number/GLC3XMG6YFGKNO7XDCGJZ57A7A/graph.json","events_json":"https://pith.science/api/pith-number/GLC3XMG6YFGKNO7XDCGJZ57A7A/events.json","paper":"https://pith.science/paper/GLC3XMG6"},"agent_actions":{"view_html":"https://pith.science/pith/GLC3XMG6YFGKNO7XDCGJZ57A7A","download_json":"https://pith.science/pith/GLC3XMG6YFGKNO7XDCGJZ57A7A.json","view_paper":"https://pith.science/paper/GLC3XMG6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1812.10242&json=true","fetch_graph":"https://pith.science/api/pith-number/GLC3XMG6YFGKNO7XDCGJZ57A7A/graph.json","fetch_events":"https://pith.science/api/pith-number/GLC3XMG6YFGKNO7XDCGJZ57A7A/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GLC3XMG6YFGKNO7XDCGJZ57A7A/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GLC3XMG6YFGKNO7XDCGJZ57A7A/action/storage_attestation","attest_author":"https://pith.science/pith/GLC3XMG6YFGKNO7XDCGJZ57A7A/action/author_attestation","sign_citation":"https://pith.science/pith/GLC3XMG6YFGKNO7XDCGJZ57A7A/action/citation_signature","submit_replication":"https://pith.science/pith/GLC3XMG6YFGKNO7XDCGJZ57A7A/action/replication_record"}},"created_at":"2026-05-17T23:57:24.685606+00:00","updated_at":"2026-05-17T23:57:24.685606+00:00"}