{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:SOTW3MWPJJMXNY2FPD76JOXGA4","short_pith_number":"pith:SOTW3MWP","schema_version":"1.0","canonical_sha256":"93a76db2cf4a5976e34578ffe4bae6073f867a52e2a4964d634df01439993d2a","source":{"kind":"arxiv","id":"2201.09543","version":1},"attestation_state":"computed","paper":{"title":"Non-rigid regions of real Grothendieck groups of gentle and special biserial algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Sota Asai","submitted_at":"2022-01-24T09:32:29Z","abstract_excerpt":"In the representation theory of finite-dimensional algebras $A$ over a field, the classification of 2-term (pre)silting complexes is an important problem. One of the useful tool is the g-vector cones associated to the 2-term presilting complexes in the real Grothendieck group $K_0(\\operatorname{\\mathsf{proj}} A)_{\\mathbb{R}}:=K_0(\\operatorname{\\mathsf{proj}} A) \\otimes_{\\mathbb{Z}} {\\mathbb{R}}$. The aim of this paper is to study the complement $\\operatorname{\\mathsf{NR}}$ of the union $\\operatorname{\\mathsf{Cone}}$ of all g-vector cones, which we call the non-rigid region. By the work of Iyam"},"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":"2201.09543","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2022-01-24T09:32:29Z","cross_cats_sorted":[],"title_canon_sha256":"f98076f5b5a4f276be3a4347209a49215ee8d6f57507af53e216e677558a27da","abstract_canon_sha256":"1258f6c4122241c012fde9fe1efb25cf2238073eafc55158e35f46ec65f0d254"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:50:58.487623Z","signature_b64":"I4dhJ3meZ8JzttCa/9OFxUNM7S4boHa40CnUMjpsg0CjwaQCBqa+MDr9mWX3cSEAQySjWQu3YmisTk7Xxi1YDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"93a76db2cf4a5976e34578ffe4bae6073f867a52e2a4964d634df01439993d2a","last_reissued_at":"2026-07-05T03:50:58.487180Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:50:58.487180Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-rigid regions of real Grothendieck groups of gentle and special biserial algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Sota Asai","submitted_at":"2022-01-24T09:32:29Z","abstract_excerpt":"In the representation theory of finite-dimensional algebras $A$ over a field, the classification of 2-term (pre)silting complexes is an important problem. One of the useful tool is the g-vector cones associated to the 2-term presilting complexes in the real Grothendieck group $K_0(\\operatorname{\\mathsf{proj}} A)_{\\mathbb{R}}:=K_0(\\operatorname{\\mathsf{proj}} A) \\otimes_{\\mathbb{Z}} {\\mathbb{R}}$. The aim of this paper is to study the complement $\\operatorname{\\mathsf{NR}}$ of the union $\\operatorname{\\mathsf{Cone}}$ of all g-vector cones, which we call the non-rigid region. By the work of Iyam"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.09543","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/2201.09543/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":"2201.09543","created_at":"2026-07-05T03:50:58.487240+00:00"},{"alias_kind":"arxiv_version","alias_value":"2201.09543v1","created_at":"2026-07-05T03:50:58.487240+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2201.09543","created_at":"2026-07-05T03:50:58.487240+00:00"},{"alias_kind":"pith_short_12","alias_value":"SOTW3MWPJJMX","created_at":"2026-07-05T03:50:58.487240+00:00"},{"alias_kind":"pith_short_16","alias_value":"SOTW3MWPJJMXNY2F","created_at":"2026-07-05T03:50:58.487240+00:00"},{"alias_kind":"pith_short_8","alias_value":"SOTW3MWP","created_at":"2026-07-05T03:50:58.487240+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.07555","citing_title":"Magnitude of module categories","ref_index":56,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SOTW3MWPJJMXNY2FPD76JOXGA4","json":"https://pith.science/pith/SOTW3MWPJJMXNY2FPD76JOXGA4.json","graph_json":"https://pith.science/api/pith-number/SOTW3MWPJJMXNY2FPD76JOXGA4/graph.json","events_json":"https://pith.science/api/pith-number/SOTW3MWPJJMXNY2FPD76JOXGA4/events.json","paper":"https://pith.science/paper/SOTW3MWP"},"agent_actions":{"view_html":"https://pith.science/pith/SOTW3MWPJJMXNY2FPD76JOXGA4","download_json":"https://pith.science/pith/SOTW3MWPJJMXNY2FPD76JOXGA4.json","view_paper":"https://pith.science/paper/SOTW3MWP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2201.09543&json=true","fetch_graph":"https://pith.science/api/pith-number/SOTW3MWPJJMXNY2FPD76JOXGA4/graph.json","fetch_events":"https://pith.science/api/pith-number/SOTW3MWPJJMXNY2FPD76JOXGA4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SOTW3MWPJJMXNY2FPD76JOXGA4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SOTW3MWPJJMXNY2FPD76JOXGA4/action/storage_attestation","attest_author":"https://pith.science/pith/SOTW3MWPJJMXNY2FPD76JOXGA4/action/author_attestation","sign_citation":"https://pith.science/pith/SOTW3MWPJJMXNY2FPD76JOXGA4/action/citation_signature","submit_replication":"https://pith.science/pith/SOTW3MWPJJMXNY2FPD76JOXGA4/action/replication_record"}},"created_at":"2026-07-05T03:50:58.487240+00:00","updated_at":"2026-07-05T03:50:58.487240+00:00"}