{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:BQAMBZ5AMJFSQGWWE4I2YGPEOZ","short_pith_number":"pith:BQAMBZ5A","schema_version":"1.0","canonical_sha256":"0c00c0e7a0624b281ad62711ac19e47654b04ae5dfc5db63987ad43211f37adb","source":{"kind":"arxiv","id":"1612.08065","version":1},"attestation_state":"computed","paper":{"title":"Homological S-Duality in 4d N=2 QFTs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Matteo Caorsi, Sergio Cecotti","submitted_at":"2016-12-23T19:14:38Z","abstract_excerpt":"The $S$-duality group $\\mathbb{S}(\\mathcal{F})$ of a 4d $\\mathcal{N}=2$ supersymmetric theory $\\mathcal{F}$ is identified with the group of triangle auto-equivalences of its cluster category $\\mathscr{C}(\\mathcal{F})$ modulo the subgroup acting trivially on the physical quantities. $\\mathbb{S}(\\mathcal{F})$ is a discrete group commensurable to a subgroup of the Siegel modular group $Sp(2g,\\mathbb{Z})$ ($g$ being the dimension of the Coulomb branch). This identification reduces the determination of the $S$-duality group of a given $\\mathcal{N}=2$ theory to a problem in homological algebra. In t"},"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":"1612.08065","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-12-23T19:14:38Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"a255a26f6e9519c5a5b654f62c3a03feafa3ada278c55b45c0e6645ba531a864","abstract_canon_sha256":"fe3298cc711220dc02ea3e8acf2c05e872b2c5cdcd177fa77398eadae17d5b8a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:04.993034Z","signature_b64":"Ep+1d+HbcZuRSQ6+G8U23aFB/Fi+iYZMc1Z4v6yZYUFAJnAn+RGrsR2eum6qeFTIjiyJjQETW6j8HO5WdK6ACg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0c00c0e7a0624b281ad62711ac19e47654b04ae5dfc5db63987ad43211f37adb","last_reissued_at":"2026-05-18T00:54:04.992645Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:04.992645Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Homological S-Duality in 4d N=2 QFTs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Matteo Caorsi, Sergio Cecotti","submitted_at":"2016-12-23T19:14:38Z","abstract_excerpt":"The $S$-duality group $\\mathbb{S}(\\mathcal{F})$ of a 4d $\\mathcal{N}=2$ supersymmetric theory $\\mathcal{F}$ is identified with the group of triangle auto-equivalences of its cluster category $\\mathscr{C}(\\mathcal{F})$ modulo the subgroup acting trivially on the physical quantities. $\\mathbb{S}(\\mathcal{F})$ is a discrete group commensurable to a subgroup of the Siegel modular group $Sp(2g,\\mathbb{Z})$ ($g$ being the dimension of the Coulomb branch). This identification reduces the determination of the $S$-duality group of a given $\\mathcal{N}=2$ theory to a problem in homological algebra. In t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.08065","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":"1612.08065","created_at":"2026-05-18T00:54:04.992708+00:00"},{"alias_kind":"arxiv_version","alias_value":"1612.08065v1","created_at":"2026-05-18T00:54:04.992708+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.08065","created_at":"2026-05-18T00:54:04.992708+00:00"},{"alias_kind":"pith_short_12","alias_value":"BQAMBZ5AMJFS","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_16","alias_value":"BQAMBZ5AMJFSQGWW","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_8","alias_value":"BQAMBZ5A","created_at":"2026-05-18T12:30:07.202191+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/BQAMBZ5AMJFSQGWWE4I2YGPEOZ","json":"https://pith.science/pith/BQAMBZ5AMJFSQGWWE4I2YGPEOZ.json","graph_json":"https://pith.science/api/pith-number/BQAMBZ5AMJFSQGWWE4I2YGPEOZ/graph.json","events_json":"https://pith.science/api/pith-number/BQAMBZ5AMJFSQGWWE4I2YGPEOZ/events.json","paper":"https://pith.science/paper/BQAMBZ5A"},"agent_actions":{"view_html":"https://pith.science/pith/BQAMBZ5AMJFSQGWWE4I2YGPEOZ","download_json":"https://pith.science/pith/BQAMBZ5AMJFSQGWWE4I2YGPEOZ.json","view_paper":"https://pith.science/paper/BQAMBZ5A","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1612.08065&json=true","fetch_graph":"https://pith.science/api/pith-number/BQAMBZ5AMJFSQGWWE4I2YGPEOZ/graph.json","fetch_events":"https://pith.science/api/pith-number/BQAMBZ5AMJFSQGWWE4I2YGPEOZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BQAMBZ5AMJFSQGWWE4I2YGPEOZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BQAMBZ5AMJFSQGWWE4I2YGPEOZ/action/storage_attestation","attest_author":"https://pith.science/pith/BQAMBZ5AMJFSQGWWE4I2YGPEOZ/action/author_attestation","sign_citation":"https://pith.science/pith/BQAMBZ5AMJFSQGWWE4I2YGPEOZ/action/citation_signature","submit_replication":"https://pith.science/pith/BQAMBZ5AMJFSQGWWE4I2YGPEOZ/action/replication_record"}},"created_at":"2026-05-18T00:54:04.992708+00:00","updated_at":"2026-05-18T00:54:04.992708+00:00"}