{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:ELK5F3QND2UWT526ZQRODIWNWJ","short_pith_number":"pith:ELK5F3QN","schema_version":"1.0","canonical_sha256":"22d5d2ee0d1ea969f75ecc22e1a2cdb26df150379c53a0ba41189c04ce83134c","source":{"kind":"arxiv","id":"2605.26224","version":1},"attestation_state":"computed","paper":{"title":"$S$-duality, boundary states, and higher-form symmetries on ALE spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.str-el","math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Mohamed M. Anber","submitted_at":"2026-05-25T18:00:09Z","abstract_excerpt":"We study Abelian $S$-duality of Maxwell theory on $A$-type asymptotically locally Euclidean (ALE) spaces. Unlike on closed four-manifolds, the Maxwell path integral on an ALE space is not naturally a scalar partition function. Rather, it decomposes into theta-function blocks labeled by flat $U(1)$ holonomy sectors on the asymptotic lens-space boundary. We interpret these blocks as components of the Hilbert-space boundary state prepared by the ALE path integral. With this interpretation, the apparent failure of ordinary modularity is replaced by vector-valued modular covariance under the action"},"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":"2605.26224","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2026-05-25T18:00:09Z","cross_cats_sorted":["cond-mat.str-el","math-ph","math.MP"],"title_canon_sha256":"726c7c54619279c88064e595afba5fb19f06f507b3545e0b0ad201d90d48f329","abstract_canon_sha256":"464e4e435076fd31567ff7a053dfe9583ddad5b017119e8ee60cbb0f31c77701"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-27T00:04:29.532725Z","signature_b64":"TpLoQz9jzX27AD/M2JZztxSBHpIfJZCB0kJXwexqV+nJr5kzrTWx1skDd8XYoM1kq+TwDsgyguctBy6dQ18DBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"22d5d2ee0d1ea969f75ecc22e1a2cdb26df150379c53a0ba41189c04ce83134c","last_reissued_at":"2026-05-27T00:04:29.532028Z","signature_status":"signed_v1","first_computed_at":"2026-05-27T00:04:29.532028Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$S$-duality, boundary states, and higher-form symmetries on ALE spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.str-el","math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Mohamed M. Anber","submitted_at":"2026-05-25T18:00:09Z","abstract_excerpt":"We study Abelian $S$-duality of Maxwell theory on $A$-type asymptotically locally Euclidean (ALE) spaces. Unlike on closed four-manifolds, the Maxwell path integral on an ALE space is not naturally a scalar partition function. Rather, it decomposes into theta-function blocks labeled by flat $U(1)$ holonomy sectors on the asymptotic lens-space boundary. We interpret these blocks as components of the Hilbert-space boundary state prepared by the ALE path integral. With this interpretation, the apparent failure of ordinary modularity is replaced by vector-valued modular covariance under the action"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.26224","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/2605.26224/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":"2605.26224","created_at":"2026-05-27T00:04:29.532152+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.26224v1","created_at":"2026-05-27T00:04:29.532152+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.26224","created_at":"2026-05-27T00:04:29.532152+00:00"},{"alias_kind":"pith_short_12","alias_value":"ELK5F3QND2UW","created_at":"2026-05-27T00:04:29.532152+00:00"},{"alias_kind":"pith_short_16","alias_value":"ELK5F3QND2UWT526","created_at":"2026-05-27T00:04:29.532152+00:00"},{"alias_kind":"pith_short_8","alias_value":"ELK5F3QN","created_at":"2026-05-27T00:04:29.532152+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/ELK5F3QND2UWT526ZQRODIWNWJ","json":"https://pith.science/pith/ELK5F3QND2UWT526ZQRODIWNWJ.json","graph_json":"https://pith.science/api/pith-number/ELK5F3QND2UWT526ZQRODIWNWJ/graph.json","events_json":"https://pith.science/api/pith-number/ELK5F3QND2UWT526ZQRODIWNWJ/events.json","paper":"https://pith.science/paper/ELK5F3QN"},"agent_actions":{"view_html":"https://pith.science/pith/ELK5F3QND2UWT526ZQRODIWNWJ","download_json":"https://pith.science/pith/ELK5F3QND2UWT526ZQRODIWNWJ.json","view_paper":"https://pith.science/paper/ELK5F3QN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.26224&json=true","fetch_graph":"https://pith.science/api/pith-number/ELK5F3QND2UWT526ZQRODIWNWJ/graph.json","fetch_events":"https://pith.science/api/pith-number/ELK5F3QND2UWT526ZQRODIWNWJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ELK5F3QND2UWT526ZQRODIWNWJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ELK5F3QND2UWT526ZQRODIWNWJ/action/storage_attestation","attest_author":"https://pith.science/pith/ELK5F3QND2UWT526ZQRODIWNWJ/action/author_attestation","sign_citation":"https://pith.science/pith/ELK5F3QND2UWT526ZQRODIWNWJ/action/citation_signature","submit_replication":"https://pith.science/pith/ELK5F3QND2UWT526ZQRODIWNWJ/action/replication_record"}},"created_at":"2026-05-27T00:04:29.532152+00:00","updated_at":"2026-05-27T00:04:29.532152+00:00"}