{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:HTAIVENRGYINFTAQL2ISAOUNEH","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"1c14bea916aeecb8427bb27d67743787c7821a50a0f520f469177526bebd66d0","cross_cats_sorted":["math.SP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-06-10T12:32:44Z","title_canon_sha256":"24484d2d0e475e9b030ff0fa8a1a05eb87de306150e0bfaa634396193c7ec10a"},"schema_version":"1.0","source":{"id":"2606.12009","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.12009","created_at":"2026-06-11T01:10:42Z"},{"alias_kind":"arxiv_version","alias_value":"2606.12009v1","created_at":"2026-06-11T01:10:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.12009","created_at":"2026-06-11T01:10:42Z"},{"alias_kind":"pith_short_12","alias_value":"HTAIVENRGYIN","created_at":"2026-06-11T01:10:42Z"},{"alias_kind":"pith_short_16","alias_value":"HTAIVENRGYINFTAQ","created_at":"2026-06-11T01:10:42Z"},{"alias_kind":"pith_short_8","alias_value":"HTAIVENR","created_at":"2026-06-11T01:10:42Z"}],"graph_snapshots":[{"event_id":"sha256:41c954bbc8c1af92c6c02a8996af1f0abb12a435ce437c343445a3fec7dc0788","target":"graph","created_at":"2026-06-11T01:10:42Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.12009/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This manuscript investigates the spectral geometry of Riemannian submersions whose fibers have a basic mean curvature. By restricting the Laplace--Beltrami operator to the space of basic functions, we reduce the spectral problem on $M$ to the spectral problem for a weighted Laplacian on the base manifold, where the weight is determined by the fiber-volume function $S$. We derive a summation formula for the reciprocal of the basic Dirichlet eigenvalues (Basel-type series). Furthermore, using the framework of Supersymmetric Quantum Mechanics (SUSYQM), we establish a supersym\\-me\\-tric duality re","authors_text":"Paulo Henryque da Costa Silva, Vicent Gimeno i Garcia","cross_cats":["math.SP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-06-10T12:32:44Z","title":"Dirichlet--Neumann duality for the Basic Spectrum of Riemannian Submersions: A Supersymmetric Perspective"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.12009","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:98db29d5f06472488770f5db0fc10de5527b3f9679a4878475c5f5421acc20fb","target":"record","created_at":"2026-06-11T01:10:42Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"1c14bea916aeecb8427bb27d67743787c7821a50a0f520f469177526bebd66d0","cross_cats_sorted":["math.SP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-06-10T12:32:44Z","title_canon_sha256":"24484d2d0e475e9b030ff0fa8a1a05eb87de306150e0bfaa634396193c7ec10a"},"schema_version":"1.0","source":{"id":"2606.12009","kind":"arxiv","version":1}},"canonical_sha256":"3cc08a91b13610d2cc105e91203a8d21c53622fa36d2b9a909c676f4940dcdb9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3cc08a91b13610d2cc105e91203a8d21c53622fa36d2b9a909c676f4940dcdb9","first_computed_at":"2026-06-11T01:10:42.535293Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-11T01:10:42.535293Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Hme9sz7My79OAq7z9LhcnfY9a3ErdJEJWQ+hy1PtXUTC907BGuuxUPZKxRJ33wpxlzUv2ltU9TEXi4w3NZkFBw==","signature_status":"signed_v1","signed_at":"2026-06-11T01:10:42.536152Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.12009","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:98db29d5f06472488770f5db0fc10de5527b3f9679a4878475c5f5421acc20fb","sha256:41c954bbc8c1af92c6c02a8996af1f0abb12a435ce437c343445a3fec7dc0788"],"state_sha256":"2ad210347285d08d6d48bfd1c96e08274c6d5db020b2a06409016920f46d94f8"}