{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:FQQOWAWQKFM2NTKFGEV7FMHLAT","short_pith_number":"pith:FQQOWAWQ","schema_version":"1.0","canonical_sha256":"2c20eb02d05159a6cd45312bf2b0eb04d29d95785d69a336d147f61e11d7265c","source":{"kind":"arxiv","id":"1410.2864","version":1},"attestation_state":"computed","paper":{"title":"Harmonic forms on ALF gravitational instantons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Guido Franchetti","submitted_at":"2014-10-10T18:41:13Z","abstract_excerpt":"We study the space of square-integrable harmonic forms over ALF gravitational instantons of type $A _{ K -1 } $ and of type $D _K $. We first calculate its dimension making use of a result by Hausel, Hunsicker and Mazzeo which relates the Hodge cohomology of a gravitational instanton $M$ to the singular cohomology of a particular compactification $X _M $ of $M$. We then exhibit an explicit basis, exact for $A _{ K -1 } $ and approximate for $D _K $, and interpret geometrically the relations between $M$, $X _M $ and their cohomologies."},"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":"1410.2864","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-10-10T18:41:13Z","cross_cats_sorted":[],"title_canon_sha256":"0997af79f4a3b5b93a2e7a53bd425a06189688b60bf977355727387b232d253e","abstract_canon_sha256":"194cd30994cf5d7c42b1ea96e417456757dfcc7b09c970a32847c549be7eb0ee"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:41:49.251170Z","signature_b64":"9GvQpzk5aT+g3E41Z1ll3L16tA7ap5xQbRtML3DEyuQFEwbo8Fo25EjhJwZq88BSPL/c0hPNJutjVQpu5tAkAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2c20eb02d05159a6cd45312bf2b0eb04d29d95785d69a336d147f61e11d7265c","last_reissued_at":"2026-05-18T01:41:49.250703Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:41:49.250703Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Harmonic forms on ALF gravitational instantons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Guido Franchetti","submitted_at":"2014-10-10T18:41:13Z","abstract_excerpt":"We study the space of square-integrable harmonic forms over ALF gravitational instantons of type $A _{ K -1 } $ and of type $D _K $. We first calculate its dimension making use of a result by Hausel, Hunsicker and Mazzeo which relates the Hodge cohomology of a gravitational instanton $M$ to the singular cohomology of a particular compactification $X _M $ of $M$. We then exhibit an explicit basis, exact for $A _{ K -1 } $ and approximate for $D _K $, and interpret geometrically the relations between $M$, $X _M $ and their cohomologies."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.2864","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":"1410.2864","created_at":"2026-05-18T01:41:49.250770+00:00"},{"alias_kind":"arxiv_version","alias_value":"1410.2864v1","created_at":"2026-05-18T01:41:49.250770+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.2864","created_at":"2026-05-18T01:41:49.250770+00:00"},{"alias_kind":"pith_short_12","alias_value":"FQQOWAWQKFM2","created_at":"2026-05-18T12:28:28.263976+00:00"},{"alias_kind":"pith_short_16","alias_value":"FQQOWAWQKFM2NTKF","created_at":"2026-05-18T12:28:28.263976+00:00"},{"alias_kind":"pith_short_8","alias_value":"FQQOWAWQ","created_at":"2026-05-18T12:28:28.263976+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/FQQOWAWQKFM2NTKFGEV7FMHLAT","json":"https://pith.science/pith/FQQOWAWQKFM2NTKFGEV7FMHLAT.json","graph_json":"https://pith.science/api/pith-number/FQQOWAWQKFM2NTKFGEV7FMHLAT/graph.json","events_json":"https://pith.science/api/pith-number/FQQOWAWQKFM2NTKFGEV7FMHLAT/events.json","paper":"https://pith.science/paper/FQQOWAWQ"},"agent_actions":{"view_html":"https://pith.science/pith/FQQOWAWQKFM2NTKFGEV7FMHLAT","download_json":"https://pith.science/pith/FQQOWAWQKFM2NTKFGEV7FMHLAT.json","view_paper":"https://pith.science/paper/FQQOWAWQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1410.2864&json=true","fetch_graph":"https://pith.science/api/pith-number/FQQOWAWQKFM2NTKFGEV7FMHLAT/graph.json","fetch_events":"https://pith.science/api/pith-number/FQQOWAWQKFM2NTKFGEV7FMHLAT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FQQOWAWQKFM2NTKFGEV7FMHLAT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FQQOWAWQKFM2NTKFGEV7FMHLAT/action/storage_attestation","attest_author":"https://pith.science/pith/FQQOWAWQKFM2NTKFGEV7FMHLAT/action/author_attestation","sign_citation":"https://pith.science/pith/FQQOWAWQKFM2NTKFGEV7FMHLAT/action/citation_signature","submit_replication":"https://pith.science/pith/FQQOWAWQKFM2NTKFGEV7FMHLAT/action/replication_record"}},"created_at":"2026-05-18T01:41:49.250770+00:00","updated_at":"2026-05-18T01:41:49.250770+00:00"}