{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:2DTTXZGYFC4OBM5TPU6KNVQ6PB","short_pith_number":"pith:2DTTXZGY","schema_version":"1.0","canonical_sha256":"d0e73be4d828b8e0b3b37d3ca6d61e7857a313d7947a1a239c873aa00bc006e8","source":{"kind":"arxiv","id":"2606.05530","version":1},"attestation_state":"computed","paper":{"title":"Hodge theory and $G_4$ fluxes in weighted projective spaces: Galois action","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"hep-th","authors_text":"Daniel L\\'opez Garcia, Hugo Fortin","submitted_at":"2026-06-04T00:21:16Z","abstract_excerpt":"We extend the explicit study of $G_4$-fluxes and general Hodge cycles from the ordinary Fermat sextic fourfold to tame Fermat-type hypersurfaces in weighted projective space. The main new feature in the weighted setting is that the Galois action on the cyclotomic period data need not preserve the $(2,2)$-subspace. As a consequence, the rational reconstruction of an integral self-dual class can involve additional middle-cohomology components, increasing the norm of the corresponding flux.\n  We work at maximally symmetric Fermat points, where the period matrices and symmetry-invariant Hodge loci"},"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":"2606.05530","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2026-06-04T00:21:16Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"8f23651fbccc8d1d4595517eeaa54ea6ca6c05f88540e1579a32b5c53c4db7f9","abstract_canon_sha256":"bed2c655908a7e12950e7c1d9de36c291f78cf240a814acd0eef5ace8b8231f6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-05T01:14:53.909708Z","signature_b64":"R44LjNpA8+ghoknwf/AoAlCKQCwxYYOsfcBEvIAp9w92Y12xw/8/l1B4R+VXUoguNbhOd5IMzK+8e96uAzv3BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d0e73be4d828b8e0b3b37d3ca6d61e7857a313d7947a1a239c873aa00bc006e8","last_reissued_at":"2026-06-05T01:14:53.909231Z","signature_status":"signed_v1","first_computed_at":"2026-06-05T01:14:53.909231Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hodge theory and $G_4$ fluxes in weighted projective spaces: Galois action","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"hep-th","authors_text":"Daniel L\\'opez Garcia, Hugo Fortin","submitted_at":"2026-06-04T00:21:16Z","abstract_excerpt":"We extend the explicit study of $G_4$-fluxes and general Hodge cycles from the ordinary Fermat sextic fourfold to tame Fermat-type hypersurfaces in weighted projective space. The main new feature in the weighted setting is that the Galois action on the cyclotomic period data need not preserve the $(2,2)$-subspace. As a consequence, the rational reconstruction of an integral self-dual class can involve additional middle-cohomology components, increasing the norm of the corresponding flux.\n  We work at maximally symmetric Fermat points, where the period matrices and symmetry-invariant Hodge loci"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.05530","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/2606.05530/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":"2606.05530","created_at":"2026-06-05T01:14:53.909291+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.05530v1","created_at":"2026-06-05T01:14:53.909291+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.05530","created_at":"2026-06-05T01:14:53.909291+00:00"},{"alias_kind":"pith_short_12","alias_value":"2DTTXZGYFC4O","created_at":"2026-06-05T01:14:53.909291+00:00"},{"alias_kind":"pith_short_16","alias_value":"2DTTXZGYFC4OBM5T","created_at":"2026-06-05T01:14:53.909291+00:00"},{"alias_kind":"pith_short_8","alias_value":"2DTTXZGY","created_at":"2026-06-05T01:14:53.909291+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/2DTTXZGYFC4OBM5TPU6KNVQ6PB","json":"https://pith.science/pith/2DTTXZGYFC4OBM5TPU6KNVQ6PB.json","graph_json":"https://pith.science/api/pith-number/2DTTXZGYFC4OBM5TPU6KNVQ6PB/graph.json","events_json":"https://pith.science/api/pith-number/2DTTXZGYFC4OBM5TPU6KNVQ6PB/events.json","paper":"https://pith.science/paper/2DTTXZGY"},"agent_actions":{"view_html":"https://pith.science/pith/2DTTXZGYFC4OBM5TPU6KNVQ6PB","download_json":"https://pith.science/pith/2DTTXZGYFC4OBM5TPU6KNVQ6PB.json","view_paper":"https://pith.science/paper/2DTTXZGY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.05530&json=true","fetch_graph":"https://pith.science/api/pith-number/2DTTXZGYFC4OBM5TPU6KNVQ6PB/graph.json","fetch_events":"https://pith.science/api/pith-number/2DTTXZGYFC4OBM5TPU6KNVQ6PB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2DTTXZGYFC4OBM5TPU6KNVQ6PB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2DTTXZGYFC4OBM5TPU6KNVQ6PB/action/storage_attestation","attest_author":"https://pith.science/pith/2DTTXZGYFC4OBM5TPU6KNVQ6PB/action/author_attestation","sign_citation":"https://pith.science/pith/2DTTXZGYFC4OBM5TPU6KNVQ6PB/action/citation_signature","submit_replication":"https://pith.science/pith/2DTTXZGYFC4OBM5TPU6KNVQ6PB/action/replication_record"}},"created_at":"2026-06-05T01:14:53.909291+00:00","updated_at":"2026-06-05T01:14:53.909291+00:00"}