{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:BLB4G4WQYWDV75KERPE7GEM5RH","short_pith_number":"pith:BLB4G4WQ","canonical_record":{"source":{"id":"2507.09345","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-07-12T16:50:29Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"aa8134cb7aad1b64752ece65f2f887a64affcbdd5502ca0f86939b3665ce3c0b","abstract_canon_sha256":"3825edc5c027c72b1675b9b5838f23ff1c2a50982c45b6107d1e9100166dbce6"},"schema_version":"1.0"},"canonical_sha256":"0ac3c372d0c5875ff5448bc9f3119d89ec8e14015bc742b8bc02b71bc5e47deb","source":{"kind":"arxiv","id":"2507.09345","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.09345","created_at":"2026-07-05T11:36:07Z"},{"alias_kind":"arxiv_version","alias_value":"2507.09345v1","created_at":"2026-07-05T11:36:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.09345","created_at":"2026-07-05T11:36:07Z"},{"alias_kind":"pith_short_12","alias_value":"BLB4G4WQYWDV","created_at":"2026-07-05T11:36:07Z"},{"alias_kind":"pith_short_16","alias_value":"BLB4G4WQYWDV75KE","created_at":"2026-07-05T11:36:07Z"},{"alias_kind":"pith_short_8","alias_value":"BLB4G4WQ","created_at":"2026-07-05T11:36:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:BLB4G4WQYWDV75KERPE7GEM5RH","target":"record","payload":{"canonical_record":{"source":{"id":"2507.09345","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-07-12T16:50:29Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"aa8134cb7aad1b64752ece65f2f887a64affcbdd5502ca0f86939b3665ce3c0b","abstract_canon_sha256":"3825edc5c027c72b1675b9b5838f23ff1c2a50982c45b6107d1e9100166dbce6"},"schema_version":"1.0"},"canonical_sha256":"0ac3c372d0c5875ff5448bc9f3119d89ec8e14015bc742b8bc02b71bc5e47deb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:36:07.465762Z","signature_b64":"0ZH/LykehrSA2KT9xlxbsDGT1jzO3lDj3d+ZZyMHsvIXnO9o1DczgDpsMgNbmyl2XORoeWKZspVnmxb+VjxCCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ac3c372d0c5875ff5448bc9f3119d89ec8e14015bc742b8bc02b71bc5e47deb","last_reissued_at":"2026-07-05T11:36:07.465354Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:36:07.465354Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.09345","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:36:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jhLzWXlTxaosUPkb6MgQBFXTr2RHP5UhG//F0EZf5jVaPM6VEXKJ7F/MLAlsW7x2CWxlg+bwrF1hjSOtFTQOBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T12:12:25.664204Z"},"content_sha256":"8548260837cc70b22cdb74037aae55f4c2932d759bd6c36463b61c70d3ec4240","schema_version":"1.0","event_id":"sha256:8548260837cc70b22cdb74037aae55f4c2932d759bd6c36463b61c70d3ec4240"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:BLB4G4WQYWDV75KERPE7GEM5RH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ulrich bundles on double coverings of projective space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Roberto Vacca","submitted_at":"2025-07-12T16:50:29Z","abstract_excerpt":"Fixed a polarised variety $X$, we can ask if it admits Ulrich bundles and, in case, what is their minimal possible rank. In this thesis, after recalling general properties of Ulrich sheaves, we show that any finite covering of $\\mathbb{P}^n$ that embeds as a divisor in a weighted projective space with weights $(1^{n+1},m)$ admits Ulrich sheaves, by using matrix factorisations. Among these varieties, we focus on double coverings of with $n\\ge3$. Through Hartshorne--Serre correspondence, which we review along the way, we prove that the general such $X$ admits a rank $2$ Ulrich sheaf if and only "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.09345","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/2507.09345/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:36:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aB5P0Asyzo429iq2DLcLga1huI3oV80l7WsugaYI0Xm4xdKMsEQdqm7Cfj1DJyCI+rB1gxjqoeH+q5B6nDWRBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T12:12:25.665176Z"},"content_sha256":"e44ef875bff66690fb4d501853efeaf477eb2316d5a52dc7317dce47048f7e30","schema_version":"1.0","event_id":"sha256:e44ef875bff66690fb4d501853efeaf477eb2316d5a52dc7317dce47048f7e30"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BLB4G4WQYWDV75KERPE7GEM5RH/bundle.json","state_url":"https://pith.science/pith/BLB4G4WQYWDV75KERPE7GEM5RH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BLB4G4WQYWDV75KERPE7GEM5RH/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-18T12:12:25Z","links":{"resolver":"https://pith.science/pith/BLB4G4WQYWDV75KERPE7GEM5RH","bundle":"https://pith.science/pith/BLB4G4WQYWDV75KERPE7GEM5RH/bundle.json","state":"https://pith.science/pith/BLB4G4WQYWDV75KERPE7GEM5RH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BLB4G4WQYWDV75KERPE7GEM5RH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:BLB4G4WQYWDV75KERPE7GEM5RH","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":"3825edc5c027c72b1675b9b5838f23ff1c2a50982c45b6107d1e9100166dbce6","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-07-12T16:50:29Z","title_canon_sha256":"aa8134cb7aad1b64752ece65f2f887a64affcbdd5502ca0f86939b3665ce3c0b"},"schema_version":"1.0","source":{"id":"2507.09345","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.09345","created_at":"2026-07-05T11:36:07Z"},{"alias_kind":"arxiv_version","alias_value":"2507.09345v1","created_at":"2026-07-05T11:36:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.09345","created_at":"2026-07-05T11:36:07Z"},{"alias_kind":"pith_short_12","alias_value":"BLB4G4WQYWDV","created_at":"2026-07-05T11:36:07Z"},{"alias_kind":"pith_short_16","alias_value":"BLB4G4WQYWDV75KE","created_at":"2026-07-05T11:36:07Z"},{"alias_kind":"pith_short_8","alias_value":"BLB4G4WQ","created_at":"2026-07-05T11:36:07Z"}],"graph_snapshots":[{"event_id":"sha256:e44ef875bff66690fb4d501853efeaf477eb2316d5a52dc7317dce47048f7e30","target":"graph","created_at":"2026-07-05T11:36:07Z","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/2507.09345/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Fixed a polarised variety $X$, we can ask if it admits Ulrich bundles and, in case, what is their minimal possible rank. In this thesis, after recalling general properties of Ulrich sheaves, we show that any finite covering of $\\mathbb{P}^n$ that embeds as a divisor in a weighted projective space with weights $(1^{n+1},m)$ admits Ulrich sheaves, by using matrix factorisations. Among these varieties, we focus on double coverings of with $n\\ge3$. Through Hartshorne--Serre correspondence, which we review along the way, we prove that the general such $X$ admits a rank $2$ Ulrich sheaf if and only ","authors_text":"Roberto Vacca","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-07-12T16:50:29Z","title":"Ulrich bundles on double coverings of projective space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.09345","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":"sha256:8548260837cc70b22cdb74037aae55f4c2932d759bd6c36463b61c70d3ec4240","target":"record","created_at":"2026-07-05T11:36:07Z","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":"3825edc5c027c72b1675b9b5838f23ff1c2a50982c45b6107d1e9100166dbce6","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-07-12T16:50:29Z","title_canon_sha256":"aa8134cb7aad1b64752ece65f2f887a64affcbdd5502ca0f86939b3665ce3c0b"},"schema_version":"1.0","source":{"id":"2507.09345","kind":"arxiv","version":1}},"canonical_sha256":"0ac3c372d0c5875ff5448bc9f3119d89ec8e14015bc742b8bc02b71bc5e47deb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0ac3c372d0c5875ff5448bc9f3119d89ec8e14015bc742b8bc02b71bc5e47deb","first_computed_at":"2026-07-05T11:36:07.465354Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:36:07.465354Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0ZH/LykehrSA2KT9xlxbsDGT1jzO3lDj3d+ZZyMHsvIXnO9o1DczgDpsMgNbmyl2XORoeWKZspVnmxb+VjxCCw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:36:07.465762Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.09345","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8548260837cc70b22cdb74037aae55f4c2932d759bd6c36463b61c70d3ec4240","sha256:e44ef875bff66690fb4d501853efeaf477eb2316d5a52dc7317dce47048f7e30"],"state_sha256":"a5b7e87672816126ae38f5ef34e58f1546e68d8df57dfac9bb6e2c99b9d47314"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hLVLegWHiwmFdHVBKNUh0MjESNVO/hoaETVSv4s919fP7Xj4fW1Rh/sf2ie68fCBemONVevsvNAOWIcYNAlnDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T12:12:25.673920Z","bundle_sha256":"bc9b5c70e5937ec7de657949f0407d45f6bf37e74ef3f402b4dbd53853da7a3a"}}