{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:U6KCPSWMYA7XVDFU2YZRIWTMPD","short_pith_number":"pith:U6KCPSWM","canonical_record":{"source":{"id":"2506.13376","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2025-06-16T11:38:17Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"85c4ab07a0498ac1617ff18eb0e3d1bed289e6f26f6a8ec95b4a3767f54fbd0c","abstract_canon_sha256":"f2e1b285381a45ff0c5dbe8f979e6f637b28b3f0257c6bb9055780d356e29fd4"},"schema_version":"1.0"},"canonical_sha256":"a79427caccc03f7a8cb4d633145a6c78dfac5cd253d2041ffb599cd375b0b99d","source":{"kind":"arxiv","id":"2506.13376","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.13376","created_at":"2026-07-05T11:22:09Z"},{"alias_kind":"arxiv_version","alias_value":"2506.13376v1","created_at":"2026-07-05T11:22:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.13376","created_at":"2026-07-05T11:22:09Z"},{"alias_kind":"pith_short_12","alias_value":"U6KCPSWMYA7X","created_at":"2026-07-05T11:22:09Z"},{"alias_kind":"pith_short_16","alias_value":"U6KCPSWMYA7XVDFU","created_at":"2026-07-05T11:22:09Z"},{"alias_kind":"pith_short_8","alias_value":"U6KCPSWM","created_at":"2026-07-05T11:22:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:U6KCPSWMYA7XVDFU2YZRIWTMPD","target":"record","payload":{"canonical_record":{"source":{"id":"2506.13376","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2025-06-16T11:38:17Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"85c4ab07a0498ac1617ff18eb0e3d1bed289e6f26f6a8ec95b4a3767f54fbd0c","abstract_canon_sha256":"f2e1b285381a45ff0c5dbe8f979e6f637b28b3f0257c6bb9055780d356e29fd4"},"schema_version":"1.0"},"canonical_sha256":"a79427caccc03f7a8cb4d633145a6c78dfac5cd253d2041ffb599cd375b0b99d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:22:09.371045Z","signature_b64":"YFmtsAA7f5FYWoA++GSgHYh/rrczMljxXSfiOLPvxRnLJD9lB7lzE6BHVLEJ/Kbj8nW+UJFMXolSuVbrExIYCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a79427caccc03f7a8cb4d633145a6c78dfac5cd253d2041ffb599cd375b0b99d","last_reissued_at":"2026-07-05T11:22:09.370416Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:22:09.370416Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.13376","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":"2026-07-05T11:22:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"abcgAnKsloB+K/Yw8C+GZZJjgTk/kVR0s2Tqzr/ahDS0MqpQGP4DPQxEgJnOuwREm/I7JqdXPx26Fx/vctreCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T06:23:27.444432Z"},"content_sha256":"074ee1e870ecac5646e8ef63e2c6becd3861fdc150b148e97c387b3deb12c6dc","schema_version":"1.0","event_id":"sha256:074ee1e870ecac5646e8ef63e2c6becd3861fdc150b148e97c387b3deb12c6dc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:U6KCPSWMYA7XVDFU2YZRIWTMPD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"ACM tilting bundles on a Geigle-Lenzing projective plane of type $(2,2,2,p)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"Jianmin Chen, Shiquan Ruan, Weikang Weng","submitted_at":"2025-06-16T11:38:17Z","abstract_excerpt":"Let $\\mathbb{X}$ be a Geigle-Lenzing projective plane of type $(2,2,2,p)$ and $\\mathsf{coh} \\mathbb{X}$ the category of coherent sheaves on $\\mathbb{X}$. This paper is devoted to study ACM tilting bundles over $\\mathbb{X}$, that is, tilting objects in the derived category $\\mathsf{D}^{\\rm b}(\\mathsf{coh} \\, \\mathbb{X})$ that are also ACM bundles. We show that a tilting bundle consisting of line bundles is the $2$-canonical tilting bundle up to degree shift. We also provide a program to construct ACM tilting bundles, which give a rich source of (almost) $2$-representation infinite algebras. As "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.13376","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/2506.13376/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":"2026-07-05T11:22:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Amu4OfWscU1fCXmEHGCa0lWp/n4OOK1DUBcE2tGcJJJ2TAFBqxrdDOvDmnL69OVu3or8meoZmuDLH5YxzGrsDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T06:23:27.445455Z"},"content_sha256":"d74e4b275b7765f578518891dfd447fad2fa1f63289bd92e1a7014aebe2a13de","schema_version":"1.0","event_id":"sha256:d74e4b275b7765f578518891dfd447fad2fa1f63289bd92e1a7014aebe2a13de"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U6KCPSWMYA7XVDFU2YZRIWTMPD/bundle.json","state_url":"https://pith.science/pith/U6KCPSWMYA7XVDFU2YZRIWTMPD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U6KCPSWMYA7XVDFU2YZRIWTMPD/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":"2026-08-11T06:23:27Z","links":{"resolver":"https://pith.science/pith/U6KCPSWMYA7XVDFU2YZRIWTMPD","bundle":"https://pith.science/pith/U6KCPSWMYA7XVDFU2YZRIWTMPD/bundle.json","state":"https://pith.science/pith/U6KCPSWMYA7XVDFU2YZRIWTMPD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U6KCPSWMYA7XVDFU2YZRIWTMPD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:U6KCPSWMYA7XVDFU2YZRIWTMPD","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":"f2e1b285381a45ff0c5dbe8f979e6f637b28b3f0257c6bb9055780d356e29fd4","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2025-06-16T11:38:17Z","title_canon_sha256":"85c4ab07a0498ac1617ff18eb0e3d1bed289e6f26f6a8ec95b4a3767f54fbd0c"},"schema_version":"1.0","source":{"id":"2506.13376","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.13376","created_at":"2026-07-05T11:22:09Z"},{"alias_kind":"arxiv_version","alias_value":"2506.13376v1","created_at":"2026-07-05T11:22:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.13376","created_at":"2026-07-05T11:22:09Z"},{"alias_kind":"pith_short_12","alias_value":"U6KCPSWMYA7X","created_at":"2026-07-05T11:22:09Z"},{"alias_kind":"pith_short_16","alias_value":"U6KCPSWMYA7XVDFU","created_at":"2026-07-05T11:22:09Z"},{"alias_kind":"pith_short_8","alias_value":"U6KCPSWM","created_at":"2026-07-05T11:22:09Z"}],"graph_snapshots":[{"event_id":"sha256:d74e4b275b7765f578518891dfd447fad2fa1f63289bd92e1a7014aebe2a13de","target":"graph","created_at":"2026-07-05T11:22:09Z","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/2506.13376/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $\\mathbb{X}$ be a Geigle-Lenzing projective plane of type $(2,2,2,p)$ and $\\mathsf{coh} \\mathbb{X}$ the category of coherent sheaves on $\\mathbb{X}$. This paper is devoted to study ACM tilting bundles over $\\mathbb{X}$, that is, tilting objects in the derived category $\\mathsf{D}^{\\rm b}(\\mathsf{coh} \\, \\mathbb{X})$ that are also ACM bundles. We show that a tilting bundle consisting of line bundles is the $2$-canonical tilting bundle up to degree shift. We also provide a program to construct ACM tilting bundles, which give a rich source of (almost) $2$-representation infinite algebras. As ","authors_text":"Jianmin Chen, Shiquan Ruan, Weikang Weng","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2025-06-16T11:38:17Z","title":"ACM tilting bundles on a Geigle-Lenzing projective plane of type $(2,2,2,p)$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.13376","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":"sha256:074ee1e870ecac5646e8ef63e2c6becd3861fdc150b148e97c387b3deb12c6dc","target":"record","created_at":"2026-07-05T11:22:09Z","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":"f2e1b285381a45ff0c5dbe8f979e6f637b28b3f0257c6bb9055780d356e29fd4","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2025-06-16T11:38:17Z","title_canon_sha256":"85c4ab07a0498ac1617ff18eb0e3d1bed289e6f26f6a8ec95b4a3767f54fbd0c"},"schema_version":"1.0","source":{"id":"2506.13376","kind":"arxiv","version":1}},"canonical_sha256":"a79427caccc03f7a8cb4d633145a6c78dfac5cd253d2041ffb599cd375b0b99d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a79427caccc03f7a8cb4d633145a6c78dfac5cd253d2041ffb599cd375b0b99d","first_computed_at":"2026-07-05T11:22:09.370416Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:22:09.370416Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YFmtsAA7f5FYWoA++GSgHYh/rrczMljxXSfiOLPvxRnLJD9lB7lzE6BHVLEJ/Kbj8nW+UJFMXolSuVbrExIYCw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:22:09.371045Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.13376","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:074ee1e870ecac5646e8ef63e2c6becd3861fdc150b148e97c387b3deb12c6dc","sha256:d74e4b275b7765f578518891dfd447fad2fa1f63289bd92e1a7014aebe2a13de"],"state_sha256":"8cd8b83c376bf4621b1251a55eddc4477ea254e067e13a2fb5aa2592e85e62c3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a7HXjMAlQ4ti3GoBQlqzCffpqRjuCSiEyvsbYxtxR0oYzvy2b29gKAb+YN2+fbloMJdtiBShEGhKbFTMpn98AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T06:23:27.451397Z","bundle_sha256":"0604b57dacb73df1a7d2d0035191893634486e832c2e55e4d5849caca406b33e"}}