{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:4E74F5X6DOZ5U4LZ2WEOSIMYYV","short_pith_number":"pith:4E74F5X6","canonical_record":{"source":{"id":"2107.03918","kind":"arxiv","version":5},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2021-07-08T15:50:26Z","cross_cats_sorted":[],"title_canon_sha256":"e2fb3517c6746574ba4d47030d3204a13f2b035aaaaa6ee26c429a113c2374d3","abstract_canon_sha256":"3f0b810d822b663616a67e384cde061383dd3bf58bf5d5d0182aa8a11239bbaa"},"schema_version":"1.0"},"canonical_sha256":"e13fc2f6fe1bb3da7179d588e92198c577e62eed9abc0ecca95b280726bab487","source":{"kind":"arxiv","id":"2107.03918","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2107.03918","created_at":"2026-07-05T08:04:10Z"},{"alias_kind":"arxiv_version","alias_value":"2107.03918v5","created_at":"2026-07-05T08:04:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.03918","created_at":"2026-07-05T08:04:10Z"},{"alias_kind":"pith_short_12","alias_value":"4E74F5X6DOZ5","created_at":"2026-07-05T08:04:10Z"},{"alias_kind":"pith_short_16","alias_value":"4E74F5X6DOZ5U4LZ","created_at":"2026-07-05T08:04:10Z"},{"alias_kind":"pith_short_8","alias_value":"4E74F5X6","created_at":"2026-07-05T08:04:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:4E74F5X6DOZ5U4LZ2WEOSIMYYV","target":"record","payload":{"canonical_record":{"source":{"id":"2107.03918","kind":"arxiv","version":5},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2021-07-08T15:50:26Z","cross_cats_sorted":[],"title_canon_sha256":"e2fb3517c6746574ba4d47030d3204a13f2b035aaaaa6ee26c429a113c2374d3","abstract_canon_sha256":"3f0b810d822b663616a67e384cde061383dd3bf58bf5d5d0182aa8a11239bbaa"},"schema_version":"1.0"},"canonical_sha256":"e13fc2f6fe1bb3da7179d588e92198c577e62eed9abc0ecca95b280726bab487","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:04:10.234530Z","signature_b64":"dbFnCQj+AjlI0MBL7rXRt//Z1O2BvbfAs/wWosy64KOTWseNYujRkM/VWZoxW5FU9RTzYAjHo1jCSGxtM8ztDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e13fc2f6fe1bb3da7179d588e92198c577e62eed9abc0ecca95b280726bab487","last_reissued_at":"2026-07-05T08:04:10.234086Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:04:10.234086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2107.03918","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:04:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c5tKqQX7hYYg/LdvSVx1Oqkd/u61Yfs8/3zrOIjqJwE4TrmQ2B7wvGok+uNZbTJfPOQrs93QOxZeYNa0WZyoDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T04:51:36.857026Z"},"content_sha256":"a619bac7d2afaa75a71daa333b6b8b36fde261e6861e93932d259cca8338a35f","schema_version":"1.0","event_id":"sha256:a619bac7d2afaa75a71daa333b6b8b36fde261e6861e93932d259cca8338a35f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:4E74F5X6DOZ5U4LZ2WEOSIMYYV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The moduli stack of principal $\\rho$-sheaves and Gieseker-Harder-Narasimhan filtrations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alfonso Zamora, Andres Fernandez Herrero, Tom\\'as L. G\\'omez","submitted_at":"2021-07-08T15:50:26Z","abstract_excerpt":"Let X be a smooth projective variety and let G be a connected reductive group, both defined over a field of characteristic 0. Given a faithful representation $\\rho$ of G into a product of general linear groups, we define a moduli stack of principal $\\rho$-sheaves that compactifies the stack of G-bundles on X. We apply the theory developed by Alper, Halpern-Leistner and Heinloth to construct a moduli space of Gieseker semistable principal $\\rho$-sheaves. This provides an intrinsic stack-theoretic construction of the moduli space of semistable singular principal bundles as constructed by Schmitt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.03918","kind":"arxiv","version":5},"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/2107.03918/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":"2026-07-05T08:04:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JMs6K1ok6wcP1gfAIWVoMbqJiP6769kbI42K4CFk3Kz1sNgJI7KdfVV7Z1negtja2QOYU6dIOgDjzkL15bwqDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T04:51:36.857563Z"},"content_sha256":"7096541e2da503b6c9efdc85c115c5877fbd146b5506f262f0f0ba7e86d72a0a","schema_version":"1.0","event_id":"sha256:7096541e2da503b6c9efdc85c115c5877fbd146b5506f262f0f0ba7e86d72a0a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4E74F5X6DOZ5U4LZ2WEOSIMYYV/bundle.json","state_url":"https://pith.science/pith/4E74F5X6DOZ5U4LZ2WEOSIMYYV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4E74F5X6DOZ5U4LZ2WEOSIMYYV/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":"2026-08-10T04:51:36Z","links":{"resolver":"https://pith.science/pith/4E74F5X6DOZ5U4LZ2WEOSIMYYV","bundle":"https://pith.science/pith/4E74F5X6DOZ5U4LZ2WEOSIMYYV/bundle.json","state":"https://pith.science/pith/4E74F5X6DOZ5U4LZ2WEOSIMYYV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4E74F5X6DOZ5U4LZ2WEOSIMYYV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:4E74F5X6DOZ5U4LZ2WEOSIMYYV","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":"3f0b810d822b663616a67e384cde061383dd3bf58bf5d5d0182aa8a11239bbaa","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2021-07-08T15:50:26Z","title_canon_sha256":"e2fb3517c6746574ba4d47030d3204a13f2b035aaaaa6ee26c429a113c2374d3"},"schema_version":"1.0","source":{"id":"2107.03918","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2107.03918","created_at":"2026-07-05T08:04:10Z"},{"alias_kind":"arxiv_version","alias_value":"2107.03918v5","created_at":"2026-07-05T08:04:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.03918","created_at":"2026-07-05T08:04:10Z"},{"alias_kind":"pith_short_12","alias_value":"4E74F5X6DOZ5","created_at":"2026-07-05T08:04:10Z"},{"alias_kind":"pith_short_16","alias_value":"4E74F5X6DOZ5U4LZ","created_at":"2026-07-05T08:04:10Z"},{"alias_kind":"pith_short_8","alias_value":"4E74F5X6","created_at":"2026-07-05T08:04:10Z"}],"graph_snapshots":[{"event_id":"sha256:7096541e2da503b6c9efdc85c115c5877fbd146b5506f262f0f0ba7e86d72a0a","target":"graph","created_at":"2026-07-05T08:04:10Z","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/2107.03918/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let X be a smooth projective variety and let G be a connected reductive group, both defined over a field of characteristic 0. Given a faithful representation $\\rho$ of G into a product of general linear groups, we define a moduli stack of principal $\\rho$-sheaves that compactifies the stack of G-bundles on X. We apply the theory developed by Alper, Halpern-Leistner and Heinloth to construct a moduli space of Gieseker semistable principal $\\rho$-sheaves. This provides an intrinsic stack-theoretic construction of the moduli space of semistable singular principal bundles as constructed by Schmitt","authors_text":"Alfonso Zamora, Andres Fernandez Herrero, Tom\\'as L. G\\'omez","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2021-07-08T15:50:26Z","title":"The moduli stack of principal $\\rho$-sheaves and Gieseker-Harder-Narasimhan filtrations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.03918","kind":"arxiv","version":5},"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:a619bac7d2afaa75a71daa333b6b8b36fde261e6861e93932d259cca8338a35f","target":"record","created_at":"2026-07-05T08:04:10Z","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":"3f0b810d822b663616a67e384cde061383dd3bf58bf5d5d0182aa8a11239bbaa","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2021-07-08T15:50:26Z","title_canon_sha256":"e2fb3517c6746574ba4d47030d3204a13f2b035aaaaa6ee26c429a113c2374d3"},"schema_version":"1.0","source":{"id":"2107.03918","kind":"arxiv","version":5}},"canonical_sha256":"e13fc2f6fe1bb3da7179d588e92198c577e62eed9abc0ecca95b280726bab487","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e13fc2f6fe1bb3da7179d588e92198c577e62eed9abc0ecca95b280726bab487","first_computed_at":"2026-07-05T08:04:10.234086Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:04:10.234086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dbFnCQj+AjlI0MBL7rXRt//Z1O2BvbfAs/wWosy64KOTWseNYujRkM/VWZoxW5FU9RTzYAjHo1jCSGxtM8ztDw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:04:10.234530Z","signed_message":"canonical_sha256_bytes"},"source_id":"2107.03918","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a619bac7d2afaa75a71daa333b6b8b36fde261e6861e93932d259cca8338a35f","sha256:7096541e2da503b6c9efdc85c115c5877fbd146b5506f262f0f0ba7e86d72a0a"],"state_sha256":"02d7d1e07350ae6abcdbc05963bb6b549fec833232a9ea91a467f7f1bca7be65"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u6DlV/q/Mf0S4pokFBrpbgJsSgmwIJSep/wO9330qMpZ+4r7K0O0UzDkJY2NOVljAGLX2RVp+tapmdD8NiBICw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T04:51:36.861170Z","bundle_sha256":"316b01f170c7ae4667b25bf1522dfade98b88090abff27e279f6dc1cfe80a4a6"}}