{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:LBKP3FBG4NV3UINK7PNPPZ5I4Q","short_pith_number":"pith:LBKP3FBG","canonical_record":{"source":{"id":"2606.06072","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-06-04T12:12:12Z","cross_cats_sorted":["math.CV","math.DG"],"title_canon_sha256":"ccfb36e5f08c7c2d4ccef044051cf19dda378a3174748dc7b7761655bf3f3b9c","abstract_canon_sha256":"0807883f73204e81114a07744603551d3832a780f83710fccd56635bb603ff49"},"schema_version":"1.0"},"canonical_sha256":"5854fd9426e36bba21aafbdaf7e7a8e41f0eb7551fa0a9da60b80767dc1f62b1","source":{"kind":"arxiv","id":"2606.06072","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.06072","created_at":"2026-06-05T01:15:32Z"},{"alias_kind":"arxiv_version","alias_value":"2606.06072v1","created_at":"2026-06-05T01:15:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.06072","created_at":"2026-06-05T01:15:32Z"},{"alias_kind":"pith_short_12","alias_value":"LBKP3FBG4NV3","created_at":"2026-06-05T01:15:32Z"},{"alias_kind":"pith_short_16","alias_value":"LBKP3FBG4NV3UINK","created_at":"2026-06-05T01:15:32Z"},{"alias_kind":"pith_short_8","alias_value":"LBKP3FBG","created_at":"2026-06-05T01:15:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:LBKP3FBG4NV3UINK7PNPPZ5I4Q","target":"record","payload":{"canonical_record":{"source":{"id":"2606.06072","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-06-04T12:12:12Z","cross_cats_sorted":["math.CV","math.DG"],"title_canon_sha256":"ccfb36e5f08c7c2d4ccef044051cf19dda378a3174748dc7b7761655bf3f3b9c","abstract_canon_sha256":"0807883f73204e81114a07744603551d3832a780f83710fccd56635bb603ff49"},"schema_version":"1.0"},"canonical_sha256":"5854fd9426e36bba21aafbdaf7e7a8e41f0eb7551fa0a9da60b80767dc1f62b1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-05T01:15:32.071733Z","signature_b64":"A8Vz0SZP8gi3xOeCx01y/rqA3EdpI5RydrKwfHjbe39HDHur48wR+TvopYDW/Ypr+mREjoG+wcAOKDkECGgTCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5854fd9426e36bba21aafbdaf7e7a8e41f0eb7551fa0a9da60b80767dc1f62b1","last_reissued_at":"2026-06-05T01:15:32.071294Z","signature_status":"signed_v1","first_computed_at":"2026-06-05T01:15:32.071294Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.06072","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":"2026-06-05T01:15:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zr8R6F6B1uIdZrWjiVCk9TUpZaqr9WcJgS1FUdMtmNlFFVvo5PH+bFfEvC2GVtDl5vgAtpG9CB3vNE8FCudQBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T09:32:42.135309Z"},"content_sha256":"bb7c8fdb225e144f7a7343601bb911d96a9dc67dda9cdf3258e64471f6903c64","schema_version":"1.0","event_id":"sha256:bb7c8fdb225e144f7a7343601bb911d96a9dc67dda9cdf3258e64471f6903c64"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:LBKP3FBG4NV3UINK7PNPPZ5I4Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Coherent sheaves on subvarieties in Hopf manifolds","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CV","math.DG"],"primary_cat":"math.AG","authors_text":"Liviu Ornea, Misha Verbitsky","submitted_at":"2026-06-04T12:12:12Z","abstract_excerpt":"We prove a version of GAGA theorem for a normal complex analytic variety $X$ equipped with an invertible holomorphic contraction $\\gamma$ with center in $x$. We show that $X$ admits a natural structure of an affine variety, and any $\\gamma$-equivariant complex analytic reflexive coherent sheaf on $X$ admits a natural algebraic structure. We prove a structure theorem for $X_0:=X\\backslash x$, showing that it admits a proper action of ${\\Bbb C}^*$, and is isomorphic to the space of non-zero vectors in the total space of an ample line bundle over the projective variety $Z:= X_0/{\\mathbb C}^*$ equ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.06072","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/2606.06072/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":"2026-06-05T01:15:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fq0t3FH4jsUIkrArHBm+4wxjuRDNlROs+zJO/qZXHqCbCwvnGXY5SeqnbjyBneNnsYcraJlWiakYGwknwolVBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T09:32:42.135749Z"},"content_sha256":"8a381079e0ee743f59578228776faeb859bef82788e19c7dd2609f0f72e664b8","schema_version":"1.0","event_id":"sha256:8a381079e0ee743f59578228776faeb859bef82788e19c7dd2609f0f72e664b8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LBKP3FBG4NV3UINK7PNPPZ5I4Q/bundle.json","state_url":"https://pith.science/pith/LBKP3FBG4NV3UINK7PNPPZ5I4Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LBKP3FBG4NV3UINK7PNPPZ5I4Q/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":"2026-06-21T09:32:42Z","links":{"resolver":"https://pith.science/pith/LBKP3FBG4NV3UINK7PNPPZ5I4Q","bundle":"https://pith.science/pith/LBKP3FBG4NV3UINK7PNPPZ5I4Q/bundle.json","state":"https://pith.science/pith/LBKP3FBG4NV3UINK7PNPPZ5I4Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LBKP3FBG4NV3UINK7PNPPZ5I4Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:LBKP3FBG4NV3UINK7PNPPZ5I4Q","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":"0807883f73204e81114a07744603551d3832a780f83710fccd56635bb603ff49","cross_cats_sorted":["math.CV","math.DG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-06-04T12:12:12Z","title_canon_sha256":"ccfb36e5f08c7c2d4ccef044051cf19dda378a3174748dc7b7761655bf3f3b9c"},"schema_version":"1.0","source":{"id":"2606.06072","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.06072","created_at":"2026-06-05T01:15:32Z"},{"alias_kind":"arxiv_version","alias_value":"2606.06072v1","created_at":"2026-06-05T01:15:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.06072","created_at":"2026-06-05T01:15:32Z"},{"alias_kind":"pith_short_12","alias_value":"LBKP3FBG4NV3","created_at":"2026-06-05T01:15:32Z"},{"alias_kind":"pith_short_16","alias_value":"LBKP3FBG4NV3UINK","created_at":"2026-06-05T01:15:32Z"},{"alias_kind":"pith_short_8","alias_value":"LBKP3FBG","created_at":"2026-06-05T01:15:32Z"}],"graph_snapshots":[{"event_id":"sha256:8a381079e0ee743f59578228776faeb859bef82788e19c7dd2609f0f72e664b8","target":"graph","created_at":"2026-06-05T01:15:32Z","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/2606.06072/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove a version of GAGA theorem for a normal complex analytic variety $X$ equipped with an invertible holomorphic contraction $\\gamma$ with center in $x$. We show that $X$ admits a natural structure of an affine variety, and any $\\gamma$-equivariant complex analytic reflexive coherent sheaf on $X$ admits a natural algebraic structure. We prove a structure theorem for $X_0:=X\\backslash x$, showing that it admits a proper action of ${\\Bbb C}^*$, and is isomorphic to the space of non-zero vectors in the total space of an ample line bundle over the projective variety $Z:= X_0/{\\mathbb C}^*$ equ","authors_text":"Liviu Ornea, Misha Verbitsky","cross_cats":["math.CV","math.DG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-06-04T12:12:12Z","title":"Coherent sheaves on subvarieties in Hopf manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.06072","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:bb7c8fdb225e144f7a7343601bb911d96a9dc67dda9cdf3258e64471f6903c64","target":"record","created_at":"2026-06-05T01:15:32Z","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":"0807883f73204e81114a07744603551d3832a780f83710fccd56635bb603ff49","cross_cats_sorted":["math.CV","math.DG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-06-04T12:12:12Z","title_canon_sha256":"ccfb36e5f08c7c2d4ccef044051cf19dda378a3174748dc7b7761655bf3f3b9c"},"schema_version":"1.0","source":{"id":"2606.06072","kind":"arxiv","version":1}},"canonical_sha256":"5854fd9426e36bba21aafbdaf7e7a8e41f0eb7551fa0a9da60b80767dc1f62b1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5854fd9426e36bba21aafbdaf7e7a8e41f0eb7551fa0a9da60b80767dc1f62b1","first_computed_at":"2026-06-05T01:15:32.071294Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-05T01:15:32.071294Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A8Vz0SZP8gi3xOeCx01y/rqA3EdpI5RydrKwfHjbe39HDHur48wR+TvopYDW/Ypr+mREjoG+wcAOKDkECGgTCA==","signature_status":"signed_v1","signed_at":"2026-06-05T01:15:32.071733Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.06072","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bb7c8fdb225e144f7a7343601bb911d96a9dc67dda9cdf3258e64471f6903c64","sha256:8a381079e0ee743f59578228776faeb859bef82788e19c7dd2609f0f72e664b8"],"state_sha256":"51c4ce58de6061ef1050d72a6473422640a07e54ba535cd9b96e76ea7db61a05"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d1/frQ7PxpuD4QO4YtbCoE8AamEMWNbXZUlAm/6RBBeIpiLdqgyKQOdT2QtdkyO/JnvlQ78O8JAR5YEMZCjyBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T09:32:42.137870Z","bundle_sha256":"50c6579e9ecce584e3cc2ccb61ddaf89f3820a226d7a1f690f8c0503c12309a0"}}