{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:DS7Q3YO4OUXDOG7HATJA7V76JI","short_pith_number":"pith:DS7Q3YO4","canonical_record":{"source":{"id":"1306.4697","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-06-19T20:41:45Z","cross_cats_sorted":[],"title_canon_sha256":"ab30995498a776f9fff5af724185cc460cc4fc730b2f63f58c5cd69aae36f2e1","abstract_canon_sha256":"c5d62654699a81274dce5f39bd5925a88199a9697d19a6cd1446fc211def8756"},"schema_version":"1.0"},"canonical_sha256":"1cbf0de1dc752e371be704d20fd7fe4a31e87d58f3d0dcce9d237210c5af85cb","source":{"kind":"arxiv","id":"1306.4697","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.4697","created_at":"2026-05-18T03:16:48Z"},{"alias_kind":"arxiv_version","alias_value":"1306.4697v2","created_at":"2026-05-18T03:16:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.4697","created_at":"2026-05-18T03:16:48Z"},{"alias_kind":"pith_short_12","alias_value":"DS7Q3YO4OUXD","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"DS7Q3YO4OUXDOG7H","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"DS7Q3YO4","created_at":"2026-05-18T12:27:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:DS7Q3YO4OUXDOG7HATJA7V76JI","target":"record","payload":{"canonical_record":{"source":{"id":"1306.4697","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-06-19T20:41:45Z","cross_cats_sorted":[],"title_canon_sha256":"ab30995498a776f9fff5af724185cc460cc4fc730b2f63f58c5cd69aae36f2e1","abstract_canon_sha256":"c5d62654699a81274dce5f39bd5925a88199a9697d19a6cd1446fc211def8756"},"schema_version":"1.0"},"canonical_sha256":"1cbf0de1dc752e371be704d20fd7fe4a31e87d58f3d0dcce9d237210c5af85cb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:16:48.917334Z","signature_b64":"TXz0t1g9t+Tvbg2cgr1hjen05pealF8PvO3MODK0CXYEr02TQZ6YdAsmEOmLTAiIEpm+rMDLVkf4h6t8PQSvAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1cbf0de1dc752e371be704d20fd7fe4a31e87d58f3d0dcce9d237210c5af85cb","last_reissued_at":"2026-05-18T03:16:48.916637Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:16:48.916637Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.4697","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:16:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vlABpWYpnWF+wWgpbF/DOUlb7Ifl1He6b6wufm5vcQwf6RyytypJtH8UfCCiMehiAkl+mik7hi/1MkYUXBM8AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T02:15:19.218421Z"},"content_sha256":"d6fc3d31ae3a1eb3679e63cfc6912bd6fb2aaf6e6dcbe3ccf589a18fa0f3d604","schema_version":"1.0","event_id":"sha256:d6fc3d31ae3a1eb3679e63cfc6912bd6fb2aaf6e6dcbe3ccf589a18fa0f3d604"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:DS7Q3YO4OUXDOG7HATJA7V76JI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Zariski Decomposition with and without support","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Roberto Laface","submitted_at":"2013-06-19T20:41:45Z","abstract_excerpt":"In this paper we study Zariski Decomposition with support in a negative definite cycle, a variation introduced by Y. Miyaoka. We provide two extensions of the original statement, which was originally meant for effective $\\Q$-divisors: we can either state it for any $\\Q$-divisor, or we can take the support to be in any cycle. Ultimately, we present a new approach to Zariski Decomposition of pseudo-effective $\\Q$-divisors, which consists in iterating Zariski Decomposition with support."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.4697","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T03:16:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QO97aNXgUXvS129P70GbaqCB8dFbrMHuSQaf3px/2qSEWWFPKAfooCW5ErW+4cg1yqbg4Q9L+xzFXZNLGJafDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T02:15:19.218757Z"},"content_sha256":"e193dd58cc32e96b12e95b29bb29eede5afa334b36a8d2341822ebaa238600bb","schema_version":"1.0","event_id":"sha256:e193dd58cc32e96b12e95b29bb29eede5afa334b36a8d2341822ebaa238600bb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DS7Q3YO4OUXDOG7HATJA7V76JI/bundle.json","state_url":"https://pith.science/pith/DS7Q3YO4OUXDOG7HATJA7V76JI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DS7Q3YO4OUXDOG7HATJA7V76JI/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":"2026-06-25T02:15:19Z","links":{"resolver":"https://pith.science/pith/DS7Q3YO4OUXDOG7HATJA7V76JI","bundle":"https://pith.science/pith/DS7Q3YO4OUXDOG7HATJA7V76JI/bundle.json","state":"https://pith.science/pith/DS7Q3YO4OUXDOG7HATJA7V76JI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DS7Q3YO4OUXDOG7HATJA7V76JI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:DS7Q3YO4OUXDOG7HATJA7V76JI","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":"c5d62654699a81274dce5f39bd5925a88199a9697d19a6cd1446fc211def8756","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-06-19T20:41:45Z","title_canon_sha256":"ab30995498a776f9fff5af724185cc460cc4fc730b2f63f58c5cd69aae36f2e1"},"schema_version":"1.0","source":{"id":"1306.4697","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.4697","created_at":"2026-05-18T03:16:48Z"},{"alias_kind":"arxiv_version","alias_value":"1306.4697v2","created_at":"2026-05-18T03:16:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.4697","created_at":"2026-05-18T03:16:48Z"},{"alias_kind":"pith_short_12","alias_value":"DS7Q3YO4OUXD","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"DS7Q3YO4OUXDOG7H","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"DS7Q3YO4","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:e193dd58cc32e96b12e95b29bb29eede5afa334b36a8d2341822ebaa238600bb","target":"graph","created_at":"2026-05-18T03:16:48Z","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"},"paper":{"abstract_excerpt":"In this paper we study Zariski Decomposition with support in a negative definite cycle, a variation introduced by Y. Miyaoka. We provide two extensions of the original statement, which was originally meant for effective $\\Q$-divisors: we can either state it for any $\\Q$-divisor, or we can take the support to be in any cycle. Ultimately, we present a new approach to Zariski Decomposition of pseudo-effective $\\Q$-divisors, which consists in iterating Zariski Decomposition with support.","authors_text":"Roberto Laface","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-06-19T20:41:45Z","title":"On Zariski Decomposition with and without support"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.4697","kind":"arxiv","version":2},"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:d6fc3d31ae3a1eb3679e63cfc6912bd6fb2aaf6e6dcbe3ccf589a18fa0f3d604","target":"record","created_at":"2026-05-18T03:16:48Z","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":"c5d62654699a81274dce5f39bd5925a88199a9697d19a6cd1446fc211def8756","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-06-19T20:41:45Z","title_canon_sha256":"ab30995498a776f9fff5af724185cc460cc4fc730b2f63f58c5cd69aae36f2e1"},"schema_version":"1.0","source":{"id":"1306.4697","kind":"arxiv","version":2}},"canonical_sha256":"1cbf0de1dc752e371be704d20fd7fe4a31e87d58f3d0dcce9d237210c5af85cb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1cbf0de1dc752e371be704d20fd7fe4a31e87d58f3d0dcce9d237210c5af85cb","first_computed_at":"2026-05-18T03:16:48.916637Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:16:48.916637Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TXz0t1g9t+Tvbg2cgr1hjen05pealF8PvO3MODK0CXYEr02TQZ6YdAsmEOmLTAiIEpm+rMDLVkf4h6t8PQSvAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:16:48.917334Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.4697","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d6fc3d31ae3a1eb3679e63cfc6912bd6fb2aaf6e6dcbe3ccf589a18fa0f3d604","sha256:e193dd58cc32e96b12e95b29bb29eede5afa334b36a8d2341822ebaa238600bb"],"state_sha256":"4bb94864ab80ba036a19abfb50ce6a29f4b12e84b10a51278d78d5b9ea37b577"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FjL0vCKQIwXdEAx1XkdhRP8oON61HOTv5NxvL+9CQoX9JDO2S/OVZ7hUJqsckq4IUlj92MXI0zWFmGmJ6WfgAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T02:15:19.220626Z","bundle_sha256":"e3d9cb0ef4e398bc7d67557047295dbd7559db9b0ee79ff93049ae74bd197c83"}}