{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:Q6MSFNO6JPVW63LBRP2KZMO47X","short_pith_number":"pith:Q6MSFNO6","canonical_record":{"source":{"id":"1406.2759","kind":"arxiv","version":8},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-06-11T01:47:52Z","cross_cats_sorted":[],"title_canon_sha256":"6b55c2c2fca3cccd326fb1ca2d3bdeb59713026533c56be8a006ed42b2b2531b","abstract_canon_sha256":"86a37fefa716aa8aeff72c3d40da4f7937495b43f9bd35b29dc77d499f6d52e5"},"schema_version":"1.0"},"canonical_sha256":"879922b5de4beb6f6d618bf4acb1dcfdd2e6d68d1e6fcc19e3b1c5c7000ea33a","source":{"kind":"arxiv","id":"1406.2759","version":8},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.2759","created_at":"2026-05-18T01:21:13Z"},{"alias_kind":"arxiv_version","alias_value":"1406.2759v8","created_at":"2026-05-18T01:21:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.2759","created_at":"2026-05-18T01:21:13Z"},{"alias_kind":"pith_short_12","alias_value":"Q6MSFNO6JPVW","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"Q6MSFNO6JPVW63LB","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"Q6MSFNO6","created_at":"2026-05-18T12:28:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:Q6MSFNO6JPVW63LBRP2KZMO47X","target":"record","payload":{"canonical_record":{"source":{"id":"1406.2759","kind":"arxiv","version":8},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-06-11T01:47:52Z","cross_cats_sorted":[],"title_canon_sha256":"6b55c2c2fca3cccd326fb1ca2d3bdeb59713026533c56be8a006ed42b2b2531b","abstract_canon_sha256":"86a37fefa716aa8aeff72c3d40da4f7937495b43f9bd35b29dc77d499f6d52e5"},"schema_version":"1.0"},"canonical_sha256":"879922b5de4beb6f6d618bf4acb1dcfdd2e6d68d1e6fcc19e3b1c5c7000ea33a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:13.901371Z","signature_b64":"xi8jftvH+GYkS9AacgKUf1rqRMl5/BwOAF1WZFk9Ce0res2j9ZgJyC997Ak0U7JJpQT3X80ictets1IWanp4Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"879922b5de4beb6f6d618bf4acb1dcfdd2e6d68d1e6fcc19e3b1c5c7000ea33a","last_reissued_at":"2026-05-18T01:21:13.900713Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:13.900713Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.2759","source_version":8,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:21:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ga2p+WkDXGhPfkJBgJIs+asZiz0CM3B03J5EoP5y72wgTkP9vKF29On8BWDnrg4kOsk+3BElLq5pGhPSsy0SAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T11:27:40.321415Z"},"content_sha256":"ee4a1c82eb83c23146a4b87c3cfaf2637f662fbf0c2c448c017b21f0294bf9bc","schema_version":"1.0","event_id":"sha256:ee4a1c82eb83c23146a4b87c3cfaf2637f662fbf0c2c448c017b21f0294bf9bc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:Q6MSFNO6JPVW63LBRP2KZMO47X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On subadditivity of the logarithmic Kodaira dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Osamu Fujino","submitted_at":"2014-06-11T01:47:52Z","abstract_excerpt":"We reduce Iitaka's subadditivity conjecture for the logarithmic Kodaira dimension to a special case of the generalized abundance conjecture by establishing an Iitaka type inequality for Nakayama's numerical Kodaira dimension. Our proof heavily depends on Nakayama's theory of $\\omega$-sheaves and $\\widehat{\\omega}$-sheaves. As an application, we prove the subadditivity of the logarithmic Kodaira dimension for affine varieties by using the minimal model program for projective klt pairs with big boundary divisor."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.2759","kind":"arxiv","version":8},"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":"2026-05-18T01:21:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/Fde5GM+Zt/WCwT38F6UMfKHxEhqiyZR5RmXbv97DJNhDY+hn5N2SPli39aC26jcoHa1PIt+xryewCUQN+CnCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T11:27:40.321751Z"},"content_sha256":"81977d4f43c21e5d5ef1f7780a7528e014b563b36de8da3c8d498aa204cc73b7","schema_version":"1.0","event_id":"sha256:81977d4f43c21e5d5ef1f7780a7528e014b563b36de8da3c8d498aa204cc73b7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q6MSFNO6JPVW63LBRP2KZMO47X/bundle.json","state_url":"https://pith.science/pith/Q6MSFNO6JPVW63LBRP2KZMO47X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q6MSFNO6JPVW63LBRP2KZMO47X/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":"2026-06-29T11:27:40Z","links":{"resolver":"https://pith.science/pith/Q6MSFNO6JPVW63LBRP2KZMO47X","bundle":"https://pith.science/pith/Q6MSFNO6JPVW63LBRP2KZMO47X/bundle.json","state":"https://pith.science/pith/Q6MSFNO6JPVW63LBRP2KZMO47X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q6MSFNO6JPVW63LBRP2KZMO47X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:Q6MSFNO6JPVW63LBRP2KZMO47X","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":"86a37fefa716aa8aeff72c3d40da4f7937495b43f9bd35b29dc77d499f6d52e5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-06-11T01:47:52Z","title_canon_sha256":"6b55c2c2fca3cccd326fb1ca2d3bdeb59713026533c56be8a006ed42b2b2531b"},"schema_version":"1.0","source":{"id":"1406.2759","kind":"arxiv","version":8}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.2759","created_at":"2026-05-18T01:21:13Z"},{"alias_kind":"arxiv_version","alias_value":"1406.2759v8","created_at":"2026-05-18T01:21:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.2759","created_at":"2026-05-18T01:21:13Z"},{"alias_kind":"pith_short_12","alias_value":"Q6MSFNO6JPVW","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"Q6MSFNO6JPVW63LB","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"Q6MSFNO6","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:81977d4f43c21e5d5ef1f7780a7528e014b563b36de8da3c8d498aa204cc73b7","target":"graph","created_at":"2026-05-18T01:21:13Z","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":"We reduce Iitaka's subadditivity conjecture for the logarithmic Kodaira dimension to a special case of the generalized abundance conjecture by establishing an Iitaka type inequality for Nakayama's numerical Kodaira dimension. Our proof heavily depends on Nakayama's theory of $\\omega$-sheaves and $\\widehat{\\omega}$-sheaves. As an application, we prove the subadditivity of the logarithmic Kodaira dimension for affine varieties by using the minimal model program for projective klt pairs with big boundary divisor.","authors_text":"Osamu Fujino","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-06-11T01:47:52Z","title":"On subadditivity of the logarithmic Kodaira dimension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.2759","kind":"arxiv","version":8},"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:ee4a1c82eb83c23146a4b87c3cfaf2637f662fbf0c2c448c017b21f0294bf9bc","target":"record","created_at":"2026-05-18T01:21:13Z","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":"86a37fefa716aa8aeff72c3d40da4f7937495b43f9bd35b29dc77d499f6d52e5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-06-11T01:47:52Z","title_canon_sha256":"6b55c2c2fca3cccd326fb1ca2d3bdeb59713026533c56be8a006ed42b2b2531b"},"schema_version":"1.0","source":{"id":"1406.2759","kind":"arxiv","version":8}},"canonical_sha256":"879922b5de4beb6f6d618bf4acb1dcfdd2e6d68d1e6fcc19e3b1c5c7000ea33a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"879922b5de4beb6f6d618bf4acb1dcfdd2e6d68d1e6fcc19e3b1c5c7000ea33a","first_computed_at":"2026-05-18T01:21:13.900713Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:13.900713Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xi8jftvH+GYkS9AacgKUf1rqRMl5/BwOAF1WZFk9Ce0res2j9ZgJyC997Ak0U7JJpQT3X80ictets1IWanp4Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:13.901371Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.2759","source_kind":"arxiv","source_version":8}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee4a1c82eb83c23146a4b87c3cfaf2637f662fbf0c2c448c017b21f0294bf9bc","sha256:81977d4f43c21e5d5ef1f7780a7528e014b563b36de8da3c8d498aa204cc73b7"],"state_sha256":"9586a7f87c0cbeb1223854e6b3dcbbac2579e7da3bc87adb0cd4991be7396891"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nVqxHMh1IGOVoih7oBU5PtsLywPQ6/+YehCpA/EIQDxpDa+HSqb0exKQfcWmWRn5kBhRp2FShkcLBWqFXp2iBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T11:27:40.323540Z","bundle_sha256":"18a2879ec701cb520246cf0c807934dc2c98a8cf6a2c0ff508c4189d3f8c5394"}}