{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:75JBUGUZKTGTZWV6TFWHXRYPGL","short_pith_number":"pith:75JBUGUZ","canonical_record":{"source":{"id":"1508.07295","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-08-28T17:58:33Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"185178d958ece20e6193b3868980606bdabd010a08828036bbaaaa2f5fd25d8a","abstract_canon_sha256":"f5633641f9edf9a5d543d0d3fdea9e6d33bbe2d952ec8427a074880c756f2c3a"},"schema_version":"1.0"},"canonical_sha256":"ff521a1a9954cd3cdabe996c7bc70f32f0cef0f00ace58215d9b1fc27c84da5d","source":{"kind":"arxiv","id":"1508.07295","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.07295","created_at":"2026-05-17T23:42:43Z"},{"alias_kind":"arxiv_version","alias_value":"1508.07295v2","created_at":"2026-05-17T23:42:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.07295","created_at":"2026-05-17T23:42:43Z"},{"alias_kind":"pith_short_12","alias_value":"75JBUGUZKTGT","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"75JBUGUZKTGTZWV6","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"75JBUGUZ","created_at":"2026-05-18T12:29:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:75JBUGUZKTGTZWV6TFWHXRYPGL","target":"record","payload":{"canonical_record":{"source":{"id":"1508.07295","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-08-28T17:58:33Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"185178d958ece20e6193b3868980606bdabd010a08828036bbaaaa2f5fd25d8a","abstract_canon_sha256":"f5633641f9edf9a5d543d0d3fdea9e6d33bbe2d952ec8427a074880c756f2c3a"},"schema_version":"1.0"},"canonical_sha256":"ff521a1a9954cd3cdabe996c7bc70f32f0cef0f00ace58215d9b1fc27c84da5d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:43.856870Z","signature_b64":"IbXwsmrFb18WJ8WXdl2JILmD2V0hIR4Uwv8pTbrmXyzDOme1D+a2+1+fSXzEL2cnoozrqFm7SoSZD+f3ypfjAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ff521a1a9954cd3cdabe996c7bc70f32f0cef0f00ace58215d9b1fc27c84da5d","last_reissued_at":"2026-05-17T23:42:43.856111Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:43.856111Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.07295","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":"2026-05-17T23:42:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xavycDzz+EvhLg6jJUp232rI8TqhNY3c//qvIPm+7uFel287x4apiwrhAa/N4Zr1b7+8Qm9yvhz4fk9gACzPDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T22:06:17.554605Z"},"content_sha256":"edf897d3226631657c9319198c3fa4930e0d252e8d518b3aa03bc2c24b5edc80","schema_version":"1.0","event_id":"sha256:edf897d3226631657c9319198c3fa4930e0d252e8d518b3aa03bc2c24b5edc80"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:75JBUGUZKTGTZWV6TFWHXRYPGL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The $F$-different and a canonical bundle formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Karl Schwede, Omprokash Das","submitted_at":"2015-08-28T17:58:33Z","abstract_excerpt":"We study the structure of Frobenius splittings (and generalizations thereof) induced on compatible subvarieties $W \\subseteq X$. In particular, if the compatible splitting comes from a compatible splitting of a divisor on some birational model $E \\subseteq X' \\to X$ (ie, this is a log canonical center), then we show that the divisor corresponding to the splitting on $W$ is bounded below by the divisorial part of the different as studied by Kawamata, Shokurov, Ambro and others. We also show that difference between the divisor associated to the splitting and the divisorial part of the different "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07295","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":"2026-05-17T23:42:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PQEZpOuldwodLnE7ZA8aVhG1k6EfN5Gllsm51rh8Q6eW5wHsq5DCb+KOMWQ0B174MDRDCJWQm/yMAieY8w27BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T22:06:17.555079Z"},"content_sha256":"73d4bfd0a9e1dc435004605c2f351d2f3b36a5246a35b092b4f607ef19a16dad","schema_version":"1.0","event_id":"sha256:73d4bfd0a9e1dc435004605c2f351d2f3b36a5246a35b092b4f607ef19a16dad"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/75JBUGUZKTGTZWV6TFWHXRYPGL/bundle.json","state_url":"https://pith.science/pith/75JBUGUZKTGTZWV6TFWHXRYPGL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/75JBUGUZKTGTZWV6TFWHXRYPGL/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":"2026-06-22T22:06:17Z","links":{"resolver":"https://pith.science/pith/75JBUGUZKTGTZWV6TFWHXRYPGL","bundle":"https://pith.science/pith/75JBUGUZKTGTZWV6TFWHXRYPGL/bundle.json","state":"https://pith.science/pith/75JBUGUZKTGTZWV6TFWHXRYPGL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/75JBUGUZKTGTZWV6TFWHXRYPGL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:75JBUGUZKTGTZWV6TFWHXRYPGL","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":"f5633641f9edf9a5d543d0d3fdea9e6d33bbe2d952ec8427a074880c756f2c3a","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-08-28T17:58:33Z","title_canon_sha256":"185178d958ece20e6193b3868980606bdabd010a08828036bbaaaa2f5fd25d8a"},"schema_version":"1.0","source":{"id":"1508.07295","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.07295","created_at":"2026-05-17T23:42:43Z"},{"alias_kind":"arxiv_version","alias_value":"1508.07295v2","created_at":"2026-05-17T23:42:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.07295","created_at":"2026-05-17T23:42:43Z"},{"alias_kind":"pith_short_12","alias_value":"75JBUGUZKTGT","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"75JBUGUZKTGTZWV6","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"75JBUGUZ","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:73d4bfd0a9e1dc435004605c2f351d2f3b36a5246a35b092b4f607ef19a16dad","target":"graph","created_at":"2026-05-17T23:42:43Z","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 study the structure of Frobenius splittings (and generalizations thereof) induced on compatible subvarieties $W \\subseteq X$. In particular, if the compatible splitting comes from a compatible splitting of a divisor on some birational model $E \\subseteq X' \\to X$ (ie, this is a log canonical center), then we show that the divisor corresponding to the splitting on $W$ is bounded below by the divisorial part of the different as studied by Kawamata, Shokurov, Ambro and others. We also show that difference between the divisor associated to the splitting and the divisorial part of the different ","authors_text":"Karl Schwede, Omprokash Das","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-08-28T17:58:33Z","title":"The $F$-different and a canonical bundle formula"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07295","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:edf897d3226631657c9319198c3fa4930e0d252e8d518b3aa03bc2c24b5edc80","target":"record","created_at":"2026-05-17T23:42:43Z","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":"f5633641f9edf9a5d543d0d3fdea9e6d33bbe2d952ec8427a074880c756f2c3a","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-08-28T17:58:33Z","title_canon_sha256":"185178d958ece20e6193b3868980606bdabd010a08828036bbaaaa2f5fd25d8a"},"schema_version":"1.0","source":{"id":"1508.07295","kind":"arxiv","version":2}},"canonical_sha256":"ff521a1a9954cd3cdabe996c7bc70f32f0cef0f00ace58215d9b1fc27c84da5d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ff521a1a9954cd3cdabe996c7bc70f32f0cef0f00ace58215d9b1fc27c84da5d","first_computed_at":"2026-05-17T23:42:43.856111Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:43.856111Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IbXwsmrFb18WJ8WXdl2JILmD2V0hIR4Uwv8pTbrmXyzDOme1D+a2+1+fSXzEL2cnoozrqFm7SoSZD+f3ypfjAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:43.856870Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.07295","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:edf897d3226631657c9319198c3fa4930e0d252e8d518b3aa03bc2c24b5edc80","sha256:73d4bfd0a9e1dc435004605c2f351d2f3b36a5246a35b092b4f607ef19a16dad"],"state_sha256":"5b64c03e3c965033d40f68940d80fb36ffb14175bb8aca579e1b842ee07f61d9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v/v1biCrf9KJIeHJn0ROwugRELtsF5TF2cC3z9n45LwOX0BOlH/X7+2B6oW31lBOHbIaCDGGX709XA5oOfsQBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T22:06:17.557616Z","bundle_sha256":"f32651df377395545a1eea541133cd73ba2246dfdc71c98d976d94ea6fe0f7d4"}}