{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:64YLF422S42VOAIBVJS2TFK6PL","short_pith_number":"pith:64YLF422","canonical_record":{"source":{"id":"math/0703162","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2007-03-06T16:41:30Z","cross_cats_sorted":["math.CV","math.DG"],"title_canon_sha256":"8266fc377acfffa669b60d18c8407aae85eb6a0f784513242b32f54f1150179e","abstract_canon_sha256":"f76b71cb5de1daec78502e1a2d54e05e2b7de19a0f9f0c35c03437d6c8b16603"},"schema_version":"1.0"},"canonical_sha256":"f730b2f35a9735570101aa65a9955e7ac69c917379760327406778a491634db2","source":{"kind":"arxiv","id":"math/0703162","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0703162","created_at":"2026-05-18T02:57:45Z"},{"alias_kind":"arxiv_version","alias_value":"math/0703162v3","created_at":"2026-05-18T02:57:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0703162","created_at":"2026-05-18T02:57:45Z"},{"alias_kind":"pith_short_12","alias_value":"64YLF422S42V","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"64YLF422S42VOAIB","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"64YLF422","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:64YLF422S42VOAIBVJS2TFK6PL","target":"record","payload":{"canonical_record":{"source":{"id":"math/0703162","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2007-03-06T16:41:30Z","cross_cats_sorted":["math.CV","math.DG"],"title_canon_sha256":"8266fc377acfffa669b60d18c8407aae85eb6a0f784513242b32f54f1150179e","abstract_canon_sha256":"f76b71cb5de1daec78502e1a2d54e05e2b7de19a0f9f0c35c03437d6c8b16603"},"schema_version":"1.0"},"canonical_sha256":"f730b2f35a9735570101aa65a9955e7ac69c917379760327406778a491634db2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:45.238743Z","signature_b64":"DHVSQt3nSH/4y+NiRSrJnakpRoZTLUWXOrwSyw57pvVDFZ7jU0yYFriZBj455bC19VX4BlZcV4KefljIJhl9Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f730b2f35a9735570101aa65a9955e7ac69c917379760327406778a491634db2","last_reissued_at":"2026-05-18T02:57:45.238364Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:45.238364Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0703162","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:57:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x+e82oY4gX6evlaDgApXzs7+eoE8pOMXLgJ0XCNDsQUuliH1TIjir1AENbuWIcz5UgHph3sr5udaFD2NDIebBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T17:28:31.637733Z"},"content_sha256":"9f20470b3dc3c53c63ced9fb9f1bfa4a1f6b620c271a2469a6ade7334842d5ab","schema_version":"1.0","event_id":"sha256:9f20470b3dc3c53c63ced9fb9f1bfa4a1f6b620c271a2469a6ade7334842d5ab"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:64YLF422S42VOAIBVJS2TFK6PL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Positive toric fibrations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.DG"],"primary_cat":"math.AG","authors_text":"Misha Verbitsky","submitted_at":"2007-03-06T16:41:30Z","abstract_excerpt":"A principal toric bundle $M$ is a complex manifold equipped with a free holomorphic action of a compact complex torus $T$. Such a manifold is fibered over $M/T$, with fiber $T$. We discuss the notion of positivity in fiber bundles and define positive toric bundles. Given an irreducible complex subvariety $X\\subset M$ of a positive principal toric bundle, we show that either $X$ is $T$-invariant, or it lies in an orbit of $T$-action. For principal elliptic bundles, this theorem is known (math.AG/0403430). As follows from Borel-Remmert-Tits theorem, any compact simply connected homogeneous compl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0703162","kind":"arxiv","version":3},"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":"2026-05-18T02:57:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l5MNTuadB9lNw8YwCh4zzlasCRwVCXYSqLwK2+TanYeRWApmTALdN3trVecGFfXpP1kDSyQlq/q+QVR0Hr/MDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T17:28:31.638082Z"},"content_sha256":"16c21bc8890f580073d6ac6aa9d0d34761db8b9c1a536167e4b66c1075d8a183","schema_version":"1.0","event_id":"sha256:16c21bc8890f580073d6ac6aa9d0d34761db8b9c1a536167e4b66c1075d8a183"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/64YLF422S42VOAIBVJS2TFK6PL/bundle.json","state_url":"https://pith.science/pith/64YLF422S42VOAIBVJS2TFK6PL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/64YLF422S42VOAIBVJS2TFK6PL/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":"2026-06-01T17:28:31Z","links":{"resolver":"https://pith.science/pith/64YLF422S42VOAIBVJS2TFK6PL","bundle":"https://pith.science/pith/64YLF422S42VOAIBVJS2TFK6PL/bundle.json","state":"https://pith.science/pith/64YLF422S42VOAIBVJS2TFK6PL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/64YLF422S42VOAIBVJS2TFK6PL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:64YLF422S42VOAIBVJS2TFK6PL","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":"f76b71cb5de1daec78502e1a2d54e05e2b7de19a0f9f0c35c03437d6c8b16603","cross_cats_sorted":["math.CV","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2007-03-06T16:41:30Z","title_canon_sha256":"8266fc377acfffa669b60d18c8407aae85eb6a0f784513242b32f54f1150179e"},"schema_version":"1.0","source":{"id":"math/0703162","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0703162","created_at":"2026-05-18T02:57:45Z"},{"alias_kind":"arxiv_version","alias_value":"math/0703162v3","created_at":"2026-05-18T02:57:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0703162","created_at":"2026-05-18T02:57:45Z"},{"alias_kind":"pith_short_12","alias_value":"64YLF422S42V","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"64YLF422S42VOAIB","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"64YLF422","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:16c21bc8890f580073d6ac6aa9d0d34761db8b9c1a536167e4b66c1075d8a183","target":"graph","created_at":"2026-05-18T02:57:45Z","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":"A principal toric bundle $M$ is a complex manifold equipped with a free holomorphic action of a compact complex torus $T$. Such a manifold is fibered over $M/T$, with fiber $T$. We discuss the notion of positivity in fiber bundles and define positive toric bundles. Given an irreducible complex subvariety $X\\subset M$ of a positive principal toric bundle, we show that either $X$ is $T$-invariant, or it lies in an orbit of $T$-action. For principal elliptic bundles, this theorem is known (math.AG/0403430). As follows from Borel-Remmert-Tits theorem, any compact simply connected homogeneous compl","authors_text":"Misha Verbitsky","cross_cats":["math.CV","math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2007-03-06T16:41:30Z","title":"Positive toric fibrations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0703162","kind":"arxiv","version":3},"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":"sha256:9f20470b3dc3c53c63ced9fb9f1bfa4a1f6b620c271a2469a6ade7334842d5ab","target":"record","created_at":"2026-05-18T02:57:45Z","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":"f76b71cb5de1daec78502e1a2d54e05e2b7de19a0f9f0c35c03437d6c8b16603","cross_cats_sorted":["math.CV","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2007-03-06T16:41:30Z","title_canon_sha256":"8266fc377acfffa669b60d18c8407aae85eb6a0f784513242b32f54f1150179e"},"schema_version":"1.0","source":{"id":"math/0703162","kind":"arxiv","version":3}},"canonical_sha256":"f730b2f35a9735570101aa65a9955e7ac69c917379760327406778a491634db2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f730b2f35a9735570101aa65a9955e7ac69c917379760327406778a491634db2","first_computed_at":"2026-05-18T02:57:45.238364Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:45.238364Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DHVSQt3nSH/4y+NiRSrJnakpRoZTLUWXOrwSyw57pvVDFZ7jU0yYFriZBj455bC19VX4BlZcV4KefljIJhl9Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:45.238743Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0703162","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9f20470b3dc3c53c63ced9fb9f1bfa4a1f6b620c271a2469a6ade7334842d5ab","sha256:16c21bc8890f580073d6ac6aa9d0d34761db8b9c1a536167e4b66c1075d8a183"],"state_sha256":"cef9b43ad8594f720fd045d7ea9932b1c59e5ff7af7198869a7ef2a625f2a898"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1lQJxnb/im6R1RhIII/u/wu/6S3Xw43tmNrn9Q4e/SI4uQ6bnfp3GkaD0QI5MwPvcQhJEo9q5aQPEtFtSsN2AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T17:28:31.640004Z","bundle_sha256":"63b28b936a1f6bab3fbcc5c78ef668891a56215cfa6f2389557a5469f11de570"}}