{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:NU77YX5XUQAJXLLJAY6LZVB4DC","short_pith_number":"pith:NU77YX5X","canonical_record":{"source":{"id":"1111.0614","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-11-02T19:23:32Z","cross_cats_sorted":[],"title_canon_sha256":"dfa9f61167e478ca9b315adb8805173f9fab59678bd1d082ae5148b17ea7ce83","abstract_canon_sha256":"539781e1fa46889481caa1466ef1d3223f49fd6008b1411b5dc792d83416e7e1"},"schema_version":"1.0"},"canonical_sha256":"6d3ffc5fb7a4009bad69063cbcd43c189ee9d095316981b31d7fea6dd49845f8","source":{"kind":"arxiv","id":"1111.0614","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.0614","created_at":"2026-05-18T04:09:44Z"},{"alias_kind":"arxiv_version","alias_value":"1111.0614v1","created_at":"2026-05-18T04:09:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.0614","created_at":"2026-05-18T04:09:44Z"},{"alias_kind":"pith_short_12","alias_value":"NU77YX5XUQAJ","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"NU77YX5XUQAJXLLJ","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"NU77YX5X","created_at":"2026-05-18T12:26:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:NU77YX5XUQAJXLLJAY6LZVB4DC","target":"record","payload":{"canonical_record":{"source":{"id":"1111.0614","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-11-02T19:23:32Z","cross_cats_sorted":[],"title_canon_sha256":"dfa9f61167e478ca9b315adb8805173f9fab59678bd1d082ae5148b17ea7ce83","abstract_canon_sha256":"539781e1fa46889481caa1466ef1d3223f49fd6008b1411b5dc792d83416e7e1"},"schema_version":"1.0"},"canonical_sha256":"6d3ffc5fb7a4009bad69063cbcd43c189ee9d095316981b31d7fea6dd49845f8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:09:44.606610Z","signature_b64":"kAK0CmL6oG8xhZD+veOSx2mG31JRbMy5xLVB8zAqf4j97sLV1RQqNGiLDdhv24B2WcnJxYzb5PVsXZbPTcj7AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6d3ffc5fb7a4009bad69063cbcd43c189ee9d095316981b31d7fea6dd49845f8","last_reissued_at":"2026-05-18T04:09:44.606067Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:09:44.606067Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.0614","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":"2026-05-18T04:09:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mco2eW1QKOtIirTTlR+7GvH1z29f2bhl3Tq3COYdJNddSMv/X9ZCgfl9TBz5uPFT62Hs2cPXpezQ9UTT4yPFDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T11:55:34.930279Z"},"content_sha256":"17a2b73e59d2f1103452ebdf9bf7c279593cf2571dfebaca023eb88f32761185","schema_version":"1.0","event_id":"sha256:17a2b73e59d2f1103452ebdf9bf7c279593cf2571dfebaca023eb88f32761185"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:NU77YX5XUQAJXLLJAY6LZVB4DC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"General Bezout-type theorems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Pinaki Mondal","submitted_at":"2011-11-02T19:23:32Z","abstract_excerpt":"In this sequel to arxiv:arXiv:1012.0835 we develop Bezout type theorems for semidegrees (including an explicit formula for {\\em iterated semidegrees}) and an inequality for subdegrees. In addition we prove (in case of surfaces) a Bernstein type theorem for the number of solutions of two polynomials in terms of the mixed volume of planar convex polygons associated to them (via the theory of Kaveh-Khovanskii and Lazarsfeld-Mustata."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.0614","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":""},"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":"2026-05-18T04:09:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SzuLBnaAqINxwwNOIShu/qqvBj4OMW40q8GjLKsjiTQU/uUVEkez6LA2OTflTFVJOsA+v/krcq0OfITFTn8nBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T11:55:34.930655Z"},"content_sha256":"6b1be0ab74f0e0cb9ad3597bc267dc209705ba6a35dab2074f5499b776d582fe","schema_version":"1.0","event_id":"sha256:6b1be0ab74f0e0cb9ad3597bc267dc209705ba6a35dab2074f5499b776d582fe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NU77YX5XUQAJXLLJAY6LZVB4DC/bundle.json","state_url":"https://pith.science/pith/NU77YX5XUQAJXLLJAY6LZVB4DC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NU77YX5XUQAJXLLJAY6LZVB4DC/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":"2026-06-25T11:55:34Z","links":{"resolver":"https://pith.science/pith/NU77YX5XUQAJXLLJAY6LZVB4DC","bundle":"https://pith.science/pith/NU77YX5XUQAJXLLJAY6LZVB4DC/bundle.json","state":"https://pith.science/pith/NU77YX5XUQAJXLLJAY6LZVB4DC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NU77YX5XUQAJXLLJAY6LZVB4DC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:NU77YX5XUQAJXLLJAY6LZVB4DC","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":"539781e1fa46889481caa1466ef1d3223f49fd6008b1411b5dc792d83416e7e1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-11-02T19:23:32Z","title_canon_sha256":"dfa9f61167e478ca9b315adb8805173f9fab59678bd1d082ae5148b17ea7ce83"},"schema_version":"1.0","source":{"id":"1111.0614","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.0614","created_at":"2026-05-18T04:09:44Z"},{"alias_kind":"arxiv_version","alias_value":"1111.0614v1","created_at":"2026-05-18T04:09:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.0614","created_at":"2026-05-18T04:09:44Z"},{"alias_kind":"pith_short_12","alias_value":"NU77YX5XUQAJ","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"NU77YX5XUQAJXLLJ","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"NU77YX5X","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:6b1be0ab74f0e0cb9ad3597bc267dc209705ba6a35dab2074f5499b776d582fe","target":"graph","created_at":"2026-05-18T04:09:44Z","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 sequel to arxiv:arXiv:1012.0835 we develop Bezout type theorems for semidegrees (including an explicit formula for {\\em iterated semidegrees}) and an inequality for subdegrees. In addition we prove (in case of surfaces) a Bernstein type theorem for the number of solutions of two polynomials in terms of the mixed volume of planar convex polygons associated to them (via the theory of Kaveh-Khovanskii and Lazarsfeld-Mustata.","authors_text":"Pinaki Mondal","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-11-02T19:23:32Z","title":"General Bezout-type theorems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.0614","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":"sha256:17a2b73e59d2f1103452ebdf9bf7c279593cf2571dfebaca023eb88f32761185","target":"record","created_at":"2026-05-18T04:09:44Z","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":"539781e1fa46889481caa1466ef1d3223f49fd6008b1411b5dc792d83416e7e1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-11-02T19:23:32Z","title_canon_sha256":"dfa9f61167e478ca9b315adb8805173f9fab59678bd1d082ae5148b17ea7ce83"},"schema_version":"1.0","source":{"id":"1111.0614","kind":"arxiv","version":1}},"canonical_sha256":"6d3ffc5fb7a4009bad69063cbcd43c189ee9d095316981b31d7fea6dd49845f8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6d3ffc5fb7a4009bad69063cbcd43c189ee9d095316981b31d7fea6dd49845f8","first_computed_at":"2026-05-18T04:09:44.606067Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:09:44.606067Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kAK0CmL6oG8xhZD+veOSx2mG31JRbMy5xLVB8zAqf4j97sLV1RQqNGiLDdhv24B2WcnJxYzb5PVsXZbPTcj7AA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:09:44.606610Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.0614","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:17a2b73e59d2f1103452ebdf9bf7c279593cf2571dfebaca023eb88f32761185","sha256:6b1be0ab74f0e0cb9ad3597bc267dc209705ba6a35dab2074f5499b776d582fe"],"state_sha256":"a65b6385a4256f8a3a1bd32c35d3630c8c075cc5045a493e2c4e1a86f0bed6aa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9Jhvkyko1dTgJEddlWgJqvloPTItW2AfAaNwYBHTOdmWyZ+hjGv7KMVaYmSv6rgHu+1IN7Eo4Dl1dxQVPp8LBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T11:55:34.932637Z","bundle_sha256":"d144f55dc1171b375bb57948667430580a06ee9d7d323202f273124781eafc56"}}