{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:CMPIO2CXRROVESNYZPPIOF6LER","short_pith_number":"pith:CMPIO2CX","canonical_record":{"source":{"id":"1610.06612","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2016-10-20T21:24:24Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"3bd0d3f43a02f40cbf70df2848eaeabfc73ec4d2d29e0808ce5ea33e014ccf17","abstract_canon_sha256":"f831e603fe244ec616641c88d73f93871a04b2c2b7b94a6bee377dfac4b43ab8"},"schema_version":"1.0"},"canonical_sha256":"131e8768578c5d5249b8cbde8717cb2454c2141aa893819a99c69e63ad0c4b98","source":{"kind":"arxiv","id":"1610.06612","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.06612","created_at":"2026-05-18T00:05:51Z"},{"alias_kind":"arxiv_version","alias_value":"1610.06612v4","created_at":"2026-05-18T00:05:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.06612","created_at":"2026-05-18T00:05:51Z"},{"alias_kind":"pith_short_12","alias_value":"CMPIO2CXRROV","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CMPIO2CXRROVESNY","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CMPIO2CX","created_at":"2026-05-18T12:30:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:CMPIO2CXRROVESNYZPPIOF6LER","target":"record","payload":{"canonical_record":{"source":{"id":"1610.06612","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2016-10-20T21:24:24Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"3bd0d3f43a02f40cbf70df2848eaeabfc73ec4d2d29e0808ce5ea33e014ccf17","abstract_canon_sha256":"f831e603fe244ec616641c88d73f93871a04b2c2b7b94a6bee377dfac4b43ab8"},"schema_version":"1.0"},"canonical_sha256":"131e8768578c5d5249b8cbde8717cb2454c2141aa893819a99c69e63ad0c4b98","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:51.527105Z","signature_b64":"wdH3rQF/Cqs2sR0r0GqUbmSLG2a613LWJQakI4SZ5BFQjcdbngK1jsiC+bQ3FSirfXynQX3bP2L+HB2rYvD2DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"131e8768578c5d5249b8cbde8717cb2454c2141aa893819a99c69e63ad0c4b98","last_reissued_at":"2026-05-18T00:05:51.526582Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:51.526582Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.06612","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:05:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5izRwAyieBY4V2q+aGmbzhyhRs81TcMoYZ6VSrIc4Eu+qXiPEeaZJ4EEFKQPfmO3RadIgxO6ufFJgfGm6rG8DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T02:32:10.730908Z"},"content_sha256":"d4a3c9b7097b8966cc3aad63e596ee721304af26996a52903fc367e27d78111f","schema_version":"1.0","event_id":"sha256:d4a3c9b7097b8966cc3aad63e596ee721304af26996a52903fc367e27d78111f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:CMPIO2CXRROVESNYZPPIOF6LER","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Toric surfaces over an arbitrary field","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.AG","authors_text":"Fei Xie","submitted_at":"2016-10-20T21:24:24Z","abstract_excerpt":"We study toric varieties over an arbitrary field with an emphasis on toric surfaces in the Merkurjev-Panin motivic category of \"K-motives\". We explore the decomposition of certain toric varieties as K-motives into products of central simple algebras, the geometric and topological information encoded in these central simple algebras, and the relationship between the decomposition of the K-motives and the semiorthogonal decomposition of the derived categories. We obtain the information mentioned above for toric surfaces by explicitly classifying all minimal smooth projective toric surfaces using"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06612","kind":"arxiv","version":4},"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":"2026-05-18T00:05:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fwAMixXcpeLUO49TqyIjcimSt2L5t1Fx2sUEHu5eY2RhL7MxSbyt6ZB28y+cDdMUY95aeI4IqvoagBpgo7qsAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T02:32:10.731476Z"},"content_sha256":"2cd860ca6d59eeb6184ca62615421cdd1335abca4741d231ed435ae5d1ae9889","schema_version":"1.0","event_id":"sha256:2cd860ca6d59eeb6184ca62615421cdd1335abca4741d231ed435ae5d1ae9889"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CMPIO2CXRROVESNYZPPIOF6LER/bundle.json","state_url":"https://pith.science/pith/CMPIO2CXRROVESNYZPPIOF6LER/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CMPIO2CXRROVESNYZPPIOF6LER/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":"2026-06-01T02:32:10Z","links":{"resolver":"https://pith.science/pith/CMPIO2CXRROVESNYZPPIOF6LER","bundle":"https://pith.science/pith/CMPIO2CXRROVESNYZPPIOF6LER/bundle.json","state":"https://pith.science/pith/CMPIO2CXRROVESNYZPPIOF6LER/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CMPIO2CXRROVESNYZPPIOF6LER/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:CMPIO2CXRROVESNYZPPIOF6LER","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":"f831e603fe244ec616641c88d73f93871a04b2c2b7b94a6bee377dfac4b43ab8","cross_cats_sorted":["math.KT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2016-10-20T21:24:24Z","title_canon_sha256":"3bd0d3f43a02f40cbf70df2848eaeabfc73ec4d2d29e0808ce5ea33e014ccf17"},"schema_version":"1.0","source":{"id":"1610.06612","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.06612","created_at":"2026-05-18T00:05:51Z"},{"alias_kind":"arxiv_version","alias_value":"1610.06612v4","created_at":"2026-05-18T00:05:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.06612","created_at":"2026-05-18T00:05:51Z"},{"alias_kind":"pith_short_12","alias_value":"CMPIO2CXRROV","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CMPIO2CXRROVESNY","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CMPIO2CX","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:2cd860ca6d59eeb6184ca62615421cdd1335abca4741d231ed435ae5d1ae9889","target":"graph","created_at":"2026-05-18T00:05:51Z","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 toric varieties over an arbitrary field with an emphasis on toric surfaces in the Merkurjev-Panin motivic category of \"K-motives\". We explore the decomposition of certain toric varieties as K-motives into products of central simple algebras, the geometric and topological information encoded in these central simple algebras, and the relationship between the decomposition of the K-motives and the semiorthogonal decomposition of the derived categories. We obtain the information mentioned above for toric surfaces by explicitly classifying all minimal smooth projective toric surfaces using","authors_text":"Fei Xie","cross_cats":["math.KT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2016-10-20T21:24:24Z","title":"Toric surfaces over an arbitrary field"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06612","kind":"arxiv","version":4},"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:d4a3c9b7097b8966cc3aad63e596ee721304af26996a52903fc367e27d78111f","target":"record","created_at":"2026-05-18T00:05:51Z","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":"f831e603fe244ec616641c88d73f93871a04b2c2b7b94a6bee377dfac4b43ab8","cross_cats_sorted":["math.KT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2016-10-20T21:24:24Z","title_canon_sha256":"3bd0d3f43a02f40cbf70df2848eaeabfc73ec4d2d29e0808ce5ea33e014ccf17"},"schema_version":"1.0","source":{"id":"1610.06612","kind":"arxiv","version":4}},"canonical_sha256":"131e8768578c5d5249b8cbde8717cb2454c2141aa893819a99c69e63ad0c4b98","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"131e8768578c5d5249b8cbde8717cb2454c2141aa893819a99c69e63ad0c4b98","first_computed_at":"2026-05-18T00:05:51.526582Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:51.526582Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wdH3rQF/Cqs2sR0r0GqUbmSLG2a613LWJQakI4SZ5BFQjcdbngK1jsiC+bQ3FSirfXynQX3bP2L+HB2rYvD2DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:51.527105Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.06612","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d4a3c9b7097b8966cc3aad63e596ee721304af26996a52903fc367e27d78111f","sha256:2cd860ca6d59eeb6184ca62615421cdd1335abca4741d231ed435ae5d1ae9889"],"state_sha256":"212944c456d1ef07c620258d2ba0bbe5927efcf34262278a1d947b641d7fee93"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gAv3rgp7o2DB7cI/iKdyODti+X+tz1CKifjBNSidK/0i2k7a4XH5qyKqTLvFft1okta7RtzyBPQ2PmV+3kjZCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T02:32:10.735757Z","bundle_sha256":"70c2adb0fad3434accef72d7b4ca0e2ec2d59d3628adda5b5456b5b482036fd8"}}