{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:C6LU7ZZFZDU56DO22LSALTS4C7","short_pith_number":"pith:C6LU7ZZF","canonical_record":{"source":{"id":"1801.04125","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-01-12T10:29:48Z","cross_cats_sorted":[],"title_canon_sha256":"6eae88e37823a9831ed6b1f2df2c1cfbcd7b7b47ec3ec6adb3d47ec6de53b1f3","abstract_canon_sha256":"b225faa8be881c36d69847ee4bc7c9f0f05bb7ee224333eb9b3676abb82abdb7"},"schema_version":"1.0"},"canonical_sha256":"17974fe725c8e9df0ddad2e405ce5c17f12403090c3e047469284168f5a0e762","source":{"kind":"arxiv","id":"1801.04125","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.04125","created_at":"2026-05-18T00:26:11Z"},{"alias_kind":"arxiv_version","alias_value":"1801.04125v1","created_at":"2026-05-18T00:26:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.04125","created_at":"2026-05-18T00:26:11Z"},{"alias_kind":"pith_short_12","alias_value":"C6LU7ZZFZDU5","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"C6LU7ZZFZDU56DO2","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"C6LU7ZZF","created_at":"2026-05-18T12:32:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:C6LU7ZZFZDU56DO22LSALTS4C7","target":"record","payload":{"canonical_record":{"source":{"id":"1801.04125","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-01-12T10:29:48Z","cross_cats_sorted":[],"title_canon_sha256":"6eae88e37823a9831ed6b1f2df2c1cfbcd7b7b47ec3ec6adb3d47ec6de53b1f3","abstract_canon_sha256":"b225faa8be881c36d69847ee4bc7c9f0f05bb7ee224333eb9b3676abb82abdb7"},"schema_version":"1.0"},"canonical_sha256":"17974fe725c8e9df0ddad2e405ce5c17f12403090c3e047469284168f5a0e762","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:11.793108Z","signature_b64":"iuDhhWzUzQqZugCbouAi/DaKYEciqtryoqnSCh5tKRJz/AXgCSgvOKSeQ584sxXjPnTeklBE2Sg2+D7tUwO2AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"17974fe725c8e9df0ddad2e405ce5c17f12403090c3e047469284168f5a0e762","last_reissued_at":"2026-05-18T00:26:11.792441Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:11.792441Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.04125","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":"2026-05-18T00:26:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7wCOqSarzH7Pff5ybHUPix7XXUrQg7I/vjSbFnVoUy79DajsbaVHH2jedaV7oCUfRaYxGA2ZMT5tw58+NRQaAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T21:28:30.991891Z"},"content_sha256":"2e40e17d13a8f0776a2f08d8b5099b9e7375a08803d6b0774e1130bdb7071405","schema_version":"1.0","event_id":"sha256:2e40e17d13a8f0776a2f08d8b5099b9e7375a08803d6b0774e1130bdb7071405"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:C6LU7ZZFZDU56DO22LSALTS4C7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Newton-Okounkov bodies and normal toric degenerations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Georg Merz","submitted_at":"2018-01-12T10:29:48Z","abstract_excerpt":"Anderson proved that the finite generation of the value semigroup $\\Gamma_{Y_\\bullet}(D)$ in the construction of the Newton-Okounkov body $\\Delta_{Y_\\bullet}(D)$ induces a toric degeneration of the corresponding variety $X$ to some toric variety $X_0$. In this case the normalization of $X_0$ is the normal toric variety corresponding to the rational polytope $\\Delta_{Y_\\bullet}(D)$. Since $X_0$ is not normal in general this correspondence is rather implicit. In this article we investigate in conditions to assure that $X_0$ is normal, by comparing the Hilbert polynomial with the Ehrhart polynomi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.04125","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":"2026-05-18T00:26:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"upbgocfmcQwHnOZDJnJMbVqTtk3Ctxv2VyVo+vdooS7PP2htTIcgrL8ZncUZ3wZad4R6+vWy61UST/yRF7ExCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T21:28:30.992602Z"},"content_sha256":"2485b1fe9ab9a612e91060854dfeba4a028316b31b0fde29aa8a33e8901783cb","schema_version":"1.0","event_id":"sha256:2485b1fe9ab9a612e91060854dfeba4a028316b31b0fde29aa8a33e8901783cb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C6LU7ZZFZDU56DO22LSALTS4C7/bundle.json","state_url":"https://pith.science/pith/C6LU7ZZFZDU56DO22LSALTS4C7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C6LU7ZZFZDU56DO22LSALTS4C7/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":"2026-06-05T21:28:30Z","links":{"resolver":"https://pith.science/pith/C6LU7ZZFZDU56DO22LSALTS4C7","bundle":"https://pith.science/pith/C6LU7ZZFZDU56DO22LSALTS4C7/bundle.json","state":"https://pith.science/pith/C6LU7ZZFZDU56DO22LSALTS4C7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C6LU7ZZFZDU56DO22LSALTS4C7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:C6LU7ZZFZDU56DO22LSALTS4C7","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":"b225faa8be881c36d69847ee4bc7c9f0f05bb7ee224333eb9b3676abb82abdb7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-01-12T10:29:48Z","title_canon_sha256":"6eae88e37823a9831ed6b1f2df2c1cfbcd7b7b47ec3ec6adb3d47ec6de53b1f3"},"schema_version":"1.0","source":{"id":"1801.04125","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.04125","created_at":"2026-05-18T00:26:11Z"},{"alias_kind":"arxiv_version","alias_value":"1801.04125v1","created_at":"2026-05-18T00:26:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.04125","created_at":"2026-05-18T00:26:11Z"},{"alias_kind":"pith_short_12","alias_value":"C6LU7ZZFZDU5","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"C6LU7ZZFZDU56DO2","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"C6LU7ZZF","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:2485b1fe9ab9a612e91060854dfeba4a028316b31b0fde29aa8a33e8901783cb","target":"graph","created_at":"2026-05-18T00:26:11Z","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":"Anderson proved that the finite generation of the value semigroup $\\Gamma_{Y_\\bullet}(D)$ in the construction of the Newton-Okounkov body $\\Delta_{Y_\\bullet}(D)$ induces a toric degeneration of the corresponding variety $X$ to some toric variety $X_0$. In this case the normalization of $X_0$ is the normal toric variety corresponding to the rational polytope $\\Delta_{Y_\\bullet}(D)$. Since $X_0$ is not normal in general this correspondence is rather implicit. In this article we investigate in conditions to assure that $X_0$ is normal, by comparing the Hilbert polynomial with the Ehrhart polynomi","authors_text":"Georg Merz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-01-12T10:29:48Z","title":"Newton-Okounkov bodies and normal toric degenerations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.04125","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":"sha256:2e40e17d13a8f0776a2f08d8b5099b9e7375a08803d6b0774e1130bdb7071405","target":"record","created_at":"2026-05-18T00:26:11Z","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":"b225faa8be881c36d69847ee4bc7c9f0f05bb7ee224333eb9b3676abb82abdb7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-01-12T10:29:48Z","title_canon_sha256":"6eae88e37823a9831ed6b1f2df2c1cfbcd7b7b47ec3ec6adb3d47ec6de53b1f3"},"schema_version":"1.0","source":{"id":"1801.04125","kind":"arxiv","version":1}},"canonical_sha256":"17974fe725c8e9df0ddad2e405ce5c17f12403090c3e047469284168f5a0e762","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"17974fe725c8e9df0ddad2e405ce5c17f12403090c3e047469284168f5a0e762","first_computed_at":"2026-05-18T00:26:11.792441Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:11.792441Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iuDhhWzUzQqZugCbouAi/DaKYEciqtryoqnSCh5tKRJz/AXgCSgvOKSeQ584sxXjPnTeklBE2Sg2+D7tUwO2AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:11.793108Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.04125","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2e40e17d13a8f0776a2f08d8b5099b9e7375a08803d6b0774e1130bdb7071405","sha256:2485b1fe9ab9a612e91060854dfeba4a028316b31b0fde29aa8a33e8901783cb"],"state_sha256":"5affdeff015edb971a0019aed60b6789d819e28328c0086a2c5492cfd3fbfa35"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YNYW7f27fJ1fQFkaoml8ECdQsloqdyxM1RS1SlMCykNLxqtWoL7Hun7xonQFpS8h+MdKMw29pTtOjf4lnzEzBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T21:28:30.996393Z","bundle_sha256":"928af676bf504848a8cb4e20cc6b83b42e2b31010c87f025011feca1943c5bf8"}}