{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:X6SV63QHE7NCX33TBX75NEOKSZ","short_pith_number":"pith:X6SV63QH","canonical_record":{"source":{"id":"2209.06044","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AG","submitted_at":"2022-09-13T14:51:54Z","cross_cats_sorted":[],"title_canon_sha256":"5b5701762b7e408994f4e461885db9a717da8945fc9484c4f9f06df3b0b07647","abstract_canon_sha256":"bd6e303e9b61d61bc2913ac4a143cf370fd7c29d9fed38d5357e0910a125eb2b"},"schema_version":"1.0"},"canonical_sha256":"bfa55f6e0727da2bef730dffd691ca9649961ecf8e7ef883bb7620c81cb60000","source":{"kind":"arxiv","id":"2209.06044","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.06044","created_at":"2026-05-20T14:03:15Z"},{"alias_kind":"arxiv_version","alias_value":"2209.06044v3","created_at":"2026-05-20T14:03:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.06044","created_at":"2026-05-20T14:03:15Z"},{"alias_kind":"pith_short_12","alias_value":"X6SV63QHE7NC","created_at":"2026-05-20T14:03:15Z"},{"alias_kind":"pith_short_16","alias_value":"X6SV63QHE7NCX33T","created_at":"2026-05-20T14:03:15Z"},{"alias_kind":"pith_short_8","alias_value":"X6SV63QH","created_at":"2026-05-20T14:03:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:X6SV63QHE7NCX33TBX75NEOKSZ","target":"record","payload":{"canonical_record":{"source":{"id":"2209.06044","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AG","submitted_at":"2022-09-13T14:51:54Z","cross_cats_sorted":[],"title_canon_sha256":"5b5701762b7e408994f4e461885db9a717da8945fc9484c4f9f06df3b0b07647","abstract_canon_sha256":"bd6e303e9b61d61bc2913ac4a143cf370fd7c29d9fed38d5357e0910a125eb2b"},"schema_version":"1.0"},"canonical_sha256":"bfa55f6e0727da2bef730dffd691ca9649961ecf8e7ef883bb7620c81cb60000","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T14:03:15.997790Z","signature_b64":"9fKRZVYxWz0bspY0kM55UprfFv2ICzkIxEVYYhi1tNeHfQ9t66hXlT18nSNJ6wvgQuj2mjEv1c7jdy7r1WzoDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bfa55f6e0727da2bef730dffd691ca9649961ecf8e7ef883bb7620c81cb60000","last_reissued_at":"2026-05-20T14:03:15.997210Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T14:03:15.997210Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2209.06044","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":"2026-05-20T14:03:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1T+jTupfsEjIGVIx+ug4YdsfmkuabGIisW6uWX6tpXVX355QoaCAPBCJ80BMsfzCZXM1M3fv26OzyzZjOON2DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T18:09:10.939219Z"},"content_sha256":"28b65f8e51d2bd1654c6e50417a6045d1eb772d4f05178ae64bcdb349895abb2","schema_version":"1.0","event_id":"sha256:28b65f8e51d2bd1654c6e50417a6045d1eb772d4f05178ae64bcdb349895abb2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:X6SV63QHE7NCX33TBX75NEOKSZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the finite generation of valuation semigroups on toric surfaces","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alex K\\\"uronya, Christian Haase, Karin Schaller, Klaus Altmann, Lena Walter","submitted_at":"2022-09-13T14:51:54Z","abstract_excerpt":"We provide a combinatorial criterion for the finite generation of a valuation semigroup associated with an ample divisor on a smooth toric surface and a non-toric valuation of maximal rank. As an application, we construct a lattice polytope such that none of the valuation semigroups of the associated polarized toric variety coming from one-parameter subgroups and centered at a non-toric point are finitely generated."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.06044","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2209.06044/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-05-20T14:03:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Dh4B2WgnNLcyILcTSjKVS5gJ7RSWfrdR8bAQ9mykAjNN9nEiWr218qcqkcN32Eb9mSt9KP88zCCl1kC0KJPVCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T18:09:10.939610Z"},"content_sha256":"8cb772b8eeffdd8845e7f5dc91186d8f5ed202aee30e0474d57feeb21dcf1b7c","schema_version":"1.0","event_id":"sha256:8cb772b8eeffdd8845e7f5dc91186d8f5ed202aee30e0474d57feeb21dcf1b7c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X6SV63QHE7NCX33TBX75NEOKSZ/bundle.json","state_url":"https://pith.science/pith/X6SV63QHE7NCX33TBX75NEOKSZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X6SV63QHE7NCX33TBX75NEOKSZ/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":"2026-06-02T18:09:10Z","links":{"resolver":"https://pith.science/pith/X6SV63QHE7NCX33TBX75NEOKSZ","bundle":"https://pith.science/pith/X6SV63QHE7NCX33TBX75NEOKSZ/bundle.json","state":"https://pith.science/pith/X6SV63QHE7NCX33TBX75NEOKSZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X6SV63QHE7NCX33TBX75NEOKSZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:X6SV63QHE7NCX33TBX75NEOKSZ","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":"bd6e303e9b61d61bc2913ac4a143cf370fd7c29d9fed38d5357e0910a125eb2b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AG","submitted_at":"2022-09-13T14:51:54Z","title_canon_sha256":"5b5701762b7e408994f4e461885db9a717da8945fc9484c4f9f06df3b0b07647"},"schema_version":"1.0","source":{"id":"2209.06044","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.06044","created_at":"2026-05-20T14:03:15Z"},{"alias_kind":"arxiv_version","alias_value":"2209.06044v3","created_at":"2026-05-20T14:03:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.06044","created_at":"2026-05-20T14:03:15Z"},{"alias_kind":"pith_short_12","alias_value":"X6SV63QHE7NC","created_at":"2026-05-20T14:03:15Z"},{"alias_kind":"pith_short_16","alias_value":"X6SV63QHE7NCX33T","created_at":"2026-05-20T14:03:15Z"},{"alias_kind":"pith_short_8","alias_value":"X6SV63QH","created_at":"2026-05-20T14:03:15Z"}],"graph_snapshots":[{"event_id":"sha256:8cb772b8eeffdd8845e7f5dc91186d8f5ed202aee30e0474d57feeb21dcf1b7c","target":"graph","created_at":"2026-05-20T14:03:15Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2209.06044/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We provide a combinatorial criterion for the finite generation of a valuation semigroup associated with an ample divisor on a smooth toric surface and a non-toric valuation of maximal rank. As an application, we construct a lattice polytope such that none of the valuation semigroups of the associated polarized toric variety coming from one-parameter subgroups and centered at a non-toric point are finitely generated.","authors_text":"Alex K\\\"uronya, Christian Haase, Karin Schaller, Klaus Altmann, Lena Walter","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AG","submitted_at":"2022-09-13T14:51:54Z","title":"On the finite generation of valuation semigroups on toric surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.06044","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":"sha256:28b65f8e51d2bd1654c6e50417a6045d1eb772d4f05178ae64bcdb349895abb2","target":"record","created_at":"2026-05-20T14:03:15Z","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":"bd6e303e9b61d61bc2913ac4a143cf370fd7c29d9fed38d5357e0910a125eb2b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AG","submitted_at":"2022-09-13T14:51:54Z","title_canon_sha256":"5b5701762b7e408994f4e461885db9a717da8945fc9484c4f9f06df3b0b07647"},"schema_version":"1.0","source":{"id":"2209.06044","kind":"arxiv","version":3}},"canonical_sha256":"bfa55f6e0727da2bef730dffd691ca9649961ecf8e7ef883bb7620c81cb60000","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bfa55f6e0727da2bef730dffd691ca9649961ecf8e7ef883bb7620c81cb60000","first_computed_at":"2026-05-20T14:03:15.997210Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T14:03:15.997210Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9fKRZVYxWz0bspY0kM55UprfFv2ICzkIxEVYYhi1tNeHfQ9t66hXlT18nSNJ6wvgQuj2mjEv1c7jdy7r1WzoDg==","signature_status":"signed_v1","signed_at":"2026-05-20T14:03:15.997790Z","signed_message":"canonical_sha256_bytes"},"source_id":"2209.06044","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:28b65f8e51d2bd1654c6e50417a6045d1eb772d4f05178ae64bcdb349895abb2","sha256:8cb772b8eeffdd8845e7f5dc91186d8f5ed202aee30e0474d57feeb21dcf1b7c"],"state_sha256":"03d0cf333cc3478e54cce688eec0ea48a3f758e059ee7ca826b85ed5e562cf3e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"45LsiqJVHeVwZev3egJ+u/6nRMZGSiwJ6L5glrm0Q1X/uXvrWGexun+d0YpkHdmiaHHg208jyg3fmIafOIc3Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T18:09:10.941663Z","bundle_sha256":"63dfd825c28ef98a64e1da63719e2fcd10105e220417b8ce8d2dd756bd04cf70"}}