{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:XAF25ZNPYSU5V6W24J76KYD35H","short_pith_number":"pith:XAF25ZNP","canonical_record":{"source":{"id":"1705.09865","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-05-27T21:08:43Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"a9e5e2abe0fadeb9d66892b351dcc8859804e3db520526ea8a2b8a130fd339b4","abstract_canon_sha256":"557eeec6fa2a159252ada66e1fdb44cef24e79adc63565a51477f6e353ab6500"},"schema_version":"1.0"},"canonical_sha256":"b80baee5afc4a9dafadae27fe5607be9fe3d1b38e17fb98a3ef213b4f9a698f1","source":{"kind":"arxiv","id":"1705.09865","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.09865","created_at":"2026-05-18T00:43:24Z"},{"alias_kind":"arxiv_version","alias_value":"1705.09865v2","created_at":"2026-05-18T00:43:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.09865","created_at":"2026-05-18T00:43:24Z"},{"alias_kind":"pith_short_12","alias_value":"XAF25ZNPYSU5","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"XAF25ZNPYSU5V6W2","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"XAF25ZNP","created_at":"2026-05-18T12:31:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:XAF25ZNPYSU5V6W24J76KYD35H","target":"record","payload":{"canonical_record":{"source":{"id":"1705.09865","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-05-27T21:08:43Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"a9e5e2abe0fadeb9d66892b351dcc8859804e3db520526ea8a2b8a130fd339b4","abstract_canon_sha256":"557eeec6fa2a159252ada66e1fdb44cef24e79adc63565a51477f6e353ab6500"},"schema_version":"1.0"},"canonical_sha256":"b80baee5afc4a9dafadae27fe5607be9fe3d1b38e17fb98a3ef213b4f9a698f1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:24.737007Z","signature_b64":"zYJzLsbdq/mOKdS2lGIrC6XNKg9DHVXtjtX+8Q1PR/BOs7mzOxThVUzraRXjXwU/+nBgZQUmhCQ99zpEZWwDAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b80baee5afc4a9dafadae27fe5607be9fe3d1b38e17fb98a3ef213b4f9a698f1","last_reissued_at":"2026-05-18T00:43:24.736524Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:24.736524Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.09865","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:43:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QIqHVhU2twgeqsj2Ea8OoIFAlMeS+Yqbe2tEC0SErU+Kfmrd1on+Ru/7RR8n94TsjjWG5u9F5gMagu4oVJevBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T05:24:45.753619Z"},"content_sha256":"3eed7c0ac2121c0daf7249c9e6a52ab08bf5fe1aaaffe5da8e3e55b1fb534fbf","schema_version":"1.0","event_id":"sha256:3eed7c0ac2121c0daf7249c9e6a52ab08bf5fe1aaaffe5da8e3e55b1fb534fbf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:XAF25ZNPYSU5V6W24J76KYD35H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Infinitely generated symbolic Rees rings of space monomial curves having negative curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Kazuhiko Kurano, Koji Nishida","submitted_at":"2017-05-27T21:08:43Z","abstract_excerpt":"In this paper, we shall study finite generation of symbolic Rees rings of the defining ideal ${\\frak p}$ of the space monomial curve $(t^a, t^b, t^c)$ for pairwise coprime integers $a$, $b$, $c$. Suppose that the base field is of characteristic $0$ and the above ideal ${\\frak p}$ is minimally generated by three polynomials. Under the assumption that the homogeneous element $\\xi$ of the minimal degree in ${\\frak p}$ is the negative curve, we determine the minimal degree of an element $\\eta$ such that the pair $\\{ \\xi, \\eta \\}$ satisfies Huneke's criterion in the case where the symbolic Rees rin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.09865","kind":"arxiv","version":2},"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":"2026-05-18T00:43:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Je2MUinG1ummXPK7lenI67R9PsPwNESTXABNeyjh/Ti+Tx1/DXogE1xaaM/l24gwK3LTRLiMXYPsiuZytcGqDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T05:24:45.754235Z"},"content_sha256":"4753cfa2a52d440e888e460e3127596d56e1fd65ae26f4abbed96688eeb17a7b","schema_version":"1.0","event_id":"sha256:4753cfa2a52d440e888e460e3127596d56e1fd65ae26f4abbed96688eeb17a7b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XAF25ZNPYSU5V6W24J76KYD35H/bundle.json","state_url":"https://pith.science/pith/XAF25ZNPYSU5V6W24J76KYD35H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XAF25ZNPYSU5V6W24J76KYD35H/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":"2026-06-12T05:24:45Z","links":{"resolver":"https://pith.science/pith/XAF25ZNPYSU5V6W24J76KYD35H","bundle":"https://pith.science/pith/XAF25ZNPYSU5V6W24J76KYD35H/bundle.json","state":"https://pith.science/pith/XAF25ZNPYSU5V6W24J76KYD35H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XAF25ZNPYSU5V6W24J76KYD35H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:XAF25ZNPYSU5V6W24J76KYD35H","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":"557eeec6fa2a159252ada66e1fdb44cef24e79adc63565a51477f6e353ab6500","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-05-27T21:08:43Z","title_canon_sha256":"a9e5e2abe0fadeb9d66892b351dcc8859804e3db520526ea8a2b8a130fd339b4"},"schema_version":"1.0","source":{"id":"1705.09865","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.09865","created_at":"2026-05-18T00:43:24Z"},{"alias_kind":"arxiv_version","alias_value":"1705.09865v2","created_at":"2026-05-18T00:43:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.09865","created_at":"2026-05-18T00:43:24Z"},{"alias_kind":"pith_short_12","alias_value":"XAF25ZNPYSU5","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"XAF25ZNPYSU5V6W2","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"XAF25ZNP","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:4753cfa2a52d440e888e460e3127596d56e1fd65ae26f4abbed96688eeb17a7b","target":"graph","created_at":"2026-05-18T00:43:24Z","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 paper, we shall study finite generation of symbolic Rees rings of the defining ideal ${\\frak p}$ of the space monomial curve $(t^a, t^b, t^c)$ for pairwise coprime integers $a$, $b$, $c$. Suppose that the base field is of characteristic $0$ and the above ideal ${\\frak p}$ is minimally generated by three polynomials. Under the assumption that the homogeneous element $\\xi$ of the minimal degree in ${\\frak p}$ is the negative curve, we determine the minimal degree of an element $\\eta$ such that the pair $\\{ \\xi, \\eta \\}$ satisfies Huneke's criterion in the case where the symbolic Rees rin","authors_text":"Kazuhiko Kurano, Koji Nishida","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-05-27T21:08:43Z","title":"Infinitely generated symbolic Rees rings of space monomial curves having negative curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.09865","kind":"arxiv","version":2},"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":"sha256:3eed7c0ac2121c0daf7249c9e6a52ab08bf5fe1aaaffe5da8e3e55b1fb534fbf","target":"record","created_at":"2026-05-18T00:43:24Z","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":"557eeec6fa2a159252ada66e1fdb44cef24e79adc63565a51477f6e353ab6500","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-05-27T21:08:43Z","title_canon_sha256":"a9e5e2abe0fadeb9d66892b351dcc8859804e3db520526ea8a2b8a130fd339b4"},"schema_version":"1.0","source":{"id":"1705.09865","kind":"arxiv","version":2}},"canonical_sha256":"b80baee5afc4a9dafadae27fe5607be9fe3d1b38e17fb98a3ef213b4f9a698f1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b80baee5afc4a9dafadae27fe5607be9fe3d1b38e17fb98a3ef213b4f9a698f1","first_computed_at":"2026-05-18T00:43:24.736524Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:24.736524Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zYJzLsbdq/mOKdS2lGIrC6XNKg9DHVXtjtX+8Q1PR/BOs7mzOxThVUzraRXjXwU/+nBgZQUmhCQ99zpEZWwDAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:24.737007Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.09865","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3eed7c0ac2121c0daf7249c9e6a52ab08bf5fe1aaaffe5da8e3e55b1fb534fbf","sha256:4753cfa2a52d440e888e460e3127596d56e1fd65ae26f4abbed96688eeb17a7b"],"state_sha256":"cbd6c1500fb56d7ca031ab92e2b1d9573de6ef2f83c12ba42ec9513bb3c2668f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hLHyWJmktDaej8aH58tDyqvS9hl+kTLTcYX85+a9DbfV/YxxkppbZpAMvB5M+bRoeYqDiaV8IunSgfisIPRvAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T05:24:45.757593Z","bundle_sha256":"d918c4ce924bc7481051305f2c2f32864daa14d22ad23a3fce1a1447b0889a2f"}}