{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:GVEAETQURJRQHFG4WDQSHWWCSI","short_pith_number":"pith:GVEAETQU","canonical_record":{"source":{"id":"1705.06339","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-17T20:29:31Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"ddcc54c05251e16dd5df971558d883f65a14b0b68b84c61c676b9a933fa1af02","abstract_canon_sha256":"a7b006a3a3465f8abb428f274759415bfc2f22c0d7495f23c75e8391b31bc868"},"schema_version":"1.0"},"canonical_sha256":"3548024e148a630394dcb0e123dac2923ff88af3f1a16987c32b89a82cb3ecaf","source":{"kind":"arxiv","id":"1705.06339","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.06339","created_at":"2026-05-18T00:40:39Z"},{"alias_kind":"arxiv_version","alias_value":"1705.06339v3","created_at":"2026-05-18T00:40:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.06339","created_at":"2026-05-18T00:40:39Z"},{"alias_kind":"pith_short_12","alias_value":"GVEAETQURJRQ","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GVEAETQURJRQHFG4","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GVEAETQU","created_at":"2026-05-18T12:31:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:GVEAETQURJRQHFG4WDQSHWWCSI","target":"record","payload":{"canonical_record":{"source":{"id":"1705.06339","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-17T20:29:31Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"ddcc54c05251e16dd5df971558d883f65a14b0b68b84c61c676b9a933fa1af02","abstract_canon_sha256":"a7b006a3a3465f8abb428f274759415bfc2f22c0d7495f23c75e8391b31bc868"},"schema_version":"1.0"},"canonical_sha256":"3548024e148a630394dcb0e123dac2923ff88af3f1a16987c32b89a82cb3ecaf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:39.986449Z","signature_b64":"8AnKh3X9+fjAHB7G04gPQWA6IvHe+Haklud3+qZ/Y3I4sOptpzj9MgSbukAoUTW8Uy4dEpF7L6OGTVN2xKh3CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3548024e148a630394dcb0e123dac2923ff88af3f1a16987c32b89a82cb3ecaf","last_reissued_at":"2026-05-18T00:40:39.985598Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:39.985598Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.06339","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":"2026-05-18T00:40:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cm3CTJdTQYq1qYWny9Ny8/roJ/C+TG3i8kDHOz+urum0Y96wySIoMTQA5AUNsf83fS75CplqOaq6s6ARW54UAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T10:04:32.557021Z"},"content_sha256":"0802709b8f5511e6ce2b7c69edad310612c93365f1c9d47a93f60d84508398cb","schema_version":"1.0","event_id":"sha256:0802709b8f5511e6ce2b7c69edad310612c93365f1c9d47a93f60d84508398cb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:GVEAETQURJRQHFG4WDQSHWWCSI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Computing minimal generating systems for some special toric ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.CO","authors_text":"Dimitrios I. Dais, Ioannis Markakis","submitted_at":"2017-05-17T20:29:31Z","abstract_excerpt":"Let $X_{P}$ be the projective toric surface associated to a lattice polytope $P$. If the number of lattice points lying on the boundary of $P$ is at least $4$, it is known that $X_{P}$ is embeddable into a suitable projective space as zero set of finitely many quadrics. In this case, the determination of a minimal generating system of the toric ideal defining $X_{P}$ is reduced to a simple Gaussian elimination."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.06339","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":""},"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":"2026-05-18T00:40:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C6ihRbP/0VAF8oB2p1tVDpd2f+yXu5ghM7Ns4FU1U040EQ6qaIEnQRMUjLA/x4T/yixN350E47rVl4fSxiitCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T10:04:32.557375Z"},"content_sha256":"546712788a6e8b0d415e19eaa38378def7ac84cac3503e9f48e914d9be94409b","schema_version":"1.0","event_id":"sha256:546712788a6e8b0d415e19eaa38378def7ac84cac3503e9f48e914d9be94409b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GVEAETQURJRQHFG4WDQSHWWCSI/bundle.json","state_url":"https://pith.science/pith/GVEAETQURJRQHFG4WDQSHWWCSI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GVEAETQURJRQHFG4WDQSHWWCSI/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":"2026-06-05T10:04:32Z","links":{"resolver":"https://pith.science/pith/GVEAETQURJRQHFG4WDQSHWWCSI","bundle":"https://pith.science/pith/GVEAETQURJRQHFG4WDQSHWWCSI/bundle.json","state":"https://pith.science/pith/GVEAETQURJRQHFG4WDQSHWWCSI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GVEAETQURJRQHFG4WDQSHWWCSI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:GVEAETQURJRQHFG4WDQSHWWCSI","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":"a7b006a3a3465f8abb428f274759415bfc2f22c0d7495f23c75e8391b31bc868","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-17T20:29:31Z","title_canon_sha256":"ddcc54c05251e16dd5df971558d883f65a14b0b68b84c61c676b9a933fa1af02"},"schema_version":"1.0","source":{"id":"1705.06339","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.06339","created_at":"2026-05-18T00:40:39Z"},{"alias_kind":"arxiv_version","alias_value":"1705.06339v3","created_at":"2026-05-18T00:40:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.06339","created_at":"2026-05-18T00:40:39Z"},{"alias_kind":"pith_short_12","alias_value":"GVEAETQURJRQ","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GVEAETQURJRQHFG4","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GVEAETQU","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:546712788a6e8b0d415e19eaa38378def7ac84cac3503e9f48e914d9be94409b","target":"graph","created_at":"2026-05-18T00:40:39Z","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":"Let $X_{P}$ be the projective toric surface associated to a lattice polytope $P$. If the number of lattice points lying on the boundary of $P$ is at least $4$, it is known that $X_{P}$ is embeddable into a suitable projective space as zero set of finitely many quadrics. In this case, the determination of a minimal generating system of the toric ideal defining $X_{P}$ is reduced to a simple Gaussian elimination.","authors_text":"Dimitrios I. Dais, Ioannis Markakis","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-17T20:29:31Z","title":"Computing minimal generating systems for some special toric ideals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.06339","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":"sha256:0802709b8f5511e6ce2b7c69edad310612c93365f1c9d47a93f60d84508398cb","target":"record","created_at":"2026-05-18T00:40:39Z","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":"a7b006a3a3465f8abb428f274759415bfc2f22c0d7495f23c75e8391b31bc868","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-17T20:29:31Z","title_canon_sha256":"ddcc54c05251e16dd5df971558d883f65a14b0b68b84c61c676b9a933fa1af02"},"schema_version":"1.0","source":{"id":"1705.06339","kind":"arxiv","version":3}},"canonical_sha256":"3548024e148a630394dcb0e123dac2923ff88af3f1a16987c32b89a82cb3ecaf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3548024e148a630394dcb0e123dac2923ff88af3f1a16987c32b89a82cb3ecaf","first_computed_at":"2026-05-18T00:40:39.985598Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:39.985598Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8AnKh3X9+fjAHB7G04gPQWA6IvHe+Haklud3+qZ/Y3I4sOptpzj9MgSbukAoUTW8Uy4dEpF7L6OGTVN2xKh3CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:39.986449Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.06339","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0802709b8f5511e6ce2b7c69edad310612c93365f1c9d47a93f60d84508398cb","sha256:546712788a6e8b0d415e19eaa38378def7ac84cac3503e9f48e914d9be94409b"],"state_sha256":"43fda501d26d67b39405b346ce87fdf0bebb38ef9daa14b2cf69ecfb413fdadc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0+zE010ANf7TKjxoE6q7/wqsXMgb+pY0+3fWimh0Ltb2PRbsaIJVyRWeajSXH8CHzYCcK2fYRFIPG03th52oBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T10:04:32.559342Z","bundle_sha256":"ff0526c0104df029af91f4df2152ac957c0052fb62b63a46590715bce26a3c56"}}