{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:ZQVEOLYZ2BYCPA5YVWLV6FSR2H","short_pith_number":"pith:ZQVEOLYZ","canonical_record":{"source":{"id":"0708.1727","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2007-08-13T15:39:52Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"e8b39c89ee90348458e846359817003b7275557b1fcda52eafd6653466ac3f84","abstract_canon_sha256":"940a3335f7c09268e88d53a60b2a7baf93a7af79a8694b0f7cd8c1f04aa05281"},"schema_version":"1.0"},"canonical_sha256":"cc2a472f19d0702783b8ad975f1651d1f80a8a9d7d024ea756bbb37c1f806f60","source":{"kind":"arxiv","id":"0708.1727","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0708.1727","created_at":"2026-05-18T04:09:15Z"},{"alias_kind":"arxiv_version","alias_value":"0708.1727v2","created_at":"2026-05-18T04:09:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0708.1727","created_at":"2026-05-18T04:09:15Z"},{"alias_kind":"pith_short_12","alias_value":"ZQVEOLYZ2BYC","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"ZQVEOLYZ2BYCPA5Y","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"ZQVEOLYZ","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:ZQVEOLYZ2BYCPA5YVWLV6FSR2H","target":"record","payload":{"canonical_record":{"source":{"id":"0708.1727","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2007-08-13T15:39:52Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"e8b39c89ee90348458e846359817003b7275557b1fcda52eafd6653466ac3f84","abstract_canon_sha256":"940a3335f7c09268e88d53a60b2a7baf93a7af79a8694b0f7cd8c1f04aa05281"},"schema_version":"1.0"},"canonical_sha256":"cc2a472f19d0702783b8ad975f1651d1f80a8a9d7d024ea756bbb37c1f806f60","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:09:15.015545Z","signature_b64":"Lvb7neXMCrwyqQD+SYLungG04mGP4hYQPz0jF0bGR+kp7raIa8jNCMfiOJfD4e9j78x3tLvLupfjADuNsXgiDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cc2a472f19d0702783b8ad975f1651d1f80a8a9d7d024ea756bbb37c1f806f60","last_reissued_at":"2026-05-18T04:09:15.015046Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:09:15.015046Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0708.1727","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":"2026-05-18T04:09:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BnASblEPrNuR5YjGhJ20DZw3Xfk3e6H9zk5KfoaZc2vsisi+i27xz63IC9idSJf/WRYH64TbtVCkSosCbYHkCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T18:41:11.308846Z"},"content_sha256":"b553cb817768a7dd699e7fc4e394b51918d4b268b4ba0cd5a50d5647dbc7c8d7","schema_version":"1.0","event_id":"sha256:b553cb817768a7dd699e7fc4e394b51918d4b268b4ba0cd5a50d5647dbc7c8d7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:ZQVEOLYZ2BYCPA5YVWLV6FSR2H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tropical bases by regular projections","license":"","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Kerstin Hept, Thorsten Theobald","submitted_at":"2007-08-13T15:39:52Z","abstract_excerpt":"We consider the tropical variety $\\mathcal{T}(I)$ of a prime ideal $I$ generated by the polynomials $f_1, ..., f_r$ and revisit the regular projection technique introduced by Bieri and Groves from a computational point of view. In particular, we show that $I$ has a short tropical basis of cardinality at most $r + \\codim I + 1$ at the price of increased degrees, and we provide a computational description of these bases."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0708.1727","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":"2026-05-18T04:09:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FBIZUTUPIV7BbxpI+6dPgueNDuTWkwCOV+80hah4CG/bR0zHaJZsYv2Nab0vSGWOalPwlWDq8numB7impBRBBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T18:41:11.309189Z"},"content_sha256":"d656d9daf15c4f3f44571833b6b559eea4712fc30279f31d7b78380b40ec8a92","schema_version":"1.0","event_id":"sha256:d656d9daf15c4f3f44571833b6b559eea4712fc30279f31d7b78380b40ec8a92"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZQVEOLYZ2BYCPA5YVWLV6FSR2H/bundle.json","state_url":"https://pith.science/pith/ZQVEOLYZ2BYCPA5YVWLV6FSR2H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZQVEOLYZ2BYCPA5YVWLV6FSR2H/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":"2026-06-01T18:41:11Z","links":{"resolver":"https://pith.science/pith/ZQVEOLYZ2BYCPA5YVWLV6FSR2H","bundle":"https://pith.science/pith/ZQVEOLYZ2BYCPA5YVWLV6FSR2H/bundle.json","state":"https://pith.science/pith/ZQVEOLYZ2BYCPA5YVWLV6FSR2H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZQVEOLYZ2BYCPA5YVWLV6FSR2H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:ZQVEOLYZ2BYCPA5YVWLV6FSR2H","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":"940a3335f7c09268e88d53a60b2a7baf93a7af79a8694b0f7cd8c1f04aa05281","cross_cats_sorted":["math.CO"],"license":"","primary_cat":"math.AG","submitted_at":"2007-08-13T15:39:52Z","title_canon_sha256":"e8b39c89ee90348458e846359817003b7275557b1fcda52eafd6653466ac3f84"},"schema_version":"1.0","source":{"id":"0708.1727","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0708.1727","created_at":"2026-05-18T04:09:15Z"},{"alias_kind":"arxiv_version","alias_value":"0708.1727v2","created_at":"2026-05-18T04:09:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0708.1727","created_at":"2026-05-18T04:09:15Z"},{"alias_kind":"pith_short_12","alias_value":"ZQVEOLYZ2BYC","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"ZQVEOLYZ2BYCPA5Y","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"ZQVEOLYZ","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:d656d9daf15c4f3f44571833b6b559eea4712fc30279f31d7b78380b40ec8a92","target":"graph","created_at":"2026-05-18T04:09:15Z","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"},"paper":{"abstract_excerpt":"We consider the tropical variety $\\mathcal{T}(I)$ of a prime ideal $I$ generated by the polynomials $f_1, ..., f_r$ and revisit the regular projection technique introduced by Bieri and Groves from a computational point of view. In particular, we show that $I$ has a short tropical basis of cardinality at most $r + \\codim I + 1$ at the price of increased degrees, and we provide a computational description of these bases.","authors_text":"Kerstin Hept, Thorsten Theobald","cross_cats":["math.CO"],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"2007-08-13T15:39:52Z","title":"Tropical bases by regular projections"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0708.1727","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:b553cb817768a7dd699e7fc4e394b51918d4b268b4ba0cd5a50d5647dbc7c8d7","target":"record","created_at":"2026-05-18T04:09:15Z","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":"940a3335f7c09268e88d53a60b2a7baf93a7af79a8694b0f7cd8c1f04aa05281","cross_cats_sorted":["math.CO"],"license":"","primary_cat":"math.AG","submitted_at":"2007-08-13T15:39:52Z","title_canon_sha256":"e8b39c89ee90348458e846359817003b7275557b1fcda52eafd6653466ac3f84"},"schema_version":"1.0","source":{"id":"0708.1727","kind":"arxiv","version":2}},"canonical_sha256":"cc2a472f19d0702783b8ad975f1651d1f80a8a9d7d024ea756bbb37c1f806f60","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cc2a472f19d0702783b8ad975f1651d1f80a8a9d7d024ea756bbb37c1f806f60","first_computed_at":"2026-05-18T04:09:15.015046Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:09:15.015046Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Lvb7neXMCrwyqQD+SYLungG04mGP4hYQPz0jF0bGR+kp7raIa8jNCMfiOJfD4e9j78x3tLvLupfjADuNsXgiDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:09:15.015545Z","signed_message":"canonical_sha256_bytes"},"source_id":"0708.1727","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b553cb817768a7dd699e7fc4e394b51918d4b268b4ba0cd5a50d5647dbc7c8d7","sha256:d656d9daf15c4f3f44571833b6b559eea4712fc30279f31d7b78380b40ec8a92"],"state_sha256":"5ff3ce65dad48a3978ef37662315c9252b664f27c12ccedcf1444ff912070840"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wxiOKKAKMRMl8LySPYmD7C+5+BGkGjrAGThw7HmoPjHkU74zePT5VXwJo1KgwHD1HCxmJKLvuxvQrPp4tMEFBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T18:41:11.311116Z","bundle_sha256":"fef6741385bc5a398518fdee8fa4ec8e25bd04e8dfeb840acfcaf6ddbc91eebb"}}