{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:7Q3KKZVSWG4OQQW336GEI5XQUJ","short_pith_number":"pith:7Q3KKZVS","canonical_record":{"source":{"id":"1908.03486","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-08-09T15:01:20Z","cross_cats_sorted":["cs.SC"],"title_canon_sha256":"0034c73bfa2ca92b8e86e3466360bf9cb25182666f7a8e2ce0842e7301563015","abstract_canon_sha256":"f202c82b5ab97cf168ca15f8ae8ec919d7b59f20eea626bb92acaf267e04aa63"},"schema_version":"1.0"},"canonical_sha256":"fc36a566b2b1b8e842dbdf8c4476f0a2733616a0df8a0d916233fba16133ff51","source":{"kind":"arxiv","id":"1908.03486","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.03486","created_at":"2026-07-04T23:52:40Z"},{"alias_kind":"arxiv_version","alias_value":"1908.03486v1","created_at":"2026-07-04T23:52:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.03486","created_at":"2026-07-04T23:52:40Z"},{"alias_kind":"pith_short_12","alias_value":"7Q3KKZVSWG4O","created_at":"2026-07-04T23:52:40Z"},{"alias_kind":"pith_short_16","alias_value":"7Q3KKZVSWG4OQQW3","created_at":"2026-07-04T23:52:40Z"},{"alias_kind":"pith_short_8","alias_value":"7Q3KKZVS","created_at":"2026-07-04T23:52:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:7Q3KKZVSWG4OQQW336GEI5XQUJ","target":"record","payload":{"canonical_record":{"source":{"id":"1908.03486","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-08-09T15:01:20Z","cross_cats_sorted":["cs.SC"],"title_canon_sha256":"0034c73bfa2ca92b8e86e3466360bf9cb25182666f7a8e2ce0842e7301563015","abstract_canon_sha256":"f202c82b5ab97cf168ca15f8ae8ec919d7b59f20eea626bb92acaf267e04aa63"},"schema_version":"1.0"},"canonical_sha256":"fc36a566b2b1b8e842dbdf8c4476f0a2733616a0df8a0d916233fba16133ff51","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:52:40.325089Z","signature_b64":"QhXYJ22eXvpF4giGiRdbvwWTesM75EMz4iqAUOAvilNR2B5/FlEYoOAux0nLjTmeleNoYVCak0NEiK8/q2DOBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc36a566b2b1b8e842dbdf8c4476f0a2733616a0df8a0d916233fba16133ff51","last_reissued_at":"2026-07-04T23:52:40.324748Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:52:40.324748Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.03486","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":"2026-07-04T23:52:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3Fu2hdQ4Bam+K+xmDpxLMmPlP77uaq11FUMU2HU4yH35U9n78K39OnlMJo0LhwWgit+xBlUgr6mQgsUGKv4NCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T07:14:37.708889Z"},"content_sha256":"08ea6fd466494023a3975dc5c8c8eb432a2bf5ffc2dce08ae0717aeca7d88395","schema_version":"1.0","event_id":"sha256:08ea6fd466494023a3975dc5c8c8eb432a2bf5ffc2dce08ae0717aeca7d88395"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:7Q3KKZVSWG4OQQW336GEI5XQUJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Computing zero-dimensional tropical varieties via projections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC"],"primary_cat":"math.AG","authors_text":"Leon Zhang, Paul G\\\"orlach, Yue Ren","submitted_at":"2019-08-09T15:01:20Z","abstract_excerpt":"We present an algorithm for computing zero-dimensional tropical varieties using projections. Our main tools are fast unimodular transforms of lexicographical Gr\\\"obner bases. We prove that our algorithm requires only a polynomial number of arithmetic operations if given a Gr\\\"obner basis, and we demonstrate that our implementation compares favourably to other existing implementations. Applying it to the computation of general positive-dimensional tropical varieties, we argue that the complexity for calculating tropical links is dominated by the complexity of the Gr\\\"obner walk."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.03486","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.03486/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":"2026-07-04T23:52:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QWlQIzsSi3mgijY30I0f2QsDpr6ppS/uTfUwgdTUjTOv/2ts9KPfI5HWSslcD7fnjn7glMGUbvQotiwxDonVCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T07:14:37.709474Z"},"content_sha256":"569290bf322e44986a6c33c24979e001f1fe13374675dbf9d08f2d94edbf08f1","schema_version":"1.0","event_id":"sha256:569290bf322e44986a6c33c24979e001f1fe13374675dbf9d08f2d94edbf08f1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7Q3KKZVSWG4OQQW336GEI5XQUJ/bundle.json","state_url":"https://pith.science/pith/7Q3KKZVSWG4OQQW336GEI5XQUJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7Q3KKZVSWG4OQQW336GEI5XQUJ/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":"2026-08-16T07:14:37Z","links":{"resolver":"https://pith.science/pith/7Q3KKZVSWG4OQQW336GEI5XQUJ","bundle":"https://pith.science/pith/7Q3KKZVSWG4OQQW336GEI5XQUJ/bundle.json","state":"https://pith.science/pith/7Q3KKZVSWG4OQQW336GEI5XQUJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7Q3KKZVSWG4OQQW336GEI5XQUJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:7Q3KKZVSWG4OQQW336GEI5XQUJ","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":"f202c82b5ab97cf168ca15f8ae8ec919d7b59f20eea626bb92acaf267e04aa63","cross_cats_sorted":["cs.SC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-08-09T15:01:20Z","title_canon_sha256":"0034c73bfa2ca92b8e86e3466360bf9cb25182666f7a8e2ce0842e7301563015"},"schema_version":"1.0","source":{"id":"1908.03486","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.03486","created_at":"2026-07-04T23:52:40Z"},{"alias_kind":"arxiv_version","alias_value":"1908.03486v1","created_at":"2026-07-04T23:52:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.03486","created_at":"2026-07-04T23:52:40Z"},{"alias_kind":"pith_short_12","alias_value":"7Q3KKZVSWG4O","created_at":"2026-07-04T23:52:40Z"},{"alias_kind":"pith_short_16","alias_value":"7Q3KKZVSWG4OQQW3","created_at":"2026-07-04T23:52:40Z"},{"alias_kind":"pith_short_8","alias_value":"7Q3KKZVS","created_at":"2026-07-04T23:52:40Z"}],"graph_snapshots":[{"event_id":"sha256:569290bf322e44986a6c33c24979e001f1fe13374675dbf9d08f2d94edbf08f1","target":"graph","created_at":"2026-07-04T23:52:40Z","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/1908.03486/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present an algorithm for computing zero-dimensional tropical varieties using projections. Our main tools are fast unimodular transforms of lexicographical Gr\\\"obner bases. We prove that our algorithm requires only a polynomial number of arithmetic operations if given a Gr\\\"obner basis, and we demonstrate that our implementation compares favourably to other existing implementations. Applying it to the computation of general positive-dimensional tropical varieties, we argue that the complexity for calculating tropical links is dominated by the complexity of the Gr\\\"obner walk.","authors_text":"Leon Zhang, Paul G\\\"orlach, Yue Ren","cross_cats":["cs.SC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-08-09T15:01:20Z","title":"Computing zero-dimensional tropical varieties via projections"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.03486","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":"sha256:08ea6fd466494023a3975dc5c8c8eb432a2bf5ffc2dce08ae0717aeca7d88395","target":"record","created_at":"2026-07-04T23:52:40Z","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":"f202c82b5ab97cf168ca15f8ae8ec919d7b59f20eea626bb92acaf267e04aa63","cross_cats_sorted":["cs.SC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-08-09T15:01:20Z","title_canon_sha256":"0034c73bfa2ca92b8e86e3466360bf9cb25182666f7a8e2ce0842e7301563015"},"schema_version":"1.0","source":{"id":"1908.03486","kind":"arxiv","version":1}},"canonical_sha256":"fc36a566b2b1b8e842dbdf8c4476f0a2733616a0df8a0d916233fba16133ff51","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc36a566b2b1b8e842dbdf8c4476f0a2733616a0df8a0d916233fba16133ff51","first_computed_at":"2026-07-04T23:52:40.324748Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:52:40.324748Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QhXYJ22eXvpF4giGiRdbvwWTesM75EMz4iqAUOAvilNR2B5/FlEYoOAux0nLjTmeleNoYVCak0NEiK8/q2DOBQ==","signature_status":"signed_v1","signed_at":"2026-07-04T23:52:40.325089Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.03486","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:08ea6fd466494023a3975dc5c8c8eb432a2bf5ffc2dce08ae0717aeca7d88395","sha256:569290bf322e44986a6c33c24979e001f1fe13374675dbf9d08f2d94edbf08f1"],"state_sha256":"068b594a413a676a284567a6990480422db640ec63464e560d6ca1674a61232a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"paImxlcIpUErwopr0sf6o7sod2uDHicRD1S9vVECL9UmKQcs7GY/RLl+pP8f5F7MKzFvTYbIGHJV4AOdiyVCCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T07:14:37.716189Z","bundle_sha256":"6a012da1120040555b8185d74ab4b9ca0d831b2a87a60c159d7aae79185b6ccb"}}