{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:MZNHEUDYH2QVC4DC5B6E3MTJN7","short_pith_number":"pith:MZNHEUDY","canonical_record":{"source":{"id":"1612.01762","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-12-06T11:30:41Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"90e9f4bab7cfaa7d05304913904da56e676ead9c3682473257b2dec82ad0eb83","abstract_canon_sha256":"b26bcfd6bba3f4d98a799e837c648cd826b74e8a7cc8404555dfd343c85cb745"},"schema_version":"1.0"},"canonical_sha256":"665a7250783ea1517062e87c4db2696fdfef93feb3f9d4feb62eabcc473c1003","source":{"kind":"arxiv","id":"1612.01762","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.01762","created_at":"2026-05-18T00:55:47Z"},{"alias_kind":"arxiv_version","alias_value":"1612.01762v1","created_at":"2026-05-18T00:55:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.01762","created_at":"2026-05-18T00:55:47Z"},{"alias_kind":"pith_short_12","alias_value":"MZNHEUDYH2QV","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MZNHEUDYH2QVC4DC","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MZNHEUDY","created_at":"2026-05-18T12:30:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:MZNHEUDYH2QVC4DC5B6E3MTJN7","target":"record","payload":{"canonical_record":{"source":{"id":"1612.01762","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-12-06T11:30:41Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"90e9f4bab7cfaa7d05304913904da56e676ead9c3682473257b2dec82ad0eb83","abstract_canon_sha256":"b26bcfd6bba3f4d98a799e837c648cd826b74e8a7cc8404555dfd343c85cb745"},"schema_version":"1.0"},"canonical_sha256":"665a7250783ea1517062e87c4db2696fdfef93feb3f9d4feb62eabcc473c1003","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:55:47.655880Z","signature_b64":"Eb1Al9NSVUqDBIw6r8HKObiadmOIRqZqeL4DANaJFUXDdxzq0kx2p5pFUzlV2pDsKtYv8t9O1xld2yzky+SQCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"665a7250783ea1517062e87c4db2696fdfef93feb3f9d4feb62eabcc473c1003","last_reissued_at":"2026-05-18T00:55:47.655390Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:55:47.655390Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.01762","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":"2026-05-18T00:55:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FQnjm1gvKmfCteqX74jOzzJKek5n/Si1yRiQHO7NkKB46CIlhNG6tXJKLXTiSFQ4UosxIObZ2cNXa3fbjkgqBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T08:22:14.346627Z"},"content_sha256":"413ee7037ac5ed882085fb1b844474177fccdc27278b7e21ec00ac8d32c4cb2d","schema_version":"1.0","event_id":"sha256:413ee7037ac5ed882085fb1b844474177fccdc27278b7e21ec00ac8d32c4cb2d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:MZNHEUDYH2QVC4DC5B6E3MTJN7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Computing tropical varieties over fields with valuation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Thomas Markwig, Yue Ren","submitted_at":"2016-12-06T11:30:41Z","abstract_excerpt":"We show how tropical varieties of ideals I over a field K with non-trivial valuation can be traced back to tropical varieties of ideals in R[[t]][x] over some dense subring R in its ring of integers. Moreover, for homogeneous ideals, we present algorithms on how the latter can be computed in finite time, provided that generators are polynomial in t. While doing so, we also comment on the computation of the Groebner polytope structure and p-adic Groebner bases using our framework. All algorithms solely rely on existing standard basis techniques."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.01762","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":""},"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":"2026-05-18T00:55:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ga32BNsubpgsExWtAW2G/2a0ZN3nslgpiKsJFuHsMmMA7vN9TxcbZItxrsJ0kdcwCVs5TU2lTYbVjKQgHwNQDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T08:22:14.347265Z"},"content_sha256":"f497d79aeeaa459cdaf434981f3ade427d801201270994b79f5347690a55f7db","schema_version":"1.0","event_id":"sha256:f497d79aeeaa459cdaf434981f3ade427d801201270994b79f5347690a55f7db"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MZNHEUDYH2QVC4DC5B6E3MTJN7/bundle.json","state_url":"https://pith.science/pith/MZNHEUDYH2QVC4DC5B6E3MTJN7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MZNHEUDYH2QVC4DC5B6E3MTJN7/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":"2026-06-04T08:22:14Z","links":{"resolver":"https://pith.science/pith/MZNHEUDYH2QVC4DC5B6E3MTJN7","bundle":"https://pith.science/pith/MZNHEUDYH2QVC4DC5B6E3MTJN7/bundle.json","state":"https://pith.science/pith/MZNHEUDYH2QVC4DC5B6E3MTJN7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MZNHEUDYH2QVC4DC5B6E3MTJN7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:MZNHEUDYH2QVC4DC5B6E3MTJN7","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":"b26bcfd6bba3f4d98a799e837c648cd826b74e8a7cc8404555dfd343c85cb745","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-12-06T11:30:41Z","title_canon_sha256":"90e9f4bab7cfaa7d05304913904da56e676ead9c3682473257b2dec82ad0eb83"},"schema_version":"1.0","source":{"id":"1612.01762","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.01762","created_at":"2026-05-18T00:55:47Z"},{"alias_kind":"arxiv_version","alias_value":"1612.01762v1","created_at":"2026-05-18T00:55:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.01762","created_at":"2026-05-18T00:55:47Z"},{"alias_kind":"pith_short_12","alias_value":"MZNHEUDYH2QV","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MZNHEUDYH2QVC4DC","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MZNHEUDY","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:f497d79aeeaa459cdaf434981f3ade427d801201270994b79f5347690a55f7db","target":"graph","created_at":"2026-05-18T00:55:47Z","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 show how tropical varieties of ideals I over a field K with non-trivial valuation can be traced back to tropical varieties of ideals in R[[t]][x] over some dense subring R in its ring of integers. Moreover, for homogeneous ideals, we present algorithms on how the latter can be computed in finite time, provided that generators are polynomial in t. While doing so, we also comment on the computation of the Groebner polytope structure and p-adic Groebner bases using our framework. All algorithms solely rely on existing standard basis techniques.","authors_text":"Thomas Markwig, Yue Ren","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-12-06T11:30:41Z","title":"Computing tropical varieties over fields with valuation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.01762","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":"sha256:413ee7037ac5ed882085fb1b844474177fccdc27278b7e21ec00ac8d32c4cb2d","target":"record","created_at":"2026-05-18T00:55:47Z","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":"b26bcfd6bba3f4d98a799e837c648cd826b74e8a7cc8404555dfd343c85cb745","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-12-06T11:30:41Z","title_canon_sha256":"90e9f4bab7cfaa7d05304913904da56e676ead9c3682473257b2dec82ad0eb83"},"schema_version":"1.0","source":{"id":"1612.01762","kind":"arxiv","version":1}},"canonical_sha256":"665a7250783ea1517062e87c4db2696fdfef93feb3f9d4feb62eabcc473c1003","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"665a7250783ea1517062e87c4db2696fdfef93feb3f9d4feb62eabcc473c1003","first_computed_at":"2026-05-18T00:55:47.655390Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:47.655390Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Eb1Al9NSVUqDBIw6r8HKObiadmOIRqZqeL4DANaJFUXDdxzq0kx2p5pFUzlV2pDsKtYv8t9O1xld2yzky+SQCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:47.655880Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.01762","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:413ee7037ac5ed882085fb1b844474177fccdc27278b7e21ec00ac8d32c4cb2d","sha256:f497d79aeeaa459cdaf434981f3ade427d801201270994b79f5347690a55f7db"],"state_sha256":"c9d1963b0b6ca5ca856ebe232309e98151d911cc3f9141483c2b8cd0408b675c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xZWr3JCuM15LY8ZnaBs548wW/55K32x7v8F2JHUbrHCtAHVZFsJ+eyVgxM59xXh7LZ5zQZKxsSgp2YAZxtqxDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T08:22:14.350554Z","bundle_sha256":"42f6f2722a32a8a94444b7d18aafae0bbf0347d442dfcb93e8aae5d628642506"}}