{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:7QZDCNWCC2O55VUHPMNEUCPZQO","short_pith_number":"pith:7QZDCNWC","canonical_record":{"source":{"id":"1709.08594","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-09-25T16:51:21Z","cross_cats_sorted":[],"title_canon_sha256":"f334fdfe1fbd159b72aec70b2a6ef040ceb9a56bb29fe2db4cd968cbe6b49d25","abstract_canon_sha256":"5e942f384bae6edbe45c79882dba034d9bc69cfc677dc050887255e4da4dc031"},"schema_version":"1.0"},"canonical_sha256":"fc323136c2169dded6877b1a4a09f983a46fe8570f041b683f1dedd722315605","source":{"kind":"arxiv","id":"1709.08594","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.08594","created_at":"2026-05-18T00:21:38Z"},{"alias_kind":"arxiv_version","alias_value":"1709.08594v2","created_at":"2026-05-18T00:21:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.08594","created_at":"2026-05-18T00:21:38Z"},{"alias_kind":"pith_short_12","alias_value":"7QZDCNWCC2O5","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"7QZDCNWCC2O55VUH","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"7QZDCNWC","created_at":"2026-05-18T12:31:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:7QZDCNWCC2O55VUHPMNEUCPZQO","target":"record","payload":{"canonical_record":{"source":{"id":"1709.08594","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-09-25T16:51:21Z","cross_cats_sorted":[],"title_canon_sha256":"f334fdfe1fbd159b72aec70b2a6ef040ceb9a56bb29fe2db4cd968cbe6b49d25","abstract_canon_sha256":"5e942f384bae6edbe45c79882dba034d9bc69cfc677dc050887255e4da4dc031"},"schema_version":"1.0"},"canonical_sha256":"fc323136c2169dded6877b1a4a09f983a46fe8570f041b683f1dedd722315605","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:38.711430Z","signature_b64":"c0jR49HKhkxVgMoslRmXeAS5ALURHTrxqD9JeyKl7WFSL03/35zGSri78FWDwpUB9CZQbCvA2jgdVzoqww2SCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc323136c2169dded6877b1a4a09f983a46fe8570f041b683f1dedd722315605","last_reissued_at":"2026-05-18T00:21:38.710799Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:38.710799Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.08594","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":"2026-05-18T00:21:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c2qnB+qHr4+WLv8oVwG8e8boDebnsF/CtD+M1Wzkr7Prt83LLAsiMti3MxDNoZWXNJPYUvxGRzmMy6eYe5KODw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T16:28:34.107672Z"},"content_sha256":"2ef1fb18e64427474325273b5557741997aae8af6cbf589a42e48c08631f01b2","schema_version":"1.0","event_id":"sha256:2ef1fb18e64427474325273b5557741997aae8af6cbf589a42e48c08631f01b2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:7QZDCNWCC2O55VUHPMNEUCPZQO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Upper bounds on Betti numbers of tropical prevarieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Dima Grigoriev, Nicolai Vorobjov","submitted_at":"2017-09-25T16:51:21Z","abstract_excerpt":"We prove upper bounds on the sum of Betti numbers of tropical prevarieties in dense and sparse settings. In the dense setting the bound is in terms of the volume of Minkowski sum of Newton polytopes of defining tropical polynomials, or, alternatively, via the maximal degree of these polynomials. In sparse setting, the bound involves the number of the monomials."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.08594","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":"2026-05-18T00:21:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1Ta4mXojJHgED+Tq9i7iJ8SbNJMzOxJIM7r9DcMjnhR+jhfnlzjHPr9aCo9rYp3nhJsw5imwVdZnuZibolorDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T16:28:34.108499Z"},"content_sha256":"6d80110906709def5f6b4b57fea881bad5a28f5c0a451d9c5978b1f2f8a3a74b","schema_version":"1.0","event_id":"sha256:6d80110906709def5f6b4b57fea881bad5a28f5c0a451d9c5978b1f2f8a3a74b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7QZDCNWCC2O55VUHPMNEUCPZQO/bundle.json","state_url":"https://pith.science/pith/7QZDCNWCC2O55VUHPMNEUCPZQO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7QZDCNWCC2O55VUHPMNEUCPZQO/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":"2026-05-31T16:28:34Z","links":{"resolver":"https://pith.science/pith/7QZDCNWCC2O55VUHPMNEUCPZQO","bundle":"https://pith.science/pith/7QZDCNWCC2O55VUHPMNEUCPZQO/bundle.json","state":"https://pith.science/pith/7QZDCNWCC2O55VUHPMNEUCPZQO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7QZDCNWCC2O55VUHPMNEUCPZQO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:7QZDCNWCC2O55VUHPMNEUCPZQO","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":"5e942f384bae6edbe45c79882dba034d9bc69cfc677dc050887255e4da4dc031","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-09-25T16:51:21Z","title_canon_sha256":"f334fdfe1fbd159b72aec70b2a6ef040ceb9a56bb29fe2db4cd968cbe6b49d25"},"schema_version":"1.0","source":{"id":"1709.08594","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.08594","created_at":"2026-05-18T00:21:38Z"},{"alias_kind":"arxiv_version","alias_value":"1709.08594v2","created_at":"2026-05-18T00:21:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.08594","created_at":"2026-05-18T00:21:38Z"},{"alias_kind":"pith_short_12","alias_value":"7QZDCNWCC2O5","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"7QZDCNWCC2O55VUH","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"7QZDCNWC","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:6d80110906709def5f6b4b57fea881bad5a28f5c0a451d9c5978b1f2f8a3a74b","target":"graph","created_at":"2026-05-18T00:21:38Z","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 prove upper bounds on the sum of Betti numbers of tropical prevarieties in dense and sparse settings. In the dense setting the bound is in terms of the volume of Minkowski sum of Newton polytopes of defining tropical polynomials, or, alternatively, via the maximal degree of these polynomials. In sparse setting, the bound involves the number of the monomials.","authors_text":"Dima Grigoriev, Nicolai Vorobjov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-09-25T16:51:21Z","title":"Upper bounds on Betti numbers of tropical prevarieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.08594","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":"sha256:2ef1fb18e64427474325273b5557741997aae8af6cbf589a42e48c08631f01b2","target":"record","created_at":"2026-05-18T00:21:38Z","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":"5e942f384bae6edbe45c79882dba034d9bc69cfc677dc050887255e4da4dc031","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-09-25T16:51:21Z","title_canon_sha256":"f334fdfe1fbd159b72aec70b2a6ef040ceb9a56bb29fe2db4cd968cbe6b49d25"},"schema_version":"1.0","source":{"id":"1709.08594","kind":"arxiv","version":2}},"canonical_sha256":"fc323136c2169dded6877b1a4a09f983a46fe8570f041b683f1dedd722315605","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc323136c2169dded6877b1a4a09f983a46fe8570f041b683f1dedd722315605","first_computed_at":"2026-05-18T00:21:38.710799Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:38.710799Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c0jR49HKhkxVgMoslRmXeAS5ALURHTrxqD9JeyKl7WFSL03/35zGSri78FWDwpUB9CZQbCvA2jgdVzoqww2SCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:38.711430Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.08594","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ef1fb18e64427474325273b5557741997aae8af6cbf589a42e48c08631f01b2","sha256:6d80110906709def5f6b4b57fea881bad5a28f5c0a451d9c5978b1f2f8a3a74b"],"state_sha256":"cc22c9a9dd29059644d58f72d9146c547860001874f3cc4fd8eefffb05949dab"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TBn813a1A6gLOkc9l1VvNsT94Z5zSWABpNrMMepyNoS9xRv0BfK5CU9QH2tEx564kc0jh+t2DNTw3C6g7dFlDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T16:28:34.112545Z","bundle_sha256":"0b34e5c4165cb6a3807d257131199a9e8eb83d34245250af5862f6f2601b49fd"}}