{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:6XSHJQPGPRQF7PJE2BGW7AABJL","short_pith_number":"pith:6XSHJQPG","canonical_record":{"source":{"id":"1805.02030","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-05-05T09:37:37Z","cross_cats_sorted":[],"title_canon_sha256":"b0a0b19ce664b05a5b26b7b3695bde39e921f912f29ce1829a1ca06d9ff3e66a","abstract_canon_sha256":"fd36c4fd496a67c4e497c14274df1b00c4a8f5e4250df9cf6ac2f505899982a9"},"schema_version":"1.0"},"canonical_sha256":"f5e474c1e67c605fbd24d04d6f80014af49098f1f44d5e8b73564b45411b3a2f","source":{"kind":"arxiv","id":"1805.02030","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.02030","created_at":"2026-07-05T00:18:49Z"},{"alias_kind":"arxiv_version","alias_value":"1805.02030v2","created_at":"2026-07-05T00:18:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.02030","created_at":"2026-07-05T00:18:49Z"},{"alias_kind":"pith_short_12","alias_value":"6XSHJQPGPRQF","created_at":"2026-07-05T00:18:49Z"},{"alias_kind":"pith_short_16","alias_value":"6XSHJQPGPRQF7PJE","created_at":"2026-07-05T00:18:49Z"},{"alias_kind":"pith_short_8","alias_value":"6XSHJQPG","created_at":"2026-07-05T00:18:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:6XSHJQPGPRQF7PJE2BGW7AABJL","target":"record","payload":{"canonical_record":{"source":{"id":"1805.02030","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-05-05T09:37:37Z","cross_cats_sorted":[],"title_canon_sha256":"b0a0b19ce664b05a5b26b7b3695bde39e921f912f29ce1829a1ca06d9ff3e66a","abstract_canon_sha256":"fd36c4fd496a67c4e497c14274df1b00c4a8f5e4250df9cf6ac2f505899982a9"},"schema_version":"1.0"},"canonical_sha256":"f5e474c1e67c605fbd24d04d6f80014af49098f1f44d5e8b73564b45411b3a2f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:18:49.086487Z","signature_b64":"/+sZXoAZrFD1/Jog09mRM8rW9RsOJIuWqNWfco3QmYTMp8Pm2NwDPdwJl5ED1DxO+o6NhibybXqmXW7e45wwCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f5e474c1e67c605fbd24d04d6f80014af49098f1f44d5e8b73564b45411b3a2f","last_reissued_at":"2026-07-05T00:18:49.086131Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:18:49.086131Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.02030","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":"2026-07-05T00:18:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Niqzc64dZv2O6jpzUDnk6YeeLrGeOq4aeYhToWSdNMDY8u+MD1VqRTvMPpbm3NPu4hHjw8PjV3sKN98ANeDrDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T00:58:09.745085Z"},"content_sha256":"b75fa40899e36959beb7bd971e2e75ab61ae5825934e500bcc25669f12e965c3","schema_version":"1.0","event_id":"sha256:b75fa40899e36959beb7bd971e2e75ab61ae5825934e500bcc25669f12e965c3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:6XSHJQPGPRQF7PJE2BGW7AABJL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bounding the Betti numbers of real hypersurfaces near the tropical limit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Arthur Renaudineau, Kristin Shaw","submitted_at":"2018-05-05T09:37:37Z","abstract_excerpt":"We prove a bound conjectured by Itenberg on the Betti numbers of real algebraic hypersurfaces near non-singular tropical limits. These bounds are given in terms of the Hodge numbers of the complexification. To prove the conjecture we introduce a real variant of tropical homology and define a filtration on the corresponding chain complex inspired by Kalinin's filtration. The spectral sequence associated to this filtration converges to the homology groups of the real algebraic variety and we show that the terms of the first page are tropical homology groups with $\\mathbb{Z}_2$-coefficients. The "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.02030","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1805.02030/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":"2026-07-05T00:18:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hFjD/MAUMVJws/pMVmFuWnqdfrkIIZnD4zCfTgvejvL1oGfN1mcKjFtX8OiXqS0eBZDINv9eNFnYRMnNb1nXAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T00:58:09.745593Z"},"content_sha256":"46d2d007789280b1daf86930ae5b4318d8143df71cba817b2f7301ec459bc2e4","schema_version":"1.0","event_id":"sha256:46d2d007789280b1daf86930ae5b4318d8143df71cba817b2f7301ec459bc2e4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6XSHJQPGPRQF7PJE2BGW7AABJL/bundle.json","state_url":"https://pith.science/pith/6XSHJQPGPRQF7PJE2BGW7AABJL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6XSHJQPGPRQF7PJE2BGW7AABJL/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":"2026-08-16T00:58:09Z","links":{"resolver":"https://pith.science/pith/6XSHJQPGPRQF7PJE2BGW7AABJL","bundle":"https://pith.science/pith/6XSHJQPGPRQF7PJE2BGW7AABJL/bundle.json","state":"https://pith.science/pith/6XSHJQPGPRQF7PJE2BGW7AABJL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6XSHJQPGPRQF7PJE2BGW7AABJL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:6XSHJQPGPRQF7PJE2BGW7AABJL","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":"fd36c4fd496a67c4e497c14274df1b00c4a8f5e4250df9cf6ac2f505899982a9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-05-05T09:37:37Z","title_canon_sha256":"b0a0b19ce664b05a5b26b7b3695bde39e921f912f29ce1829a1ca06d9ff3e66a"},"schema_version":"1.0","source":{"id":"1805.02030","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.02030","created_at":"2026-07-05T00:18:49Z"},{"alias_kind":"arxiv_version","alias_value":"1805.02030v2","created_at":"2026-07-05T00:18:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.02030","created_at":"2026-07-05T00:18:49Z"},{"alias_kind":"pith_short_12","alias_value":"6XSHJQPGPRQF","created_at":"2026-07-05T00:18:49Z"},{"alias_kind":"pith_short_16","alias_value":"6XSHJQPGPRQF7PJE","created_at":"2026-07-05T00:18:49Z"},{"alias_kind":"pith_short_8","alias_value":"6XSHJQPG","created_at":"2026-07-05T00:18:49Z"}],"graph_snapshots":[{"event_id":"sha256:46d2d007789280b1daf86930ae5b4318d8143df71cba817b2f7301ec459bc2e4","target":"graph","created_at":"2026-07-05T00:18:49Z","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/1805.02030/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove a bound conjectured by Itenberg on the Betti numbers of real algebraic hypersurfaces near non-singular tropical limits. These bounds are given in terms of the Hodge numbers of the complexification. To prove the conjecture we introduce a real variant of tropical homology and define a filtration on the corresponding chain complex inspired by Kalinin's filtration. The spectral sequence associated to this filtration converges to the homology groups of the real algebraic variety and we show that the terms of the first page are tropical homology groups with $\\mathbb{Z}_2$-coefficients. The ","authors_text":"Arthur Renaudineau, Kristin Shaw","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-05-05T09:37:37Z","title":"Bounding the Betti numbers of real hypersurfaces near the tropical limit"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.02030","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:b75fa40899e36959beb7bd971e2e75ab61ae5825934e500bcc25669f12e965c3","target":"record","created_at":"2026-07-05T00:18:49Z","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":"fd36c4fd496a67c4e497c14274df1b00c4a8f5e4250df9cf6ac2f505899982a9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-05-05T09:37:37Z","title_canon_sha256":"b0a0b19ce664b05a5b26b7b3695bde39e921f912f29ce1829a1ca06d9ff3e66a"},"schema_version":"1.0","source":{"id":"1805.02030","kind":"arxiv","version":2}},"canonical_sha256":"f5e474c1e67c605fbd24d04d6f80014af49098f1f44d5e8b73564b45411b3a2f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f5e474c1e67c605fbd24d04d6f80014af49098f1f44d5e8b73564b45411b3a2f","first_computed_at":"2026-07-05T00:18:49.086131Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:18:49.086131Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/+sZXoAZrFD1/Jog09mRM8rW9RsOJIuWqNWfco3QmYTMp8Pm2NwDPdwJl5ED1DxO+o6NhibybXqmXW7e45wwCA==","signature_status":"signed_v1","signed_at":"2026-07-05T00:18:49.086487Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.02030","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b75fa40899e36959beb7bd971e2e75ab61ae5825934e500bcc25669f12e965c3","sha256:46d2d007789280b1daf86930ae5b4318d8143df71cba817b2f7301ec459bc2e4"],"state_sha256":"db21c187251d03359f82d43d27688b0068a18e50db4ca9f479c05609fb30160d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dQ2owFOBDUYnDYzDEvRpOK9sFvyDYgcR9J1L9ZeNA5uiLNGSLMxGLNduS5zLjj4n1GNo5rSZTUy6CIUPjtzrCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T00:58:09.749900Z","bundle_sha256":"d10b28fad0ba8133dcabcbf0c8e200d18c9849294d0d99e8efda0323326857e0"}}