{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:XLJIGGLDTMJAZNSSSTK4CPDRF4","short_pith_number":"pith:XLJIGGLD","canonical_record":{"source":{"id":"2412.20748","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2024-12-30T06:43:11Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"e8b21c5c6ad34e38a97be2446684a922bbadadde9254a997e81e10bb568f0e20","abstract_canon_sha256":"b94984b341917763dd48c0ad5e415ac1f86c6190bfc2840e74f4fdb7758b641b"},"schema_version":"1.0"},"canonical_sha256":"bad28319639b120cb65294d5c13c712f35184a0111e46de072a3052ce42d69f7","source":{"kind":"arxiv","id":"2412.20748","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.20748","created_at":"2026-05-18T03:09:46Z"},{"alias_kind":"arxiv_version","alias_value":"2412.20748v4","created_at":"2026-05-18T03:09:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.20748","created_at":"2026-05-18T03:09:46Z"},{"alias_kind":"pith_short_12","alias_value":"XLJIGGLDTMJA","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"XLJIGGLDTMJAZNSS","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"XLJIGGLD","created_at":"2026-05-18T12:33:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:XLJIGGLDTMJAZNSSSTK4CPDRF4","target":"record","payload":{"canonical_record":{"source":{"id":"2412.20748","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2024-12-30T06:43:11Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"e8b21c5c6ad34e38a97be2446684a922bbadadde9254a997e81e10bb568f0e20","abstract_canon_sha256":"b94984b341917763dd48c0ad5e415ac1f86c6190bfc2840e74f4fdb7758b641b"},"schema_version":"1.0"},"canonical_sha256":"bad28319639b120cb65294d5c13c712f35184a0111e46de072a3052ce42d69f7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:09:46.315975Z","signature_b64":"SSC2iR9OyDLESTfStStqUI4w8v5xnM24M67RgVxQifAHjI2xCIVJnIk+R5fyZs/H/lIcamOE2tUsKyL1sgFfBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bad28319639b120cb65294d5c13c712f35184a0111e46de072a3052ce42d69f7","last_reissued_at":"2026-05-18T03:09:46.314101Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:09:46.314101Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2412.20748","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:09:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XSYyOQ6VvTO+nagpzIbDAopMyLD09aKhQ4S4Q/jd5y07gIAQUzZtdUSG8bLKzJgPdF2ZdGuCYX3ZnlbQj4x/Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T00:04:50.351675Z"},"content_sha256":"a2440f6dd7f9352226f0390043a58fcb98c859c28dfd6ba9ad9ca9c04aa541d1","schema_version":"1.0","event_id":"sha256:a2440f6dd7f9352226f0390043a58fcb98c859c28dfd6ba9ad9ca9c04aa541d1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:XLJIGGLDTMJAZNSSSTK4CPDRF4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tropical intersection homology","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Ryota Mikami","submitted_at":"2024-12-30T06:43:11Z","abstract_excerpt":"Numerical equivalence of algebraic cycles is defined abstractly by intersection numbers. Classically, for smooth complex proper toric varieties, the quotients by numerical equivalence with rational coefficients can be described geometrically as singular cohomology. They are also expressed in terms of tropical geometry, tropical cohomology, introduced by Itenberg-Katzarkov-Mikhalkin-Zharkov. This paper aims to generalize this to suitable pairs of smooth proper varieties and divisors by introducing a tropical analog of intersection homology."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.20748","kind":"arxiv","version":4},"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":"2026-05-18T03:09:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w7aI3Erxu9dJPbKBGUVbLD9u/fZXCeegFxbx4qgOiyyV19y1eArZbcWVWZeFGGDFquMaxuwEleiI3hKq/bxUAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T00:04:50.352443Z"},"content_sha256":"ec42a92ec90abd058a4b4ea3bfdc7deea61e2e5fc3cdf24ef7f23e0b0b166158","schema_version":"1.0","event_id":"sha256:ec42a92ec90abd058a4b4ea3bfdc7deea61e2e5fc3cdf24ef7f23e0b0b166158"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XLJIGGLDTMJAZNSSSTK4CPDRF4/bundle.json","state_url":"https://pith.science/pith/XLJIGGLDTMJAZNSSSTK4CPDRF4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XLJIGGLDTMJAZNSSSTK4CPDRF4/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":"2026-06-12T00:04:50Z","links":{"resolver":"https://pith.science/pith/XLJIGGLDTMJAZNSSSTK4CPDRF4","bundle":"https://pith.science/pith/XLJIGGLDTMJAZNSSSTK4CPDRF4/bundle.json","state":"https://pith.science/pith/XLJIGGLDTMJAZNSSSTK4CPDRF4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XLJIGGLDTMJAZNSSSTK4CPDRF4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:XLJIGGLDTMJAZNSSSTK4CPDRF4","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":"b94984b341917763dd48c0ad5e415ac1f86c6190bfc2840e74f4fdb7758b641b","cross_cats_sorted":["math.NT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2024-12-30T06:43:11Z","title_canon_sha256":"e8b21c5c6ad34e38a97be2446684a922bbadadde9254a997e81e10bb568f0e20"},"schema_version":"1.0","source":{"id":"2412.20748","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.20748","created_at":"2026-05-18T03:09:46Z"},{"alias_kind":"arxiv_version","alias_value":"2412.20748v4","created_at":"2026-05-18T03:09:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.20748","created_at":"2026-05-18T03:09:46Z"},{"alias_kind":"pith_short_12","alias_value":"XLJIGGLDTMJA","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"XLJIGGLDTMJAZNSS","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"XLJIGGLD","created_at":"2026-05-18T12:33:37Z"}],"graph_snapshots":[{"event_id":"sha256:ec42a92ec90abd058a4b4ea3bfdc7deea61e2e5fc3cdf24ef7f23e0b0b166158","target":"graph","created_at":"2026-05-18T03:09:46Z","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":"Numerical equivalence of algebraic cycles is defined abstractly by intersection numbers. Classically, for smooth complex proper toric varieties, the quotients by numerical equivalence with rational coefficients can be described geometrically as singular cohomology. They are also expressed in terms of tropical geometry, tropical cohomology, introduced by Itenberg-Katzarkov-Mikhalkin-Zharkov. This paper aims to generalize this to suitable pairs of smooth proper varieties and divisors by introducing a tropical analog of intersection homology.","authors_text":"Ryota Mikami","cross_cats":["math.NT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2024-12-30T06:43:11Z","title":"Tropical intersection homology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.20748","kind":"arxiv","version":4},"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:a2440f6dd7f9352226f0390043a58fcb98c859c28dfd6ba9ad9ca9c04aa541d1","target":"record","created_at":"2026-05-18T03:09:46Z","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":"b94984b341917763dd48c0ad5e415ac1f86c6190bfc2840e74f4fdb7758b641b","cross_cats_sorted":["math.NT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2024-12-30T06:43:11Z","title_canon_sha256":"e8b21c5c6ad34e38a97be2446684a922bbadadde9254a997e81e10bb568f0e20"},"schema_version":"1.0","source":{"id":"2412.20748","kind":"arxiv","version":4}},"canonical_sha256":"bad28319639b120cb65294d5c13c712f35184a0111e46de072a3052ce42d69f7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bad28319639b120cb65294d5c13c712f35184a0111e46de072a3052ce42d69f7","first_computed_at":"2026-05-18T03:09:46.314101Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:09:46.314101Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SSC2iR9OyDLESTfStStqUI4w8v5xnM24M67RgVxQifAHjI2xCIVJnIk+R5fyZs/H/lIcamOE2tUsKyL1sgFfBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:09:46.315975Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.20748","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a2440f6dd7f9352226f0390043a58fcb98c859c28dfd6ba9ad9ca9c04aa541d1","sha256:ec42a92ec90abd058a4b4ea3bfdc7deea61e2e5fc3cdf24ef7f23e0b0b166158"],"state_sha256":"4df83dfd4259048c0064744750e87292f3f6caaa6db67954558c09a643710383"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/tYBXqLXw0hzqJaBhSmDr4MWjGv9jn4mWmuXdjnG27W/MrYljQmBhqt3GCLstaqtZwTVxhSdx5OyE/M0vTStDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T00:04:50.357054Z","bundle_sha256":"6e236804ac5d396d53c648752c2b6784555c17c947b6dbbb38ffcb8166f5d459"}}