{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:TMGYV5DJOL7Q7ABZFNQGJTLMGK","short_pith_number":"pith:TMGYV5DJ","schema_version":"1.0","canonical_sha256":"9b0d8af46972ff0f80392b6064cd6c32b1cbe205f35665769b7672d397ff8d6c","source":{"kind":"arxiv","id":"1506.07407","version":1},"attestation_state":"computed","paper":{"title":"Tropical surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Kristin Shaw","submitted_at":"2015-06-24T15:03:17Z","abstract_excerpt":"We present tools and definitions to study abstract tropical manifolds in dimension 2, which we call simply tropical surfaces. This includes explicit descriptions of intersection numbers of 1-cycles, normal bundles to some curves and tropical Chern cycles and numbers. We provide a new method for constructing tropical surfaces, called the tropical sum, similar to the fiber sum of usual manifolds. We prove a tropical adjunction formula for curves in compact tropical surfaces satisfying a local condition, a partial Castelnuovo-Enriques criterion for contracting (-1)-curves, and also invariance of "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1506.07407","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-06-24T15:03:17Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"d52289627c42d4e7dd4b28060a389a1aae2effb31a2b830e3ff776b091397e90","abstract_canon_sha256":"445bae88d09119be87935cd4ba0eefc0333c04debbfdfd998626988031378f52"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:39:54.138602Z","signature_b64":"GqrYvLib0PHQT2jJTx+aX1E390c9MPkKJEHuFHAOqrpoxqNyU9JHSJN61VCGGjcahRZ0eEzR53SIfZ5cMIBQAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b0d8af46972ff0f80392b6064cd6c32b1cbe205f35665769b7672d397ff8d6c","last_reissued_at":"2026-05-18T01:39:54.137923Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:39:54.137923Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tropical surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Kristin Shaw","submitted_at":"2015-06-24T15:03:17Z","abstract_excerpt":"We present tools and definitions to study abstract tropical manifolds in dimension 2, which we call simply tropical surfaces. This includes explicit descriptions of intersection numbers of 1-cycles, normal bundles to some curves and tropical Chern cycles and numbers. We provide a new method for constructing tropical surfaces, called the tropical sum, similar to the fiber sum of usual manifolds. We prove a tropical adjunction formula for curves in compact tropical surfaces satisfying a local condition, a partial Castelnuovo-Enriques criterion for contracting (-1)-curves, and also invariance of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.07407","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1506.07407","created_at":"2026-05-18T01:39:54.138027+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.07407v1","created_at":"2026-05-18T01:39:54.138027+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.07407","created_at":"2026-05-18T01:39:54.138027+00:00"},{"alias_kind":"pith_short_12","alias_value":"TMGYV5DJOL7Q","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_16","alias_value":"TMGYV5DJOL7Q7ABZ","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_8","alias_value":"TMGYV5DJ","created_at":"2026-05-18T12:29:42.218222+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1906.09245","citing_title":"A sheaf-theoretic approach to tropical homology","ref_index":11,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TMGYV5DJOL7Q7ABZFNQGJTLMGK","json":"https://pith.science/pith/TMGYV5DJOL7Q7ABZFNQGJTLMGK.json","graph_json":"https://pith.science/api/pith-number/TMGYV5DJOL7Q7ABZFNQGJTLMGK/graph.json","events_json":"https://pith.science/api/pith-number/TMGYV5DJOL7Q7ABZFNQGJTLMGK/events.json","paper":"https://pith.science/paper/TMGYV5DJ"},"agent_actions":{"view_html":"https://pith.science/pith/TMGYV5DJOL7Q7ABZFNQGJTLMGK","download_json":"https://pith.science/pith/TMGYV5DJOL7Q7ABZFNQGJTLMGK.json","view_paper":"https://pith.science/paper/TMGYV5DJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.07407&json=true","fetch_graph":"https://pith.science/api/pith-number/TMGYV5DJOL7Q7ABZFNQGJTLMGK/graph.json","fetch_events":"https://pith.science/api/pith-number/TMGYV5DJOL7Q7ABZFNQGJTLMGK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TMGYV5DJOL7Q7ABZFNQGJTLMGK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TMGYV5DJOL7Q7ABZFNQGJTLMGK/action/storage_attestation","attest_author":"https://pith.science/pith/TMGYV5DJOL7Q7ABZFNQGJTLMGK/action/author_attestation","sign_citation":"https://pith.science/pith/TMGYV5DJOL7Q7ABZFNQGJTLMGK/action/citation_signature","submit_replication":"https://pith.science/pith/TMGYV5DJOL7Q7ABZFNQGJTLMGK/action/replication_record"}},"created_at":"2026-05-18T01:39:54.138027+00:00","updated_at":"2026-05-18T01:39:54.138027+00:00"}