{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:PUZPBKQAEKXXEEU7CS5ESWJ233","short_pith_number":"pith:PUZPBKQA","schema_version":"1.0","canonical_sha256":"7d32f0aa0022af72129f14ba49593adecde9a3bf2a5bdeecb379dc961fe15dbf","source":{"kind":"arxiv","id":"1104.3307","version":2},"attestation_state":"computed","paper":{"title":"Irreducible cycles and points in special position in moduli spaces for tropical curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Andreas Gathmann, Franziska Schroeter","submitted_at":"2011-04-17T11:39:29Z","abstract_excerpt":"In the first part of this paper, we discuss the notion of irreducibility of cycles in the moduli spaces of n-marked rational tropical curves. We prove that Psi-classes and vital divisors are irreducible, and that locally irreducible divisors are also globally irreducible for n \\leq 6. In the second part of the paper, we show that the locus of point configurations in (\\R^2)^n in special position for counting rational plane curves (defined in two different ways) can be given the structure a tropical cycle of codimension 1. In addition, we compute explicitly the weights of this cycle."},"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":"1104.3307","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-04-17T11:39:29Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"59b00011f3908395c1f9117157d7c4001d2fdca0ac9bcdaaf933ec588614e70f","abstract_canon_sha256":"d994b18ee8dda14e57ae7fd12e64f1fa194e80d318bd31331f38bc523330c97f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:13:43.828240Z","signature_b64":"wIniawiZMOxD/8mvUH3+ubA1CkgKZU9i+AtvFGUQdrtlXNiSxv7wWe7IS+56rVYwhScTM8/AEkc8v1nzyc4oAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7d32f0aa0022af72129f14ba49593adecde9a3bf2a5bdeecb379dc961fe15dbf","last_reissued_at":"2026-05-18T03:13:43.827668Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:13:43.827668Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Irreducible cycles and points in special position in moduli spaces for tropical curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Andreas Gathmann, Franziska Schroeter","submitted_at":"2011-04-17T11:39:29Z","abstract_excerpt":"In the first part of this paper, we discuss the notion of irreducibility of cycles in the moduli spaces of n-marked rational tropical curves. We prove that Psi-classes and vital divisors are irreducible, and that locally irreducible divisors are also globally irreducible for n \\leq 6. In the second part of the paper, we show that the locus of point configurations in (\\R^2)^n in special position for counting rational plane curves (defined in two different ways) can be given the structure a tropical cycle of codimension 1. In addition, we compute explicitly the weights of this cycle."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.3307","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1104.3307","created_at":"2026-05-18T03:13:43.827765+00:00"},{"alias_kind":"arxiv_version","alias_value":"1104.3307v2","created_at":"2026-05-18T03:13:43.827765+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.3307","created_at":"2026-05-18T03:13:43.827765+00:00"},{"alias_kind":"pith_short_12","alias_value":"PUZPBKQAEKXX","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_16","alias_value":"PUZPBKQAEKXXEEU7","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_8","alias_value":"PUZPBKQA","created_at":"2026-05-18T12:26:39.201973+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PUZPBKQAEKXXEEU7CS5ESWJ233","json":"https://pith.science/pith/PUZPBKQAEKXXEEU7CS5ESWJ233.json","graph_json":"https://pith.science/api/pith-number/PUZPBKQAEKXXEEU7CS5ESWJ233/graph.json","events_json":"https://pith.science/api/pith-number/PUZPBKQAEKXXEEU7CS5ESWJ233/events.json","paper":"https://pith.science/paper/PUZPBKQA"},"agent_actions":{"view_html":"https://pith.science/pith/PUZPBKQAEKXXEEU7CS5ESWJ233","download_json":"https://pith.science/pith/PUZPBKQAEKXXEEU7CS5ESWJ233.json","view_paper":"https://pith.science/paper/PUZPBKQA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1104.3307&json=true","fetch_graph":"https://pith.science/api/pith-number/PUZPBKQAEKXXEEU7CS5ESWJ233/graph.json","fetch_events":"https://pith.science/api/pith-number/PUZPBKQAEKXXEEU7CS5ESWJ233/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PUZPBKQAEKXXEEU7CS5ESWJ233/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PUZPBKQAEKXXEEU7CS5ESWJ233/action/storage_attestation","attest_author":"https://pith.science/pith/PUZPBKQAEKXXEEU7CS5ESWJ233/action/author_attestation","sign_citation":"https://pith.science/pith/PUZPBKQAEKXXEEU7CS5ESWJ233/action/citation_signature","submit_replication":"https://pith.science/pith/PUZPBKQAEKXXEEU7CS5ESWJ233/action/replication_record"}},"created_at":"2026-05-18T03:13:43.827765+00:00","updated_at":"2026-05-18T03:13:43.827765+00:00"}