{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:5CIJTNFVYHYMTJDX7X6B45NERW","short_pith_number":"pith:5CIJTNFV","schema_version":"1.0","canonical_sha256":"e89099b4b5c1f0c9a477fdfc1e75a48da0ad4c6f58a54fb3252bd985fcdb5a90","source":{"kind":"arxiv","id":"1604.08917","version":1},"attestation_state":"computed","paper":{"title":"A compactification of the moduli space of self-maps of $\\mathbb{CP}^1$ using stable maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Johannes Schmitt","submitted_at":"2016-04-29T17:10:44Z","abstract_excerpt":"We present a new compactification $M(d,n)$ of the moduli space of self-maps of $\\mathbb{CP}^1$ of degree $d$ with $n$ markings. It is constructed via GIT from the stable maps moduli space $\\ ar M_{0,n}(\\mathbb{CP}^1 \\times \\mathbb{CP}^1, (1,d))$. We show that it is the coarse moduli space of a smooth Deligne-Mumford stack and we compute its rational Picard group. Using the recursive boundary structure inherited from the stable maps space, we give an explicit algorithm for computing top-intersection numbers of divisors on $M(d,n)$. We also study the $m$-fold iteration map $M(d,n) \\dashrightarro"},"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":"1604.08917","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-04-29T17:10:44Z","cross_cats_sorted":[],"title_canon_sha256":"5262fde08932dd94f0b02a38de09268b68c0f1337948a0147c560777e0ccdc5a","abstract_canon_sha256":"6d6f086f44d3237621a006222a434fde4bcaa886da2bcd0f2c5734c59347df6e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:01.430563Z","signature_b64":"BVkehyGleifDRgrWmDbsm6SiwFqiA48bEvdTsCEoLPGCbzgMow2xHK3ncIRZcRPCIL0hVYaB/uTGsxplLb9pDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e89099b4b5c1f0c9a477fdfc1e75a48da0ad4c6f58a54fb3252bd985fcdb5a90","last_reissued_at":"2026-05-18T01:16:01.429829Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:01.429829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A compactification of the moduli space of self-maps of $\\mathbb{CP}^1$ using stable maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Johannes Schmitt","submitted_at":"2016-04-29T17:10:44Z","abstract_excerpt":"We present a new compactification $M(d,n)$ of the moduli space of self-maps of $\\mathbb{CP}^1$ of degree $d$ with $n$ markings. It is constructed via GIT from the stable maps moduli space $\\ ar M_{0,n}(\\mathbb{CP}^1 \\times \\mathbb{CP}^1, (1,d))$. We show that it is the coarse moduli space of a smooth Deligne-Mumford stack and we compute its rational Picard group. Using the recursive boundary structure inherited from the stable maps space, we give an explicit algorithm for computing top-intersection numbers of divisors on $M(d,n)$. We also study the $m$-fold iteration map $M(d,n) \\dashrightarro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.08917","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":"1604.08917","created_at":"2026-05-18T01:16:01.429946+00:00"},{"alias_kind":"arxiv_version","alias_value":"1604.08917v1","created_at":"2026-05-18T01:16:01.429946+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.08917","created_at":"2026-05-18T01:16:01.429946+00:00"},{"alias_kind":"pith_short_12","alias_value":"5CIJTNFVYHYM","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_16","alias_value":"5CIJTNFVYHYMTJDX","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_8","alias_value":"5CIJTNFV","created_at":"2026-05-18T12:30:01.593930+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/5CIJTNFVYHYMTJDX7X6B45NERW","json":"https://pith.science/pith/5CIJTNFVYHYMTJDX7X6B45NERW.json","graph_json":"https://pith.science/api/pith-number/5CIJTNFVYHYMTJDX7X6B45NERW/graph.json","events_json":"https://pith.science/api/pith-number/5CIJTNFVYHYMTJDX7X6B45NERW/events.json","paper":"https://pith.science/paper/5CIJTNFV"},"agent_actions":{"view_html":"https://pith.science/pith/5CIJTNFVYHYMTJDX7X6B45NERW","download_json":"https://pith.science/pith/5CIJTNFVYHYMTJDX7X6B45NERW.json","view_paper":"https://pith.science/paper/5CIJTNFV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1604.08917&json=true","fetch_graph":"https://pith.science/api/pith-number/5CIJTNFVYHYMTJDX7X6B45NERW/graph.json","fetch_events":"https://pith.science/api/pith-number/5CIJTNFVYHYMTJDX7X6B45NERW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5CIJTNFVYHYMTJDX7X6B45NERW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5CIJTNFVYHYMTJDX7X6B45NERW/action/storage_attestation","attest_author":"https://pith.science/pith/5CIJTNFVYHYMTJDX7X6B45NERW/action/author_attestation","sign_citation":"https://pith.science/pith/5CIJTNFVYHYMTJDX7X6B45NERW/action/citation_signature","submit_replication":"https://pith.science/pith/5CIJTNFVYHYMTJDX7X6B45NERW/action/replication_record"}},"created_at":"2026-05-18T01:16:01.429946+00:00","updated_at":"2026-05-18T01:16:01.429946+00:00"}