{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:IIW3KXCK25THGPS6QM47P3KC63","short_pith_number":"pith:IIW3KXCK","schema_version":"1.0","canonical_sha256":"422db55c4ad766733e5e8339f7ed42f6e9eb897f723e9db5897c1afe524f5aeb","source":{"kind":"arxiv","id":"2607.05826","version":1},"attestation_state":"computed","paper":{"title":"Rigidity of maps between configuration spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.GR"],"primary_cat":"math.GT","authors_text":"Daniel Minahan, Jeroen Schillewaert, Peter Huxford, Rodrigo de Pool","submitted_at":"2026-07-07T04:41:00Z","abstract_excerpt":"Let $n\\geq5$ and $m\\geq3$. Let $\\Phi\\colon\\mathrm{B}_n\\to\\mathrm{B}_m$ be a homomorphism of braid groups. We prove that if the image of $\\Phi$ is irreducible and not cyclic, then $m=n$ and $\\Phi$ agrees with an automorphism modulo the center $Z(\\mathrm{B}_m)$. This resolves in the affirmative a conjecture of Chen, Kordek, and Margalit. It also provides a partial resolution to a problem on the K3 problem list. As a consequence, we prove that every holomorphic map $\\mathrm{UConf}_n(\\mathbb{C})\\to\\mathrm{UConf}_m(\\mathbb{C})$ for $n\\geq5$ and $m\\geq3$ is affine equivalent to either a constant map"},"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":"2607.05826","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2026-07-07T04:41:00Z","cross_cats_sorted":["math.AG","math.GR"],"title_canon_sha256":"57af42ba7e236f28778464c97322234750b221275d4785bdca4353567ec14018","abstract_canon_sha256":"814bb51f5d5c9a13ec95fa22412395732ebd59b40ff6f3002f6582cf2e9cd29e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-08T01:18:47.204710Z","signature_b64":"RQ0maiSCLS2YsnEKTKW1bkUN4n3hczAjdJ8DZSfjJprf1q4N6qpqVYHJS4Bl6/gJtT3tKMclUIgVl7i7Xdg6AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"422db55c4ad766733e5e8339f7ed42f6e9eb897f723e9db5897c1afe524f5aeb","last_reissued_at":"2026-07-08T01:18:47.204215Z","signature_status":"signed_v1","first_computed_at":"2026-07-08T01:18:47.204215Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rigidity of maps between configuration spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.GR"],"primary_cat":"math.GT","authors_text":"Daniel Minahan, Jeroen Schillewaert, Peter Huxford, Rodrigo de Pool","submitted_at":"2026-07-07T04:41:00Z","abstract_excerpt":"Let $n\\geq5$ and $m\\geq3$. Let $\\Phi\\colon\\mathrm{B}_n\\to\\mathrm{B}_m$ be a homomorphism of braid groups. We prove that if the image of $\\Phi$ is irreducible and not cyclic, then $m=n$ and $\\Phi$ agrees with an automorphism modulo the center $Z(\\mathrm{B}_m)$. This resolves in the affirmative a conjecture of Chen, Kordek, and Margalit. It also provides a partial resolution to a problem on the K3 problem list. As a consequence, we prove that every holomorphic map $\\mathrm{UConf}_n(\\mathbb{C})\\to\\mathrm{UConf}_m(\\mathbb{C})$ for $n\\geq5$ and $m\\geq3$ is affine equivalent to either a constant map"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.05826","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.05826/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2607.05826","created_at":"2026-07-08T01:18:47.204298+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.05826v1","created_at":"2026-07-08T01:18:47.204298+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.05826","created_at":"2026-07-08T01:18:47.204298+00:00"},{"alias_kind":"pith_short_12","alias_value":"IIW3KXCK25TH","created_at":"2026-07-08T01:18:47.204298+00:00"},{"alias_kind":"pith_short_16","alias_value":"IIW3KXCK25THGPS6","created_at":"2026-07-08T01:18:47.204298+00:00"},{"alias_kind":"pith_short_8","alias_value":"IIW3KXCK","created_at":"2026-07-08T01:18:47.204298+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/IIW3KXCK25THGPS6QM47P3KC63","json":"https://pith.science/pith/IIW3KXCK25THGPS6QM47P3KC63.json","graph_json":"https://pith.science/api/pith-number/IIW3KXCK25THGPS6QM47P3KC63/graph.json","events_json":"https://pith.science/api/pith-number/IIW3KXCK25THGPS6QM47P3KC63/events.json","paper":"https://pith.science/paper/IIW3KXCK"},"agent_actions":{"view_html":"https://pith.science/pith/IIW3KXCK25THGPS6QM47P3KC63","download_json":"https://pith.science/pith/IIW3KXCK25THGPS6QM47P3KC63.json","view_paper":"https://pith.science/paper/IIW3KXCK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.05826&json=true","fetch_graph":"https://pith.science/api/pith-number/IIW3KXCK25THGPS6QM47P3KC63/graph.json","fetch_events":"https://pith.science/api/pith-number/IIW3KXCK25THGPS6QM47P3KC63/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IIW3KXCK25THGPS6QM47P3KC63/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IIW3KXCK25THGPS6QM47P3KC63/action/storage_attestation","attest_author":"https://pith.science/pith/IIW3KXCK25THGPS6QM47P3KC63/action/author_attestation","sign_citation":"https://pith.science/pith/IIW3KXCK25THGPS6QM47P3KC63/action/citation_signature","submit_replication":"https://pith.science/pith/IIW3KXCK25THGPS6QM47P3KC63/action/replication_record"}},"created_at":"2026-07-08T01:18:47.204298+00:00","updated_at":"2026-07-08T01:18:47.204298+00:00"}