{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:SHBVN6H534EFHKXFP657INNWJT","short_pith_number":"pith:SHBVN6H5","schema_version":"1.0","canonical_sha256":"91c356f8fddf0853aae57fbbf435b64ce3f7974e43280a970b8dc92ee50eef38","source":{"kind":"arxiv","id":"1302.2380","version":2},"attestation_state":"computed","paper":{"title":"Rigidity of thin disk configurations, via fixed-point index","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.MG","authors_text":"Andrey M. Mishchenko","submitted_at":"2013-02-11T00:40:46Z","abstract_excerpt":"We prove some rigidity theorems for configurations of closed disks. First, fix two collections $\\mathcal{C}$ and $\\tilde{\\mathcal{C}}$ of closed disks in the Riemann sphere $\\hat{\\mathbb{C}}$, sharing a contact graph which (mostly-)triangulates $\\hat{\\mathbb{C}}$, so that for all corresponding pairs of intersecting disks $D_i, D_j \\in \\mathcal{C}$ and $\\tilde D_i, \\tilde D_j \\in \\tilde{\\mathcal{C}}$ we have that the overlap angle between $D_i$ and $D_j$ agrees with that between $\\tilde D_i$ and $\\tilde D_j$. We require the extra condition that the collections are \"thin\", meaning that no pair o"},"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":"1302.2380","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.MG","submitted_at":"2013-02-11T00:40:46Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"3730a630a21b406cc29cc2be4488236584f1cf6a2703398dc77c74dd9a960484","abstract_canon_sha256":"be9f469ddd528f971fc0b223087d327b12e81bda9c36e931079d29bd22ea90bf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:55.697092Z","signature_b64":"rg9ucfIz3r6Rd0GQJdP7cxzoQwgQoOatj+1INd9ZbVxRJ0W21RjgZJEGhVnQ01NHknYO+U0ou49lCGOhNPVzAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"91c356f8fddf0853aae57fbbf435b64ce3f7974e43280a970b8dc92ee50eef38","last_reissued_at":"2026-05-18T01:30:55.696553Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:55.696553Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rigidity of thin disk configurations, via fixed-point index","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.MG","authors_text":"Andrey M. Mishchenko","submitted_at":"2013-02-11T00:40:46Z","abstract_excerpt":"We prove some rigidity theorems for configurations of closed disks. First, fix two collections $\\mathcal{C}$ and $\\tilde{\\mathcal{C}}$ of closed disks in the Riemann sphere $\\hat{\\mathbb{C}}$, sharing a contact graph which (mostly-)triangulates $\\hat{\\mathbb{C}}$, so that for all corresponding pairs of intersecting disks $D_i, D_j \\in \\mathcal{C}$ and $\\tilde D_i, \\tilde D_j \\in \\tilde{\\mathcal{C}}$ we have that the overlap angle between $D_i$ and $D_j$ agrees with that between $\\tilde D_i$ and $\\tilde D_j$. We require the extra condition that the collections are \"thin\", meaning that no pair o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.2380","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":"1302.2380","created_at":"2026-05-18T01:30:55.696616+00:00"},{"alias_kind":"arxiv_version","alias_value":"1302.2380v2","created_at":"2026-05-18T01:30:55.696616+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.2380","created_at":"2026-05-18T01:30:55.696616+00:00"},{"alias_kind":"pith_short_12","alias_value":"SHBVN6H534EF","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_16","alias_value":"SHBVN6H534EFHKXF","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_8","alias_value":"SHBVN6H5","created_at":"2026-05-18T12:27:59.945178+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/SHBVN6H534EFHKXFP657INNWJT","json":"https://pith.science/pith/SHBVN6H534EFHKXFP657INNWJT.json","graph_json":"https://pith.science/api/pith-number/SHBVN6H534EFHKXFP657INNWJT/graph.json","events_json":"https://pith.science/api/pith-number/SHBVN6H534EFHKXFP657INNWJT/events.json","paper":"https://pith.science/paper/SHBVN6H5"},"agent_actions":{"view_html":"https://pith.science/pith/SHBVN6H534EFHKXFP657INNWJT","download_json":"https://pith.science/pith/SHBVN6H534EFHKXFP657INNWJT.json","view_paper":"https://pith.science/paper/SHBVN6H5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1302.2380&json=true","fetch_graph":"https://pith.science/api/pith-number/SHBVN6H534EFHKXFP657INNWJT/graph.json","fetch_events":"https://pith.science/api/pith-number/SHBVN6H534EFHKXFP657INNWJT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SHBVN6H534EFHKXFP657INNWJT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SHBVN6H534EFHKXFP657INNWJT/action/storage_attestation","attest_author":"https://pith.science/pith/SHBVN6H534EFHKXFP657INNWJT/action/author_attestation","sign_citation":"https://pith.science/pith/SHBVN6H534EFHKXFP657INNWJT/action/citation_signature","submit_replication":"https://pith.science/pith/SHBVN6H534EFHKXFP657INNWJT/action/replication_record"}},"created_at":"2026-05-18T01:30:55.696616+00:00","updated_at":"2026-05-18T01:30:55.696616+00:00"}