{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:P45UK3SJCOF4QW6HEUBGTWCCUM","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"9b664260f77edbfc8c71387ae23fe08a44bde8de2fd499e876fd098fe6293e74","cross_cats_sorted":["math.CO","math.GN","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-12-05T03:23:58Z","title_canon_sha256":"afee1bfaf879c73e1abf022ead694de8d70be8c016157bcded35159ca76e76a8"},"schema_version":"1.0","source":{"id":"2412.03846","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.03846","created_at":"2026-07-05T10:02:55Z"},{"alias_kind":"arxiv_version","alias_value":"2412.03846v3","created_at":"2026-07-05T10:02:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.03846","created_at":"2026-07-05T10:02:55Z"},{"alias_kind":"pith_short_12","alias_value":"P45UK3SJCOF4","created_at":"2026-07-05T10:02:55Z"},{"alias_kind":"pith_short_16","alias_value":"P45UK3SJCOF4QW6H","created_at":"2026-07-05T10:02:55Z"},{"alias_kind":"pith_short_8","alias_value":"P45UK3SJ","created_at":"2026-07-05T10:02:55Z"}],"graph_snapshots":[{"event_id":"sha256:133f0aaa9d29c1446f87566ec2c6e5a48b3daad332d674ed54c6a9a78b6503ed","target":"graph","created_at":"2026-07-05T10:02:55Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2412.03846/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"As a topic of mathematics, \"arrangements\", systems of hyperplanes, circles, and general (regular) submanifolds, attract us strongly. We present a natural elementary study of arrangements of circles. It is also a kind of new studies. Our study is closely related to geometry and singularity theory of Morse(-Bott) functions. Regions surrounded by circles are regarded as images of real algebraic maps and composing them with projections gives Morse-Bott functions: this observation is natural, and surprisingly, recently presented first, by the author. We present a systematic way of constructing such","authors_text":"Naoki Kitazawa","cross_cats":["math.CO","math.GN","math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-12-05T03:23:58Z","title":"Arrangements of small circles for Morse-Bott functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.03846","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:356daeb0496729814b71bc702f566aed92b8c477b1f9ed310b95f5e85ed68e00","target":"record","created_at":"2026-07-05T10:02:55Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"9b664260f77edbfc8c71387ae23fe08a44bde8de2fd499e876fd098fe6293e74","cross_cats_sorted":["math.CO","math.GN","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-12-05T03:23:58Z","title_canon_sha256":"afee1bfaf879c73e1abf022ead694de8d70be8c016157bcded35159ca76e76a8"},"schema_version":"1.0","source":{"id":"2412.03846","kind":"arxiv","version":3}},"canonical_sha256":"7f3b456e49138bc85bc7250269d842a31cab95bc8000391d217bc967f18d3f48","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f3b456e49138bc85bc7250269d842a31cab95bc8000391d217bc967f18d3f48","first_computed_at":"2026-07-05T10:02:55.643545Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:02:55.643545Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NB6O0Ih9IA25GkWGLILqT6OI4fmkrnkISMqHIpCHq3vpMUPbCJcFPmOichiXF96MIt14/u49OC4yzFDwKfSWAA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:02:55.643956Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.03846","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:356daeb0496729814b71bc702f566aed92b8c477b1f9ed310b95f5e85ed68e00","sha256:133f0aaa9d29c1446f87566ec2c6e5a48b3daad332d674ed54c6a9a78b6503ed"],"state_sha256":"31f929a1221bcae83865f7bec48367593c3f7846ccadaefb85644ff6f849291b"}