{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:6ALYQCFTDAOZQBEQGS6UUGRY2Q","merge_version":"pith-open-graph-merge-v1","event_count":3,"valid_event_count":3,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"459ccf2d840bf16745dfa3825b499668aafc0fca502c039e2339bd317a7a099d","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-08-09T07:10:33Z","title_canon_sha256":"ade1450f75738180476eb0c44d9dfd5b229da76ec6cf5241ecbc09c519a541f0"},"schema_version":"1.0","source":{"id":"2608.08533","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.08533","created_at":"2026-08-11T01:22:53Z"},{"alias_kind":"arxiv_version","alias_value":"2608.08533v1","created_at":"2026-08-11T01:22:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.08533","created_at":"2026-08-11T01:22:53Z"},{"alias_kind":"pith_short_12","alias_value":"6ALYQCFTDAOZ","created_at":"2026-08-11T01:22:53Z"},{"alias_kind":"pith_short_16","alias_value":"6ALYQCFTDAOZQBEQ","created_at":"2026-08-11T01:22:53Z"},{"alias_kind":"pith_short_8","alias_value":"6ALYQCFT","created_at":"2026-08-11T01:22:53Z"}],"graph_snapshots":[{"event_id":"sha256:71cb0a1e2fb5c825c97d34afe55e6ac2ec0935d4ea912e0c88d2ac720d9d6e2b","target":"graph","created_at":"2026-08-11T01:22:53Z","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/2608.08533/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that the Feldman--Ilmanen--Knopf (FIK) blowdown singularity has a nonempty open nonlinear formation basin in the full space of smooth Riemannian metrics and, on a smaller neighborhood, local marked first-order asymptotic moduli. Given a closed connected oriented Riemannian four-manifold, an implantation point, and a positive time bound, its oriented blow-up admits a relatively $C^{2,\\alpha}$-open set of smooth metrics whose Ricci flows form, before that time, a localized FIK singularity with global Type-I curvature control. No symmetry, K\\\"ahler condition, or finite-dimensional tuning","authors_text":"Henry Shin","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-08-09T07:10:33Z","title":"Open full-metric formation and local marked first-order asymptotic moduli of FIK blowdown singularities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.08533","kind":"arxiv","version":1},"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:dcf7060ac9a8f1afb0c844380fc5ff208d822a0184a79e9d4961b23bdfc293c1","target":"record","created_at":"2026-08-11T01:22:53Z","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":"459ccf2d840bf16745dfa3825b499668aafc0fca502c039e2339bd317a7a099d","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-08-09T07:10:33Z","title_canon_sha256":"ade1450f75738180476eb0c44d9dfd5b229da76ec6cf5241ecbc09c519a541f0"},"schema_version":"1.0","source":{"id":"2608.08533","kind":"arxiv","version":1}},"canonical_sha256":"f0178808b3181d98049034bd4a1a38d4302f35ec4b9b37a5538c08fd97417548","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f0178808b3181d98049034bd4a1a38d4302f35ec4b9b37a5538c08fd97417548","first_computed_at":"2026-08-11T01:22:53.557481Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-11T01:22:53.557481Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GTyDKhBmwJPUTosx/5+aUdXVT/6XRcnfx6R2NuQR2y8VcpT0Cp7uCREYqpt9ejevs2RTKQ8VXdPWc9tNTTI+AA==","signature_status":"signed_v1","signed_at":"2026-08-11T01:22:53.559900Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.08533","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dcf7060ac9a8f1afb0c844380fc5ff208d822a0184a79e9d4961b23bdfc293c1","sha256:71cb0a1e2fb5c825c97d34afe55e6ac2ec0935d4ea912e0c88d2ac720d9d6e2b","sha256:e286f1b888648b927da3af2a7cf4b26dc745d4a37cacb665b540cdf19d4f3096"],"state_sha256":"ce5de63d99ff80bda118bcefd93f6c3e75d5925b7ca741ec7bfb87845f5353b6"}