{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:OGRKTDJP47HGNNRGZWOITNOK2C","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":"ac928ac9be89dfb37b989e8fef4f5f3e0e16cc9cc5651763722b5f91d7cfb38b","cross_cats_sorted":[],"license":"","primary_cat":"math.AP","submitted_at":"2006-12-22T04:16:47Z","title_canon_sha256":"d82a7dfe7e59fce07cfe627ad4e6f359f0703c064bec98c2a031c0e5bd724fb9"},"schema_version":"1.0","source":{"id":"math/0612680","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0612680","created_at":"2026-05-18T03:03:22Z"},{"alias_kind":"arxiv_version","alias_value":"math/0612680v1","created_at":"2026-05-18T03:03:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0612680","created_at":"2026-05-18T03:03:22Z"},{"alias_kind":"pith_short_12","alias_value":"OGRKTDJP47HG","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"OGRKTDJP47HGNNRG","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"OGRKTDJP","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:fec5ff4c6055a2e896fa68c5ff0982fffde26a03ace5f8d34fa9fc74836344be","target":"graph","created_at":"2026-05-18T03:03:22Z","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"},"paper":{"abstract_excerpt":"We establish two global subellipticity properties of positive symmetric second-order partial differential operators on $L_2(\\Ri^d)$. First, if $m \\in \\Ni$ then we consider operators $H_0$ with coefficients in $W^{m+1,\\infty}(\\Ri^d)$ and domain $D(H_0)=W^{\\infty,2}(\\Ri^d)$ satisfying the subellipticity property \\[ c (\\phi, (I+H_0)\\phi)\\geq \\|\\Delta^{\\gamma/2} \\phi\\|_2^2 \\] for some $c>0$ and $\\gamma\\in<0,1]$, uniformly for all $\\phi\\in W^{\\infty,2}(\\Ri^d)$, where $\\Delta$ denotes the usual Laplacian. Then we prove that $D(H^\\alpha) \\subseteq D(\\Delta^{\\alpha \\gamma})$ for all $\\alpha \\in [0,2^{","authors_text":"A.F.M. ter Elst, Derek W. Robinson","cross_cats":[],"headline":"","license":"","primary_cat":"math.AP","submitted_at":"2006-12-22T04:16:47Z","title":"Uniform subellipticity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0612680","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:d8fa5a6cad0b21e2956ba85112fec8579192d5790f07bd2f0d24a9eddddbffc9","target":"record","created_at":"2026-05-18T03:03:22Z","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":"ac928ac9be89dfb37b989e8fef4f5f3e0e16cc9cc5651763722b5f91d7cfb38b","cross_cats_sorted":[],"license":"","primary_cat":"math.AP","submitted_at":"2006-12-22T04:16:47Z","title_canon_sha256":"d82a7dfe7e59fce07cfe627ad4e6f359f0703c064bec98c2a031c0e5bd724fb9"},"schema_version":"1.0","source":{"id":"math/0612680","kind":"arxiv","version":1}},"canonical_sha256":"71a2a98d2fe7ce66b626cd9c89b5cad09b10df4d4be0eda371a8e17047540a90","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"71a2a98d2fe7ce66b626cd9c89b5cad09b10df4d4be0eda371a8e17047540a90","first_computed_at":"2026-05-18T03:03:22.952461Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:03:22.952461Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vY17xSi2w+fiKMcGsqBEHTvmeT7zArUq/i4upeYvoyBI100eThYvjUeKO8SsH2JTfWmDhtP4SjcUNBkDt3/GDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:03:22.953117Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0612680","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d8fa5a6cad0b21e2956ba85112fec8579192d5790f07bd2f0d24a9eddddbffc9","sha256:fec5ff4c6055a2e896fa68c5ff0982fffde26a03ace5f8d34fa9fc74836344be"],"state_sha256":"5b39a30cc9fd8b12cd356a76d63df085c95c7107b93786f68cbeb34763284eff"}