{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:RNLIHAOV4TRDWM5AHRXJKG4XSH","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":"fa0d20144bf42d464adaa5081ad30b262f0735a0a489315deb286ee88c8bad19","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2011-10-28T21:48:49Z","title_canon_sha256":"17d53772403eb21ebe83362cfd26c7104bc5a1fa3b7146c561caf422fa6ab195"},"schema_version":"1.0","source":{"id":"1110.6473","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.6473","created_at":"2026-05-18T01:33:49Z"},{"alias_kind":"arxiv_version","alias_value":"1110.6473v2","created_at":"2026-05-18T01:33:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.6473","created_at":"2026-05-18T01:33:49Z"},{"alias_kind":"pith_short_12","alias_value":"RNLIHAOV4TRD","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RNLIHAOV4TRDWM5A","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RNLIHAOV","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:cd61882fbb9dff6c43b5bf19fafc67ecb1ef187455935e7af80ae9d4cbc93709","target":"graph","created_at":"2026-05-18T01:33:49Z","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 show that any combinatorial triangulation on n vertices can be transformed into a 4-connected one using at most floor((3n - 9)/5) edge flips. We also give an example of an infinite family of triangulations that requires this many flips to be made 4-connected, showing that our bound is tight. In addition, for n >= 19, we improve the upper bound on the number of flips required to transform any 4-connected triangulation into the canonical triangulation (the triangulation with two dominant vertices), matching the known lower bound of 2n - 15. Our results imply a new upper bound on the diameter ","authors_text":"Andr\\'e van Renssen, Dana Jansens, Maria Saumell, Prosenjit Bose, Sander Verdonschot","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2011-10-28T21:48:49Z","title":"Making triangulations 4-connected using flips"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6473","kind":"arxiv","version":2},"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":"sha256:9ec0caaf2b30ebccec191942ceacccda1a48d38d503853005ba0ebd8c7d26ae7","target":"record","created_at":"2026-05-18T01:33:49Z","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":"fa0d20144bf42d464adaa5081ad30b262f0735a0a489315deb286ee88c8bad19","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2011-10-28T21:48:49Z","title_canon_sha256":"17d53772403eb21ebe83362cfd26c7104bc5a1fa3b7146c561caf422fa6ab195"},"schema_version":"1.0","source":{"id":"1110.6473","kind":"arxiv","version":2}},"canonical_sha256":"8b568381d5e4e23b33a03c6e951b9791d3bd88acb00bac02c2563e9cae4fda4f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8b568381d5e4e23b33a03c6e951b9791d3bd88acb00bac02c2563e9cae4fda4f","first_computed_at":"2026-05-18T01:33:49.481506Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:49.481506Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+rhSXxfuPaXbzl8NS4l7LS6EX2ItnpR2K56HZ/rqvg02lCPsV3G9VwYF9RKIC3IvK+8a+Wr8iVAxtkBS3YxkDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:49.482035Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.6473","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9ec0caaf2b30ebccec191942ceacccda1a48d38d503853005ba0ebd8c7d26ae7","sha256:cd61882fbb9dff6c43b5bf19fafc67ecb1ef187455935e7af80ae9d4cbc93709"],"state_sha256":"334ea529f7fb6e52edc39d402ae52ff8913e44143a9c71aa01d69a4196796808"}