{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:A6KZOCCVV5I2I7KMUUNFPYXFS3","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":"41a5188e82209ec53aaf61fc8b1b9a33ff033d7d556f29f667e61c726715ae89","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2017-03-17T07:39:55Z","title_canon_sha256":"c2a08d6429b59d811a34f2b14e5ecacf2b9c091d62f00b168581db73cb2d4539"},"schema_version":"1.0","source":{"id":"1703.05914","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.05914","created_at":"2026-05-18T00:48:31Z"},{"alias_kind":"arxiv_version","alias_value":"1703.05914v1","created_at":"2026-05-18T00:48:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.05914","created_at":"2026-05-18T00:48:31Z"},{"alias_kind":"pith_short_12","alias_value":"A6KZOCCVV5I2","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"A6KZOCCVV5I2I7KM","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"A6KZOCCV","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:21829861474c1096e254197b03fcf913b60d8258374895a7eead2fd16fe413e7","target":"graph","created_at":"2026-05-18T00:48:31Z","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 describe non-locally connected planar continua via the concepts of fiber and numerical scale.\n  Given a continuum $X\\subset\\mathbb{C}$ and $x\\in\\partial X$, we show that the set of points $y\\in \\partial X$ that cannot be separated from $x$ by any finite set $C\\subset \\partial X$ is a continuum. This continuum is called the {\\em modified fiber} $F_x^*$ of $X$ at $x$. If $x\\in X^o$, we set $F^*_x=\\{x\\}$. For $x\\in X$, we show that $F_x^*=\\{x\\}$ implies that $X$ is locally connected at $x$. We also give a concrete planar continuum $X$, which is locally connected at a point $x\\in X$ while the f","authors_text":"Beno\\^it Loridant, Jun Luo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2017-03-17T07:39:55Z","title":"Fibers and local connectedness of planar continua"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.05914","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:c3b8a0cf3667f8f6463dfe7570c5e0cb61fd5b036cda23c82afdfb8487d81dbe","target":"record","created_at":"2026-05-18T00:48:31Z","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":"41a5188e82209ec53aaf61fc8b1b9a33ff033d7d556f29f667e61c726715ae89","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2017-03-17T07:39:55Z","title_canon_sha256":"c2a08d6429b59d811a34f2b14e5ecacf2b9c091d62f00b168581db73cb2d4539"},"schema_version":"1.0","source":{"id":"1703.05914","kind":"arxiv","version":1}},"canonical_sha256":"0795970855af51a47d4ca51a57e2e596f6ab3154a2566b33596dab7260d4a6d4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0795970855af51a47d4ca51a57e2e596f6ab3154a2566b33596dab7260d4a6d4","first_computed_at":"2026-05-18T00:48:31.756217Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:31.756217Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yZ+OLVE9m7bX0gRnVEhKVvS9nhzTFT6R/VjZdgns5lnx4Hoznj77/nFuhMKeK+g59GMblwXrjtRvCefz41GoBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:31.756623Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.05914","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c3b8a0cf3667f8f6463dfe7570c5e0cb61fd5b036cda23c82afdfb8487d81dbe","sha256:21829861474c1096e254197b03fcf913b60d8258374895a7eead2fd16fe413e7"],"state_sha256":"225827dd6818aa31ffff5ad23b66c50f23ba58680fd216a70dd3c19d79c9a63b"}