{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:2W66AUTL2WTHHEMSEST6LW6IKX","short_pith_number":"pith:2W66AUTL","schema_version":"1.0","canonical_sha256":"d5bde0526bd5a673919224a7e5dbc855f2affca8b46835b164b67ed08842cdf7","source":{"kind":"arxiv","id":"1411.6776","version":1},"attestation_state":"computed","paper":{"title":"A numerical scale for non locally connected planar continua","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Beno\\^it Loridant, Jun Luo, Timo Jolivet","submitted_at":"2014-11-25T09:14:12Z","abstract_excerpt":"We introduce a numerical scale to quantify to which extent a planar continuum is not locally connected. For a locally connected continuum, the numerical scale is zero; for a continuum like the topologist's sine curve, the scale is one; for an indecomposable continuum, it is infinite. Among others, we shall pose a new problem that may be of some interest: can we estimate the scale from above for the Mandelbrot set $\\mathcal{M}$ ?"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1411.6776","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2014-11-25T09:14:12Z","cross_cats_sorted":[],"title_canon_sha256":"870b8705ab6a9180533fb41459d71c86b1260bfda53db7fad0b0653af4d0f3a0","abstract_canon_sha256":"cfb867784682b0fd6100b484e0abcde9cbfe2dcd16aa512727248f52000de75f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:18.734864Z","signature_b64":"KI8Kd3OVSOGim0VsEHcBXw6OIpXLySk5uC/sfy8f8TiPYzvAndsLUWYkyVYrdlN0h9s8wbyK9sxoTq+QwnqlCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d5bde0526bd5a673919224a7e5dbc855f2affca8b46835b164b67ed08842cdf7","last_reissued_at":"2026-05-18T01:19:18.734251Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:18.734251Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A numerical scale for non locally connected planar continua","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Beno\\^it Loridant, Jun Luo, Timo Jolivet","submitted_at":"2014-11-25T09:14:12Z","abstract_excerpt":"We introduce a numerical scale to quantify to which extent a planar continuum is not locally connected. For a locally connected continuum, the numerical scale is zero; for a continuum like the topologist's sine curve, the scale is one; for an indecomposable continuum, it is infinite. Among others, we shall pose a new problem that may be of some interest: can we estimate the scale from above for the Mandelbrot set $\\mathcal{M}$ ?"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.6776","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1411.6776","created_at":"2026-05-18T01:19:18.734359+00:00"},{"alias_kind":"arxiv_version","alias_value":"1411.6776v1","created_at":"2026-05-18T01:19:18.734359+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.6776","created_at":"2026-05-18T01:19:18.734359+00:00"},{"alias_kind":"pith_short_12","alias_value":"2W66AUTL2WTH","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_16","alias_value":"2W66AUTL2WTHHEMS","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_8","alias_value":"2W66AUTL","created_at":"2026-05-18T12:28:11.866339+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2W66AUTL2WTHHEMSEST6LW6IKX","json":"https://pith.science/pith/2W66AUTL2WTHHEMSEST6LW6IKX.json","graph_json":"https://pith.science/api/pith-number/2W66AUTL2WTHHEMSEST6LW6IKX/graph.json","events_json":"https://pith.science/api/pith-number/2W66AUTL2WTHHEMSEST6LW6IKX/events.json","paper":"https://pith.science/paper/2W66AUTL"},"agent_actions":{"view_html":"https://pith.science/pith/2W66AUTL2WTHHEMSEST6LW6IKX","download_json":"https://pith.science/pith/2W66AUTL2WTHHEMSEST6LW6IKX.json","view_paper":"https://pith.science/paper/2W66AUTL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1411.6776&json=true","fetch_graph":"https://pith.science/api/pith-number/2W66AUTL2WTHHEMSEST6LW6IKX/graph.json","fetch_events":"https://pith.science/api/pith-number/2W66AUTL2WTHHEMSEST6LW6IKX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2W66AUTL2WTHHEMSEST6LW6IKX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2W66AUTL2WTHHEMSEST6LW6IKX/action/storage_attestation","attest_author":"https://pith.science/pith/2W66AUTL2WTHHEMSEST6LW6IKX/action/author_attestation","sign_citation":"https://pith.science/pith/2W66AUTL2WTHHEMSEST6LW6IKX/action/citation_signature","submit_replication":"https://pith.science/pith/2W66AUTL2WTHHEMSEST6LW6IKX/action/replication_record"}},"created_at":"2026-05-18T01:19:18.734359+00:00","updated_at":"2026-05-18T01:19:18.734359+00:00"}