{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:AWD52R4WZYSY6VE7632DRRPMET","short_pith_number":"pith:AWD52R4W","schema_version":"1.0","canonical_sha256":"0587dd4796ce258f549ff6f438c5ec24c679122749ade79ac7310911e1a50c00","source":{"kind":"arxiv","id":"1209.5451","version":1},"attestation_state":"computed","paper":{"title":"n-Arc Connected Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Ana Mamatelashvili, Benjamin Espinoza, Paul Gartside","submitted_at":"2012-09-24T23:09:45Z","abstract_excerpt":"A space is `n-arc connected' (n-ac) if any family of no more than n-points are contained in an arc. For graphs the following are equivalent: (i) 7-ac, (ii) n-ac for all n, (iii) continuous injective image of a closed sub-interval of the real line, and (iv) one of a finite family of graphs. General continua that are aleph_0-ac are characterized. The complexity of characterizing n-ac graphs for n=2,3,4,5 is determined to be strictly higher than that of the stated characterization of 7-ac graphs."},"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":"1209.5451","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2012-09-24T23:09:45Z","cross_cats_sorted":[],"title_canon_sha256":"df422c965c501d7fa99338fb4979fc42cc76a83111f9a452388a05de659434b7","abstract_canon_sha256":"82124592f67aaabc1ea5c76c563d43f36d974f08333af4d1abc645cc1fec7207"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:44:48.489524Z","signature_b64":"edbufNBY2fxoUXxwpiGHFnyYOTEPkb2OCMLim+MAiUu38266e9Hmd4V1p7B967ujjjZogzKyZDkR3JsRFNZqCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0587dd4796ce258f549ff6f438c5ec24c679122749ade79ac7310911e1a50c00","last_reissued_at":"2026-05-18T03:44:48.488525Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:44:48.488525Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"n-Arc Connected Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Ana Mamatelashvili, Benjamin Espinoza, Paul Gartside","submitted_at":"2012-09-24T23:09:45Z","abstract_excerpt":"A space is `n-arc connected' (n-ac) if any family of no more than n-points are contained in an arc. For graphs the following are equivalent: (i) 7-ac, (ii) n-ac for all n, (iii) continuous injective image of a closed sub-interval of the real line, and (iv) one of a finite family of graphs. General continua that are aleph_0-ac are characterized. The complexity of characterizing n-ac graphs for n=2,3,4,5 is determined to be strictly higher than that of the stated characterization of 7-ac graphs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.5451","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":"1209.5451","created_at":"2026-05-18T03:44:48.488661+00:00"},{"alias_kind":"arxiv_version","alias_value":"1209.5451v1","created_at":"2026-05-18T03:44:48.488661+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.5451","created_at":"2026-05-18T03:44:48.488661+00:00"},{"alias_kind":"pith_short_12","alias_value":"AWD52R4WZYSY","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_16","alias_value":"AWD52R4WZYSY6VE7","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_8","alias_value":"AWD52R4W","created_at":"2026-05-18T12:26:58.693483+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/AWD52R4WZYSY6VE7632DRRPMET","json":"https://pith.science/pith/AWD52R4WZYSY6VE7632DRRPMET.json","graph_json":"https://pith.science/api/pith-number/AWD52R4WZYSY6VE7632DRRPMET/graph.json","events_json":"https://pith.science/api/pith-number/AWD52R4WZYSY6VE7632DRRPMET/events.json","paper":"https://pith.science/paper/AWD52R4W"},"agent_actions":{"view_html":"https://pith.science/pith/AWD52R4WZYSY6VE7632DRRPMET","download_json":"https://pith.science/pith/AWD52R4WZYSY6VE7632DRRPMET.json","view_paper":"https://pith.science/paper/AWD52R4W","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1209.5451&json=true","fetch_graph":"https://pith.science/api/pith-number/AWD52R4WZYSY6VE7632DRRPMET/graph.json","fetch_events":"https://pith.science/api/pith-number/AWD52R4WZYSY6VE7632DRRPMET/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AWD52R4WZYSY6VE7632DRRPMET/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AWD52R4WZYSY6VE7632DRRPMET/action/storage_attestation","attest_author":"https://pith.science/pith/AWD52R4WZYSY6VE7632DRRPMET/action/author_attestation","sign_citation":"https://pith.science/pith/AWD52R4WZYSY6VE7632DRRPMET/action/citation_signature","submit_replication":"https://pith.science/pith/AWD52R4WZYSY6VE7632DRRPMET/action/replication_record"}},"created_at":"2026-05-18T03:44:48.488661+00:00","updated_at":"2026-05-18T03:44:48.488661+00:00"}