{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:LTDDNNRLSUKXTYXGNSMJSCX4BM","short_pith_number":"pith:LTDDNNRL","schema_version":"1.0","canonical_sha256":"5cc636b62b951579e2e66c98990afc0b113dcc3449fabbe54232f44bbe605b99","source":{"kind":"arxiv","id":"1806.04008","version":1},"attestation_state":"computed","paper":{"title":"Ubiquity in graphs I: Topological ubiquity of trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Christian Elbracht, Joshua Erde, Karl Heuer, Maximilian Teegen, Max Pitz, Nathan Bowler, Pascal Gollin","submitted_at":"2018-06-11T14:15:57Z","abstract_excerpt":"Let $\\triangleleft$ be a relation between graphs. We say a graph $G$ is \\emph{$\\triangleleft$-ubiquitous} if whenever $\\Gamma$ is a graph with $nG \\triangleleft \\Gamma$ for all $n \\in \\mathbb{N}$, then one also has $\\aleph_0 G \\triangleleft \\Gamma$, where $\\alpha G$ is the disjoint union of $\\alpha$ many copies of $G$.\n  The \\emph{Ubiquity Conjecture} of Andreae, a well-known open problem in the theory of infinite graphs, asserts that every locally finite connected graph is ubiquitous with respect to the minor relation.\n  In this paper, which is the first of a series of papers making progress "},"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":"1806.04008","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-06-11T14:15:57Z","cross_cats_sorted":[],"title_canon_sha256":"f0557036b05f581796cafd56874d8bf574d44af3149c7a1385afebe5b8f00832","abstract_canon_sha256":"4304b9d1d553592338466c3a168d9b588532e0ffa5dde080a7700056ce7fe4e2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:38.846077Z","signature_b64":"yHs6anTareE8XwzQnwkJ7nUP8IFmQfJ0gDGJV+lpkEd1DWKBsxcbFSn0XRhRmeqGXNUi0uNMevUzTJw4WlCsBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5cc636b62b951579e2e66c98990afc0b113dcc3449fabbe54232f44bbe605b99","last_reissued_at":"2026-05-18T00:13:38.845291Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:38.845291Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ubiquity in graphs I: Topological ubiquity of trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Christian Elbracht, Joshua Erde, Karl Heuer, Maximilian Teegen, Max Pitz, Nathan Bowler, Pascal Gollin","submitted_at":"2018-06-11T14:15:57Z","abstract_excerpt":"Let $\\triangleleft$ be a relation between graphs. We say a graph $G$ is \\emph{$\\triangleleft$-ubiquitous} if whenever $\\Gamma$ is a graph with $nG \\triangleleft \\Gamma$ for all $n \\in \\mathbb{N}$, then one also has $\\aleph_0 G \\triangleleft \\Gamma$, where $\\alpha G$ is the disjoint union of $\\alpha$ many copies of $G$.\n  The \\emph{Ubiquity Conjecture} of Andreae, a well-known open problem in the theory of infinite graphs, asserts that every locally finite connected graph is ubiquitous with respect to the minor relation.\n  In this paper, which is the first of a series of papers making progress "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.04008","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":"1806.04008","created_at":"2026-05-18T00:13:38.845419+00:00"},{"alias_kind":"arxiv_version","alias_value":"1806.04008v1","created_at":"2026-05-18T00:13:38.845419+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.04008","created_at":"2026-05-18T00:13:38.845419+00:00"},{"alias_kind":"pith_short_12","alias_value":"LTDDNNRLSUKX","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_16","alias_value":"LTDDNNRLSUKXTYXG","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_8","alias_value":"LTDDNNRL","created_at":"2026-05-18T12:32:37.024351+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/LTDDNNRLSUKXTYXGNSMJSCX4BM","json":"https://pith.science/pith/LTDDNNRLSUKXTYXGNSMJSCX4BM.json","graph_json":"https://pith.science/api/pith-number/LTDDNNRLSUKXTYXGNSMJSCX4BM/graph.json","events_json":"https://pith.science/api/pith-number/LTDDNNRLSUKXTYXGNSMJSCX4BM/events.json","paper":"https://pith.science/paper/LTDDNNRL"},"agent_actions":{"view_html":"https://pith.science/pith/LTDDNNRLSUKXTYXGNSMJSCX4BM","download_json":"https://pith.science/pith/LTDDNNRLSUKXTYXGNSMJSCX4BM.json","view_paper":"https://pith.science/paper/LTDDNNRL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1806.04008&json=true","fetch_graph":"https://pith.science/api/pith-number/LTDDNNRLSUKXTYXGNSMJSCX4BM/graph.json","fetch_events":"https://pith.science/api/pith-number/LTDDNNRLSUKXTYXGNSMJSCX4BM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LTDDNNRLSUKXTYXGNSMJSCX4BM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LTDDNNRLSUKXTYXGNSMJSCX4BM/action/storage_attestation","attest_author":"https://pith.science/pith/LTDDNNRLSUKXTYXGNSMJSCX4BM/action/author_attestation","sign_citation":"https://pith.science/pith/LTDDNNRLSUKXTYXGNSMJSCX4BM/action/citation_signature","submit_replication":"https://pith.science/pith/LTDDNNRLSUKXTYXGNSMJSCX4BM/action/replication_record"}},"created_at":"2026-05-18T00:13:38.845419+00:00","updated_at":"2026-05-18T00:13:38.845419+00:00"}