{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:LTDDNNRLSUKXTYXGNSMJSCX4BM","short_pith_number":"pith:LTDDNNRL","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"},"canonical_sha256":"5cc636b62b951579e2e66c98990afc0b113dcc3449fabbe54232f44bbe605b99","source":{"kind":"arxiv","id":"1806.04008","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.04008","created_at":"2026-05-18T00:13:38Z"},{"alias_kind":"arxiv_version","alias_value":"1806.04008v1","created_at":"2026-05-18T00:13:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.04008","created_at":"2026-05-18T00:13:38Z"},{"alias_kind":"pith_short_12","alias_value":"LTDDNNRLSUKX","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"LTDDNNRLSUKXTYXG","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"LTDDNNRL","created_at":"2026-05-18T12:32:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:LTDDNNRLSUKXTYXGNSMJSCX4BM","target":"record","payload":{"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"},"canonical_sha256":"5cc636b62b951579e2e66c98990afc0b113dcc3449fabbe54232f44bbe605b99","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"},"source_kind":"arxiv","source_id":"1806.04008","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:13:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r1Q/EDb8yOiF26vVaGK0YGf3i5mn5QNcdSYETgDeObI4vbDd03CdhobTAMIxIRvG3j44AzUske5f/Czu93P3AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T02:44:04.308739Z"},"content_sha256":"300d8d7b6f73a0b071231a1afec373b4e45b388d33313014e34cae21c4893fdc","schema_version":"1.0","event_id":"sha256:300d8d7b6f73a0b071231a1afec373b4e45b388d33313014e34cae21c4893fdc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:LTDDNNRLSUKXTYXGNSMJSCX4BM","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:13:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+8OT139l+tr/9yC3LMxtwVfTxpkmATNaKPw+k/RzqkjiEM6bvV61HyC4/lPYqS/Y2pVINtPUD3USpyDqUZrBDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T02:44:04.309091Z"},"content_sha256":"2b0987a9df64de5e7c7b0f6fab049ac7be647268fc63225b9a74dc228e6c49c4","schema_version":"1.0","event_id":"sha256:2b0987a9df64de5e7c7b0f6fab049ac7be647268fc63225b9a74dc228e6c49c4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LTDDNNRLSUKXTYXGNSMJSCX4BM/bundle.json","state_url":"https://pith.science/pith/LTDDNNRLSUKXTYXGNSMJSCX4BM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LTDDNNRLSUKXTYXGNSMJSCX4BM/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-21T02:44:04Z","links":{"resolver":"https://pith.science/pith/LTDDNNRLSUKXTYXGNSMJSCX4BM","bundle":"https://pith.science/pith/LTDDNNRLSUKXTYXGNSMJSCX4BM/bundle.json","state":"https://pith.science/pith/LTDDNNRLSUKXTYXGNSMJSCX4BM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LTDDNNRLSUKXTYXGNSMJSCX4BM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:LTDDNNRLSUKXTYXGNSMJSCX4BM","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":"4304b9d1d553592338466c3a168d9b588532e0ffa5dde080a7700056ce7fe4e2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-06-11T14:15:57Z","title_canon_sha256":"f0557036b05f581796cafd56874d8bf574d44af3149c7a1385afebe5b8f00832"},"schema_version":"1.0","source":{"id":"1806.04008","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.04008","created_at":"2026-05-18T00:13:38Z"},{"alias_kind":"arxiv_version","alias_value":"1806.04008v1","created_at":"2026-05-18T00:13:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.04008","created_at":"2026-05-18T00:13:38Z"},{"alias_kind":"pith_short_12","alias_value":"LTDDNNRLSUKX","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"LTDDNNRLSUKXTYXG","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"LTDDNNRL","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:2b0987a9df64de5e7c7b0f6fab049ac7be647268fc63225b9a74dc228e6c49c4","target":"graph","created_at":"2026-05-18T00:13:38Z","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":"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 ","authors_text":"Christian Elbracht, Joshua Erde, Karl Heuer, Maximilian Teegen, Max Pitz, Nathan Bowler, Pascal Gollin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-06-11T14:15:57Z","title":"Ubiquity in graphs I: Topological ubiquity of trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.04008","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":"sha256:300d8d7b6f73a0b071231a1afec373b4e45b388d33313014e34cae21c4893fdc","target":"record","created_at":"2026-05-18T00:13:38Z","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":"4304b9d1d553592338466c3a168d9b588532e0ffa5dde080a7700056ce7fe4e2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-06-11T14:15:57Z","title_canon_sha256":"f0557036b05f581796cafd56874d8bf574d44af3149c7a1385afebe5b8f00832"},"schema_version":"1.0","source":{"id":"1806.04008","kind":"arxiv","version":1}},"canonical_sha256":"5cc636b62b951579e2e66c98990afc0b113dcc3449fabbe54232f44bbe605b99","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5cc636b62b951579e2e66c98990afc0b113dcc3449fabbe54232f44bbe605b99","first_computed_at":"2026-05-18T00:13:38.845291Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:38.845291Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yHs6anTareE8XwzQnwkJ7nUP8IFmQfJ0gDGJV+lpkEd1DWKBsxcbFSn0XRhRmeqGXNUi0uNMevUzTJw4WlCsBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:38.846077Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.04008","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:300d8d7b6f73a0b071231a1afec373b4e45b388d33313014e34cae21c4893fdc","sha256:2b0987a9df64de5e7c7b0f6fab049ac7be647268fc63225b9a74dc228e6c49c4"],"state_sha256":"ec011fab7f1abdd4e59e2999887cc087badef317bbaedd8c4453f16f4630c04d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pSmTJE2zK9NzS/i1wN4t0nlXXx6d7udPcYht/BLl0acFlyz8o2ZfnzF/vXCZ8If7gVdMfL9yx37aiXbTiWodCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T02:44:04.311128Z","bundle_sha256":"9ac658f749216e6ba4f14f681341d9d45fab8bdbcfb37cb3ca20f890c4be9880"}}