{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:7ALLBTQNBVYH6OMXPTA7LI3EM7","short_pith_number":"pith:7ALLBTQN","canonical_record":{"source":{"id":"1407.3604","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-07-14T11:03:23Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"12c7046ce581ca3dbedb3c3b9189127986e336ee986607145b08ee61d7af5dc8","abstract_canon_sha256":"ad2f260432c54f7c1142982657d0d1d934140922d65952d1ea03138bda44a4de"},"schema_version":"1.0"},"canonical_sha256":"f816b0ce0d0d707f39977cc1f5a36467de95f3e3500160b06229a9bcc335c15b","source":{"kind":"arxiv","id":"1407.3604","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.3604","created_at":"2026-05-18T02:47:42Z"},{"alias_kind":"arxiv_version","alias_value":"1407.3604v1","created_at":"2026-05-18T02:47:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.3604","created_at":"2026-05-18T02:47:42Z"},{"alias_kind":"pith_short_12","alias_value":"7ALLBTQNBVYH","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"7ALLBTQNBVYH6OMX","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"7ALLBTQN","created_at":"2026-05-18T12:28:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:7ALLBTQNBVYH6OMXPTA7LI3EM7","target":"record","payload":{"canonical_record":{"source":{"id":"1407.3604","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-07-14T11:03:23Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"12c7046ce581ca3dbedb3c3b9189127986e336ee986607145b08ee61d7af5dc8","abstract_canon_sha256":"ad2f260432c54f7c1142982657d0d1d934140922d65952d1ea03138bda44a4de"},"schema_version":"1.0"},"canonical_sha256":"f816b0ce0d0d707f39977cc1f5a36467de95f3e3500160b06229a9bcc335c15b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:42.396517Z","signature_b64":"QlpwVe7AmQBDIzmbKoZ83Uk+joEVHTfRan9df7frp7XLBzIOaJC+pxWRaY4lJYZtxtUkyOWZeAd3xCmKbDt5Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f816b0ce0d0d707f39977cc1f5a36467de95f3e3500160b06229a9bcc335c15b","last_reissued_at":"2026-05-18T02:47:42.395798Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:42.395798Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.3604","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":"2026-05-18T02:47:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J6LqsfMHplHi52YSpoCqH2dy4iz4BfMDFRyXlD0nTzf+5e8IIZdmYvWcCGHBah3HReRgMIgbtYkc+PmH71GuBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T03:11:27.444154Z"},"content_sha256":"97eeb5ed35dc4b24f023d8c736673da2cf7c5d18c4387cc62f03e508618ac4e4","schema_version":"1.0","event_id":"sha256:97eeb5ed35dc4b24f023d8c736673da2cf7c5d18c4387cc62f03e508618ac4e4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:7ALLBTQNBVYH6OMXPTA7LI3EM7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Davies-trees in infinite combinatorics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.LO","authors_text":"Daniel T. Soukup","submitted_at":"2014-07-14T11:03:23Z","abstract_excerpt":"This short note, prepared for the Logic Colloquium 2014, provides an introduction to Davies-trees and presents new applications in infinite combinatorics. In particular, we give new and simple proofs to the following theorems of P. Komj\\'ath: every $n$-almost disjoint family of sets is essentially disjoint for any $n\\in \\mathbb N$; $\\mathbb R^2$ is the union of $n+2$ clouds if the continuum is at most $\\aleph_n$ for any $n\\in \\mathbb N$; every uncountably chromatic graph contains $n$-connected uncountably chromatic subgraphs for every $n\\in \\mathbb N$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.3604","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":"2026-05-18T02:47:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hllPuTe2DDMZOqEus0TrD5LW5/ZfxpPmLwHfyQyHLiUbSZrS63TME5nbhfVWkKj+238xU/QWmVptSzDJyAYiDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T03:11:27.444715Z"},"content_sha256":"313a112f6f90ad1c21996edbac2830abda365912bf56bbfd25e4a3917556aa03","schema_version":"1.0","event_id":"sha256:313a112f6f90ad1c21996edbac2830abda365912bf56bbfd25e4a3917556aa03"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7ALLBTQNBVYH6OMXPTA7LI3EM7/bundle.json","state_url":"https://pith.science/pith/7ALLBTQNBVYH6OMXPTA7LI3EM7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7ALLBTQNBVYH6OMXPTA7LI3EM7/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":"2026-06-03T03:11:27Z","links":{"resolver":"https://pith.science/pith/7ALLBTQNBVYH6OMXPTA7LI3EM7","bundle":"https://pith.science/pith/7ALLBTQNBVYH6OMXPTA7LI3EM7/bundle.json","state":"https://pith.science/pith/7ALLBTQNBVYH6OMXPTA7LI3EM7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7ALLBTQNBVYH6OMXPTA7LI3EM7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:7ALLBTQNBVYH6OMXPTA7LI3EM7","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":"ad2f260432c54f7c1142982657d0d1d934140922d65952d1ea03138bda44a4de","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-07-14T11:03:23Z","title_canon_sha256":"12c7046ce581ca3dbedb3c3b9189127986e336ee986607145b08ee61d7af5dc8"},"schema_version":"1.0","source":{"id":"1407.3604","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.3604","created_at":"2026-05-18T02:47:42Z"},{"alias_kind":"arxiv_version","alias_value":"1407.3604v1","created_at":"2026-05-18T02:47:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.3604","created_at":"2026-05-18T02:47:42Z"},{"alias_kind":"pith_short_12","alias_value":"7ALLBTQNBVYH","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"7ALLBTQNBVYH6OMX","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"7ALLBTQN","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:313a112f6f90ad1c21996edbac2830abda365912bf56bbfd25e4a3917556aa03","target":"graph","created_at":"2026-05-18T02:47:42Z","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":"This short note, prepared for the Logic Colloquium 2014, provides an introduction to Davies-trees and presents new applications in infinite combinatorics. In particular, we give new and simple proofs to the following theorems of P. Komj\\'ath: every $n$-almost disjoint family of sets is essentially disjoint for any $n\\in \\mathbb N$; $\\mathbb R^2$ is the union of $n+2$ clouds if the continuum is at most $\\aleph_n$ for any $n\\in \\mathbb N$; every uncountably chromatic graph contains $n$-connected uncountably chromatic subgraphs for every $n\\in \\mathbb N$.","authors_text":"Daniel T. Soukup","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-07-14T11:03:23Z","title":"Davies-trees in infinite combinatorics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.3604","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":"sha256:97eeb5ed35dc4b24f023d8c736673da2cf7c5d18c4387cc62f03e508618ac4e4","target":"record","created_at":"2026-05-18T02:47:42Z","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":"ad2f260432c54f7c1142982657d0d1d934140922d65952d1ea03138bda44a4de","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-07-14T11:03:23Z","title_canon_sha256":"12c7046ce581ca3dbedb3c3b9189127986e336ee986607145b08ee61d7af5dc8"},"schema_version":"1.0","source":{"id":"1407.3604","kind":"arxiv","version":1}},"canonical_sha256":"f816b0ce0d0d707f39977cc1f5a36467de95f3e3500160b06229a9bcc335c15b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f816b0ce0d0d707f39977cc1f5a36467de95f3e3500160b06229a9bcc335c15b","first_computed_at":"2026-05-18T02:47:42.395798Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:47:42.395798Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QlpwVe7AmQBDIzmbKoZ83Uk+joEVHTfRan9df7frp7XLBzIOaJC+pxWRaY4lJYZtxtUkyOWZeAd3xCmKbDt5Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:47:42.396517Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.3604","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:97eeb5ed35dc4b24f023d8c736673da2cf7c5d18c4387cc62f03e508618ac4e4","sha256:313a112f6f90ad1c21996edbac2830abda365912bf56bbfd25e4a3917556aa03"],"state_sha256":"aaf90ae3cc3da7114d8ab8284a5013c2fba72227d6ea411dcf4205147e0a586a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hB9eATRU8zGAJDWbWxwjSgd8r/EY6bLpL6FvjO6saqSzdVXRZFkZBISjk4tjpeGNdgIIVD7OMUrvR5VUySWOCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T03:11:27.447380Z","bundle_sha256":"32a815a69a9909e60d0b0c7691f986bc7be06178ad46a9f8bc3436ffad0d8db8"}}