{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:6WASXEKQVQGY6A56PKSN5TI7KC","short_pith_number":"pith:6WASXEKQ","canonical_record":{"source":{"id":"1802.06143","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-02-16T22:02:22Z","cross_cats_sorted":[],"title_canon_sha256":"e62b6344d77964e799e072be4d3a7d0e85453f35ede1af33c063817a6b7ef781","abstract_canon_sha256":"e8fce8d4fb0681bf66d2a7a0153cbfa29332f3c0e784584e9c56c3205d558f75"},"schema_version":"1.0"},"canonical_sha256":"f5812b9150ac0d8f03be7aa4decd1f508e3a2cdbce74b4f452851dfb087ca915","source":{"kind":"arxiv","id":"1802.06143","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.06143","created_at":"2026-05-18T00:23:04Z"},{"alias_kind":"arxiv_version","alias_value":"1802.06143v1","created_at":"2026-05-18T00:23:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.06143","created_at":"2026-05-18T00:23:04Z"},{"alias_kind":"pith_short_12","alias_value":"6WASXEKQVQGY","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"6WASXEKQVQGY6A56","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"6WASXEKQ","created_at":"2026-05-18T12:32:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:6WASXEKQVQGY6A56PKSN5TI7KC","target":"record","payload":{"canonical_record":{"source":{"id":"1802.06143","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-02-16T22:02:22Z","cross_cats_sorted":[],"title_canon_sha256":"e62b6344d77964e799e072be4d3a7d0e85453f35ede1af33c063817a6b7ef781","abstract_canon_sha256":"e8fce8d4fb0681bf66d2a7a0153cbfa29332f3c0e784584e9c56c3205d558f75"},"schema_version":"1.0"},"canonical_sha256":"f5812b9150ac0d8f03be7aa4decd1f508e3a2cdbce74b4f452851dfb087ca915","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:04.320116Z","signature_b64":"p6wEplLXX/4+zuRAbARn57AbeEzcFGbCYNz5MTHYLcrjgOxURSPxk+SawWqsfZJCM2jdsqVQdZ31sCGHg62KBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f5812b9150ac0d8f03be7aa4decd1f508e3a2cdbce74b4f452851dfb087ca915","last_reissued_at":"2026-05-18T00:23:04.319521Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:04.319521Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.06143","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":"2026-05-18T00:23:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1JB902cxcTNZVRX0d1DclycC6OVRJV31Qb1dYw9cuuBuEF/DYqNNx+6H8mhBklpF0ZymqICVRry1z3mowlZYDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T03:00:30.576789Z"},"content_sha256":"e2148227b6db264b8c235318fcf7164605ae74d71c343162a085dbf92b0b7c48","schema_version":"1.0","event_id":"sha256:e2148227b6db264b8c235318fcf7164605ae74d71c343162a085dbf92b0b7c48"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:6WASXEKQVQGY6A56PKSN5TI7KC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Tur\\'an density of $\\{1, 3\\}$-Hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Linyuan Lu, Shuliang Bai","submitted_at":"2018-02-16T22:02:22Z","abstract_excerpt":"In this paper, we consider the Tur\\'an problems on $\\{1,3\\}$-hypergraphs. We prove that a $\\{1, 3\\}$-hypergraph is degenerate if and only if it's $H^{\\{1, 3\\}}_5$-colorable, where $H^{\\{1, 3\\}}_5$ is a hypergraph with vertex set $V=[5]$ and edge set $E=\\{\\{2\\}, \\{3\\}, \\{1, 2, 4\\}, \\{1, 3, 5\\}, \\{1, 4, 5\\}\\}.$ Using this result, we further prove that for any finite set $R$ of distinct positive integers, except the case $R=\\{1, 2\\}$, there always exist non-trivial degenerate $R$-graphs. We also compute the Tur\\'an densities of some small $\\{1,3\\}$-hypergraphs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.06143","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":"2026-05-18T00:23:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qwb71opgwjFbJt/GImVyeDxE/qgrFIxbAbjg4nFK9rF12TAUQ1s8E5H2GC+gZW4ssWqDoClfCb5ggSUYYoUqDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T03:00:30.577155Z"},"content_sha256":"b343a3f60fb133d2e4ef90db11084a37584364fbfc12af0d3f561b672ab5df90","schema_version":"1.0","event_id":"sha256:b343a3f60fb133d2e4ef90db11084a37584364fbfc12af0d3f561b672ab5df90"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6WASXEKQVQGY6A56PKSN5TI7KC/bundle.json","state_url":"https://pith.science/pith/6WASXEKQVQGY6A56PKSN5TI7KC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6WASXEKQVQGY6A56PKSN5TI7KC/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":"2026-05-27T03:00:30Z","links":{"resolver":"https://pith.science/pith/6WASXEKQVQGY6A56PKSN5TI7KC","bundle":"https://pith.science/pith/6WASXEKQVQGY6A56PKSN5TI7KC/bundle.json","state":"https://pith.science/pith/6WASXEKQVQGY6A56PKSN5TI7KC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6WASXEKQVQGY6A56PKSN5TI7KC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:6WASXEKQVQGY6A56PKSN5TI7KC","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":"e8fce8d4fb0681bf66d2a7a0153cbfa29332f3c0e784584e9c56c3205d558f75","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-02-16T22:02:22Z","title_canon_sha256":"e62b6344d77964e799e072be4d3a7d0e85453f35ede1af33c063817a6b7ef781"},"schema_version":"1.0","source":{"id":"1802.06143","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.06143","created_at":"2026-05-18T00:23:04Z"},{"alias_kind":"arxiv_version","alias_value":"1802.06143v1","created_at":"2026-05-18T00:23:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.06143","created_at":"2026-05-18T00:23:04Z"},{"alias_kind":"pith_short_12","alias_value":"6WASXEKQVQGY","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"6WASXEKQVQGY6A56","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"6WASXEKQ","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:b343a3f60fb133d2e4ef90db11084a37584364fbfc12af0d3f561b672ab5df90","target":"graph","created_at":"2026-05-18T00:23:04Z","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":"In this paper, we consider the Tur\\'an problems on $\\{1,3\\}$-hypergraphs. We prove that a $\\{1, 3\\}$-hypergraph is degenerate if and only if it's $H^{\\{1, 3\\}}_5$-colorable, where $H^{\\{1, 3\\}}_5$ is a hypergraph with vertex set $V=[5]$ and edge set $E=\\{\\{2\\}, \\{3\\}, \\{1, 2, 4\\}, \\{1, 3, 5\\}, \\{1, 4, 5\\}\\}.$ Using this result, we further prove that for any finite set $R$ of distinct positive integers, except the case $R=\\{1, 2\\}$, there always exist non-trivial degenerate $R$-graphs. We also compute the Tur\\'an densities of some small $\\{1,3\\}$-hypergraphs.","authors_text":"Linyuan Lu, Shuliang Bai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-02-16T22:02:22Z","title":"On the Tur\\'an density of $\\{1, 3\\}$-Hypergraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.06143","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:e2148227b6db264b8c235318fcf7164605ae74d71c343162a085dbf92b0b7c48","target":"record","created_at":"2026-05-18T00:23:04Z","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":"e8fce8d4fb0681bf66d2a7a0153cbfa29332f3c0e784584e9c56c3205d558f75","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-02-16T22:02:22Z","title_canon_sha256":"e62b6344d77964e799e072be4d3a7d0e85453f35ede1af33c063817a6b7ef781"},"schema_version":"1.0","source":{"id":"1802.06143","kind":"arxiv","version":1}},"canonical_sha256":"f5812b9150ac0d8f03be7aa4decd1f508e3a2cdbce74b4f452851dfb087ca915","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f5812b9150ac0d8f03be7aa4decd1f508e3a2cdbce74b4f452851dfb087ca915","first_computed_at":"2026-05-18T00:23:04.319521Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:04.319521Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p6wEplLXX/4+zuRAbARn57AbeEzcFGbCYNz5MTHYLcrjgOxURSPxk+SawWqsfZJCM2jdsqVQdZ31sCGHg62KBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:04.320116Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.06143","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e2148227b6db264b8c235318fcf7164605ae74d71c343162a085dbf92b0b7c48","sha256:b343a3f60fb133d2e4ef90db11084a37584364fbfc12af0d3f561b672ab5df90"],"state_sha256":"dbbb75c93b5a9cdf69d79578006ce91fa4181f46de138fb3a29516af159e58e7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A/7XGp9QvPzNapFpmRSTkqyHol+YIEP++M0Z2FVMKCknlZEz+tp4Kl4LpFLXQalCAPy0W1aTUkECUN927tfuBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T03:00:30.580074Z","bundle_sha256":"4c06622a3f264d2f0ab5119ce7886cb9dde6950e246b916d5de83141ebc12247"}}