{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:KTWJPZRUZJWO6RD2GEGFSWWC5H","short_pith_number":"pith:KTWJPZRU","canonical_record":{"source":{"id":"2408.09029","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2024-08-16T21:54:29Z","cross_cats_sorted":[],"title_canon_sha256":"5c2e1e59f16adac1bdf207066371060829d558bd280723341dc082e5cc6efb4c","abstract_canon_sha256":"97485e4fc25a34bcc2ed9835c2bd0ab4f5e38c7d136ebb3296a587cb82cfe5a5"},"schema_version":"1.0"},"canonical_sha256":"54ec97e634ca6cef447a310c595ac2e9fda618ebcb87b58d9fcd1528237efe31","source":{"kind":"arxiv","id":"2408.09029","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2408.09029","created_at":"2026-05-18T02:44:39Z"},{"alias_kind":"arxiv_version","alias_value":"2408.09029v2","created_at":"2026-05-18T02:44:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.09029","created_at":"2026-05-18T02:44:39Z"},{"alias_kind":"pith_short_12","alias_value":"KTWJPZRUZJWO","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"KTWJPZRUZJWO6RD2","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"KTWJPZRU","created_at":"2026-05-18T12:33:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:KTWJPZRUZJWO6RD2GEGFSWWC5H","target":"record","payload":{"canonical_record":{"source":{"id":"2408.09029","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2024-08-16T21:54:29Z","cross_cats_sorted":[],"title_canon_sha256":"5c2e1e59f16adac1bdf207066371060829d558bd280723341dc082e5cc6efb4c","abstract_canon_sha256":"97485e4fc25a34bcc2ed9835c2bd0ab4f5e38c7d136ebb3296a587cb82cfe5a5"},"schema_version":"1.0"},"canonical_sha256":"54ec97e634ca6cef447a310c595ac2e9fda618ebcb87b58d9fcd1528237efe31","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:39.614966Z","signature_b64":"S1o1RzOw5fPiHojb0B5AuhBNdjUh2a7NWdVBlA5I5tFn/N7IvRnZwFK5TL3mf7w16WgJEMyze7RvmVO5uxSoDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"54ec97e634ca6cef447a310c595ac2e9fda618ebcb87b58d9fcd1528237efe31","last_reissued_at":"2026-05-18T02:44:39.614402Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:39.614402Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2408.09029","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:44:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tbm81/dOm5dZxHU5DaKhTk0CYeA3pvxVEEEGfdKd7/SOHTt2UhnuRDU0k5gFGXir6qRfj1sqlDgZNEqVwdAnAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T16:43:05.233007Z"},"content_sha256":"c0245a5140630c76a7bbda1709b8d6d7caf76a22d98a247a7eb9a6a8d8a38468","schema_version":"1.0","event_id":"sha256:c0245a5140630c76a7bbda1709b8d6d7caf76a22d98a247a7eb9a6a8d8a38468"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:KTWJPZRUZJWO6RD2GEGFSWWC5H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An Improved Tur\\'an Exponent for 2-Complexes","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Maya Sankar","submitted_at":"2024-08-16T21:54:29Z","abstract_excerpt":"The topological Tur\\'an number $\\mathrm{ex}_{\\hom}(n,X)$ of a 2-dimensional simplicial complex $X$ asks for the maximum number of edges in an $n$-vertex 3-uniform hypergraph containing no triangulation of $X$ as a subgraph. We prove that the Tur\\'an exponent of any such space $X$ is at most $8/3$, i.e., that $\\mathrm{ex}_{\\hom}(n,X)\\leq Cn^{8/3}$ for some constant $C=C(X)$. This improves on the previous exponent of $3-1/5$, due to Keevash, Long, Narayanan, and Scott. Additionally, we present new streamlined proofs of the asymptotically tight upper bounds for the topological Tur\\'an numbers of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.09029","kind":"arxiv","version":2},"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":"2026-05-18T02:44:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ixQaxwFrxJVVSn7z7KigzZ4WMNynICOOyMxJDq7BuSTVgNsoO1GPT5XNDZdSIVT1lu1/0JYkXs/LYzfHPMwHAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T16:43:05.233777Z"},"content_sha256":"d087c1dfb9713ba6111de4fae233eba8019dd27c124b60ce43e92ad871bb2df5","schema_version":"1.0","event_id":"sha256:d087c1dfb9713ba6111de4fae233eba8019dd27c124b60ce43e92ad871bb2df5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KTWJPZRUZJWO6RD2GEGFSWWC5H/bundle.json","state_url":"https://pith.science/pith/KTWJPZRUZJWO6RD2GEGFSWWC5H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KTWJPZRUZJWO6RD2GEGFSWWC5H/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":"2026-05-30T16:43:05Z","links":{"resolver":"https://pith.science/pith/KTWJPZRUZJWO6RD2GEGFSWWC5H","bundle":"https://pith.science/pith/KTWJPZRUZJWO6RD2GEGFSWWC5H/bundle.json","state":"https://pith.science/pith/KTWJPZRUZJWO6RD2GEGFSWWC5H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KTWJPZRUZJWO6RD2GEGFSWWC5H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:KTWJPZRUZJWO6RD2GEGFSWWC5H","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":"97485e4fc25a34bcc2ed9835c2bd0ab4f5e38c7d136ebb3296a587cb82cfe5a5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2024-08-16T21:54:29Z","title_canon_sha256":"5c2e1e59f16adac1bdf207066371060829d558bd280723341dc082e5cc6efb4c"},"schema_version":"1.0","source":{"id":"2408.09029","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2408.09029","created_at":"2026-05-18T02:44:39Z"},{"alias_kind":"arxiv_version","alias_value":"2408.09029v2","created_at":"2026-05-18T02:44:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.09029","created_at":"2026-05-18T02:44:39Z"},{"alias_kind":"pith_short_12","alias_value":"KTWJPZRUZJWO","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"KTWJPZRUZJWO6RD2","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"KTWJPZRU","created_at":"2026-05-18T12:33:37Z"}],"graph_snapshots":[{"event_id":"sha256:d087c1dfb9713ba6111de4fae233eba8019dd27c124b60ce43e92ad871bb2df5","target":"graph","created_at":"2026-05-18T02:44:39Z","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":"The topological Tur\\'an number $\\mathrm{ex}_{\\hom}(n,X)$ of a 2-dimensional simplicial complex $X$ asks for the maximum number of edges in an $n$-vertex 3-uniform hypergraph containing no triangulation of $X$ as a subgraph. We prove that the Tur\\'an exponent of any such space $X$ is at most $8/3$, i.e., that $\\mathrm{ex}_{\\hom}(n,X)\\leq Cn^{8/3}$ for some constant $C=C(X)$. This improves on the previous exponent of $3-1/5$, due to Keevash, Long, Narayanan, and Scott. Additionally, we present new streamlined proofs of the asymptotically tight upper bounds for the topological Tur\\'an numbers of ","authors_text":"Maya Sankar","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2024-08-16T21:54:29Z","title":"An Improved Tur\\'an Exponent for 2-Complexes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.09029","kind":"arxiv","version":2},"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:c0245a5140630c76a7bbda1709b8d6d7caf76a22d98a247a7eb9a6a8d8a38468","target":"record","created_at":"2026-05-18T02:44:39Z","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":"97485e4fc25a34bcc2ed9835c2bd0ab4f5e38c7d136ebb3296a587cb82cfe5a5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2024-08-16T21:54:29Z","title_canon_sha256":"5c2e1e59f16adac1bdf207066371060829d558bd280723341dc082e5cc6efb4c"},"schema_version":"1.0","source":{"id":"2408.09029","kind":"arxiv","version":2}},"canonical_sha256":"54ec97e634ca6cef447a310c595ac2e9fda618ebcb87b58d9fcd1528237efe31","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"54ec97e634ca6cef447a310c595ac2e9fda618ebcb87b58d9fcd1528237efe31","first_computed_at":"2026-05-18T02:44:39.614402Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:39.614402Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"S1o1RzOw5fPiHojb0B5AuhBNdjUh2a7NWdVBlA5I5tFn/N7IvRnZwFK5TL3mf7w16WgJEMyze7RvmVO5uxSoDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:39.614966Z","signed_message":"canonical_sha256_bytes"},"source_id":"2408.09029","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c0245a5140630c76a7bbda1709b8d6d7caf76a22d98a247a7eb9a6a8d8a38468","sha256:d087c1dfb9713ba6111de4fae233eba8019dd27c124b60ce43e92ad871bb2df5"],"state_sha256":"a587c7e26b81209b06531f9a6ecd93d0c919bb55bb051c92c62294d5028bc0c0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"++O3zG05/fKbCA0y3P5MhprlrxM3t517mmR3a083Pd30ltOHW2J8pfp01jSyVj8wsfnSkuHxMf6PpPGPZWgfDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T16:43:05.238241Z","bundle_sha256":"b32b38559d6927be9fac8802067518249c32046a5216b5292f9c595ce5a166f5"}}