{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:5ADDTZUU6YNDPXDZO4VTZ3LEC7","short_pith_number":"pith:5ADDTZUU","canonical_record":{"source":{"id":"1812.08447","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-12-20T09:48:17Z","cross_cats_sorted":[],"title_canon_sha256":"c2344b4d53c58d164683473b07af60b4b09f4afd38cf53902ea2a31556e30ee4","abstract_canon_sha256":"62d614afbfd9b4d12b625f77e2ad2656124d4af84ccbca4a2b0631b64bda4e1a"},"schema_version":"1.0"},"canonical_sha256":"e80639e694f61a37dc79772b3ced6417c1c2993f0acf1c99f83d0d0b425e8930","source":{"kind":"arxiv","id":"1812.08447","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.08447","created_at":"2026-05-17T23:57:49Z"},{"alias_kind":"arxiv_version","alias_value":"1812.08447v1","created_at":"2026-05-17T23:57:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.08447","created_at":"2026-05-17T23:57:49Z"},{"alias_kind":"pith_short_12","alias_value":"5ADDTZUU6YND","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5ADDTZUU6YNDPXDZ","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5ADDTZUU","created_at":"2026-05-18T12:32:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:5ADDTZUU6YNDPXDZO4VTZ3LEC7","target":"record","payload":{"canonical_record":{"source":{"id":"1812.08447","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-12-20T09:48:17Z","cross_cats_sorted":[],"title_canon_sha256":"c2344b4d53c58d164683473b07af60b4b09f4afd38cf53902ea2a31556e30ee4","abstract_canon_sha256":"62d614afbfd9b4d12b625f77e2ad2656124d4af84ccbca4a2b0631b64bda4e1a"},"schema_version":"1.0"},"canonical_sha256":"e80639e694f61a37dc79772b3ced6417c1c2993f0acf1c99f83d0d0b425e8930","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:49.961371Z","signature_b64":"4ytx6pgwh74SojYB/AzPyD7GRrHOqrrFsAOFJ/wxCKHJXoRQ8G/X0VJxaQI2Gq0O+Espk/1OcExj6Ja/W7QoCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e80639e694f61a37dc79772b3ced6417c1c2993f0acf1c99f83d0d0b425e8930","last_reissued_at":"2026-05-17T23:57:49.960660Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:49.960660Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.08447","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":"2026-05-17T23:57:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"muIVKBPRFPbsPrIo8BkWkt5GmjEkhs2ZduBnKt/epQYorp6Rfr7a9RN2IrLmyVO639RlYOb5TH4QSCh7232GAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T06:12:22.375274Z"},"content_sha256":"cf56b76d8c994cdea33e75bc7ff469e9ce71a6ad5a1f07160e9ca861e98d4a05","schema_version":"1.0","event_id":"sha256:cf56b76d8c994cdea33e75bc7ff469e9ce71a6ad5a1f07160e9ca861e98d4a05"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:5ADDTZUU6YNDPXDZO4VTZ3LEC7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Complexity of Embeddable Simplicial Complexes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Anna Gundert","submitted_at":"2018-12-20T09:48:17Z","abstract_excerpt":"This thesis addresses the question of the maximal number of $d$-simplices for a simplicial complex which is embeddable into $\\mathbb{R}^r$ for some $d \\leq r \\leq 2d$.\n  A lower bound of $f_d(C_{r + 1}(n)) = \\Omega(n^{\\lceil\\frac{r}{2}\\rceil})$, which might even be sharp, is given by the cyclic polytopes. To find an upper bound for the case $r=2d$ we look for forbidden subcomplexes. A generalization of the theorem of van Kampen and Flores yields those. Then the problem can be tackled with the methods of extremal hypergraph theory, which gives an upper bound of $O(n^{d+1-\\frac{1}{3^d}})$.\n  We "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.08447","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":"2026-05-17T23:57:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YZLva0RiP7bKYR06Uu/56xLPsvMVEEuvSZdhya495f90yLoPTPIhCkuiG2tfd349sOgrRZ9kokf4/+F7rEAnDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T06:12:22.375900Z"},"content_sha256":"d505fd02d317857c49aa653cf6c5cb36145033b6d3ba15ce3b49bd56978dc516","schema_version":"1.0","event_id":"sha256:d505fd02d317857c49aa653cf6c5cb36145033b6d3ba15ce3b49bd56978dc516"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5ADDTZUU6YNDPXDZO4VTZ3LEC7/bundle.json","state_url":"https://pith.science/pith/5ADDTZUU6YNDPXDZO4VTZ3LEC7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5ADDTZUU6YNDPXDZO4VTZ3LEC7/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":"2026-05-28T06:12:22Z","links":{"resolver":"https://pith.science/pith/5ADDTZUU6YNDPXDZO4VTZ3LEC7","bundle":"https://pith.science/pith/5ADDTZUU6YNDPXDZO4VTZ3LEC7/bundle.json","state":"https://pith.science/pith/5ADDTZUU6YNDPXDZO4VTZ3LEC7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5ADDTZUU6YNDPXDZO4VTZ3LEC7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:5ADDTZUU6YNDPXDZO4VTZ3LEC7","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":"62d614afbfd9b4d12b625f77e2ad2656124d4af84ccbca4a2b0631b64bda4e1a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-12-20T09:48:17Z","title_canon_sha256":"c2344b4d53c58d164683473b07af60b4b09f4afd38cf53902ea2a31556e30ee4"},"schema_version":"1.0","source":{"id":"1812.08447","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.08447","created_at":"2026-05-17T23:57:49Z"},{"alias_kind":"arxiv_version","alias_value":"1812.08447v1","created_at":"2026-05-17T23:57:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.08447","created_at":"2026-05-17T23:57:49Z"},{"alias_kind":"pith_short_12","alias_value":"5ADDTZUU6YND","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5ADDTZUU6YNDPXDZ","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5ADDTZUU","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:d505fd02d317857c49aa653cf6c5cb36145033b6d3ba15ce3b49bd56978dc516","target":"graph","created_at":"2026-05-17T23:57:49Z","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 thesis addresses the question of the maximal number of $d$-simplices for a simplicial complex which is embeddable into $\\mathbb{R}^r$ for some $d \\leq r \\leq 2d$.\n  A lower bound of $f_d(C_{r + 1}(n)) = \\Omega(n^{\\lceil\\frac{r}{2}\\rceil})$, which might even be sharp, is given by the cyclic polytopes. To find an upper bound for the case $r=2d$ we look for forbidden subcomplexes. A generalization of the theorem of van Kampen and Flores yields those. Then the problem can be tackled with the methods of extremal hypergraph theory, which gives an upper bound of $O(n^{d+1-\\frac{1}{3^d}})$.\n  We ","authors_text":"Anna Gundert","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-12-20T09:48:17Z","title":"On the Complexity of Embeddable Simplicial Complexes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.08447","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:cf56b76d8c994cdea33e75bc7ff469e9ce71a6ad5a1f07160e9ca861e98d4a05","target":"record","created_at":"2026-05-17T23:57:49Z","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":"62d614afbfd9b4d12b625f77e2ad2656124d4af84ccbca4a2b0631b64bda4e1a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-12-20T09:48:17Z","title_canon_sha256":"c2344b4d53c58d164683473b07af60b4b09f4afd38cf53902ea2a31556e30ee4"},"schema_version":"1.0","source":{"id":"1812.08447","kind":"arxiv","version":1}},"canonical_sha256":"e80639e694f61a37dc79772b3ced6417c1c2993f0acf1c99f83d0d0b425e8930","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e80639e694f61a37dc79772b3ced6417c1c2993f0acf1c99f83d0d0b425e8930","first_computed_at":"2026-05-17T23:57:49.960660Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:49.960660Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4ytx6pgwh74SojYB/AzPyD7GRrHOqrrFsAOFJ/wxCKHJXoRQ8G/X0VJxaQI2Gq0O+Espk/1OcExj6Ja/W7QoCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:49.961371Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.08447","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cf56b76d8c994cdea33e75bc7ff469e9ce71a6ad5a1f07160e9ca861e98d4a05","sha256:d505fd02d317857c49aa653cf6c5cb36145033b6d3ba15ce3b49bd56978dc516"],"state_sha256":"53febb377217c887013b88e624d53257ed60102ca2e956237c367d8f4528a80c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ObzaJq3yYwKRXyP9lgG0vNLYfHhphK5V9u/xYIvVoiWpeQLAJ0EstJg3uWJDLBI9W1ptYQWV3qgl5Xay+hNBAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T06:12:22.378872Z","bundle_sha256":"31eccf5f194735dc97ce654afb1a25bac81aa291ea415e9b50eb66ffbeafba26"}}