{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:RWGTGDEGJGP26HQBNNRMUHFFOO","short_pith_number":"pith:RWGTGDEG","canonical_record":{"source":{"id":"1310.5882","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-22T11:27:10Z","cross_cats_sorted":[],"title_canon_sha256":"6ac66dd7bed46f4d02df914c4d37eef8eaac488eb981c85ef5fa43e5d8b91a97","abstract_canon_sha256":"476b1de5c5d1374964af7f0493983b4149c8990f81fecdcd6cfd627a70878984"},"schema_version":"1.0"},"canonical_sha256":"8d8d330c86499faf1e016b62ca1ca573a098a42a16affa7c9792ec32be7c6ffd","source":{"kind":"arxiv","id":"1310.5882","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.5882","created_at":"2026-05-18T03:09:24Z"},{"alias_kind":"arxiv_version","alias_value":"1310.5882v1","created_at":"2026-05-18T03:09:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.5882","created_at":"2026-05-18T03:09:24Z"},{"alias_kind":"pith_short_12","alias_value":"RWGTGDEGJGP2","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"RWGTGDEGJGP26HQB","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"RWGTGDEG","created_at":"2026-05-18T12:27:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:RWGTGDEGJGP26HQBNNRMUHFFOO","target":"record","payload":{"canonical_record":{"source":{"id":"1310.5882","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-22T11:27:10Z","cross_cats_sorted":[],"title_canon_sha256":"6ac66dd7bed46f4d02df914c4d37eef8eaac488eb981c85ef5fa43e5d8b91a97","abstract_canon_sha256":"476b1de5c5d1374964af7f0493983b4149c8990f81fecdcd6cfd627a70878984"},"schema_version":"1.0"},"canonical_sha256":"8d8d330c86499faf1e016b62ca1ca573a098a42a16affa7c9792ec32be7c6ffd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:09:24.346420Z","signature_b64":"L9omrWcXLcfTpS89/DNa7VjTAJwox12OeNAoj5lzOhtOcK84GeCXfxztnmVnhGaL2d6OVmiI5q3P7QAbh5yxBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8d8d330c86499faf1e016b62ca1ca573a098a42a16affa7c9792ec32be7c6ffd","last_reissued_at":"2026-05-18T03:09:24.345776Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:09:24.345776Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.5882","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":"2026-05-18T03:09:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fpmn1pzL2VaSslDSjKWERidfkjk5gXDZ+Uz9SINpuqwuWmAsvbAnKYRNE9xOTldVBYgstQnbUyCXYxU/U2jQAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T15:39:54.915773Z"},"content_sha256":"f372fa4f090fba34a7ffaaf15f4a79b45908f822ccf99a34eb72ede4c79177bd","schema_version":"1.0","event_id":"sha256:f372fa4f090fba34a7ffaaf15f4a79b45908f822ccf99a34eb72ede4c79177bd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:RWGTGDEGJGP26HQBNNRMUHFFOO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lower bounds on the maximum number of non-crossing acyclic graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Anna de Mier, Clemens Huemer","submitted_at":"2013-10-22T11:27:10Z","abstract_excerpt":"This paper is a contribution to the problem of counting geometric graphs on point sets. More concretely, we look at the maximum numbers of non-crossing spanning trees and forests. We show that the so-called double chain point configuration of N points has Omega(12.52^N) non-crossing spanning trees and Omega(13.61^N) non-crossing forests. This improves the previous lower bounds on the maximum number of non-crossing spanning trees and of non-crossing forests among all sets of N points in general position given by Dumitrescu, Schulz, Sheffer and T\\'oth. Our analysis relies on the tools of analyti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.5882","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":"2026-05-18T03:09:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kjSGNgmvI2f6fvh9lBGa9ztBGDim4FUBVP9g+EmtU419uD3rg/Pf3902HSDrocFkXKbF+BmVJOQH1H6AhL80BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T15:39:54.916117Z"},"content_sha256":"8bc75c8bcc9221e99eb7ccd2800aab83e92ece582b43b4cb6872f758aef3bb65","schema_version":"1.0","event_id":"sha256:8bc75c8bcc9221e99eb7ccd2800aab83e92ece582b43b4cb6872f758aef3bb65"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RWGTGDEGJGP26HQBNNRMUHFFOO/bundle.json","state_url":"https://pith.science/pith/RWGTGDEGJGP26HQBNNRMUHFFOO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RWGTGDEGJGP26HQBNNRMUHFFOO/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":"2026-06-02T15:39:54Z","links":{"resolver":"https://pith.science/pith/RWGTGDEGJGP26HQBNNRMUHFFOO","bundle":"https://pith.science/pith/RWGTGDEGJGP26HQBNNRMUHFFOO/bundle.json","state":"https://pith.science/pith/RWGTGDEGJGP26HQBNNRMUHFFOO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RWGTGDEGJGP26HQBNNRMUHFFOO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:RWGTGDEGJGP26HQBNNRMUHFFOO","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":"476b1de5c5d1374964af7f0493983b4149c8990f81fecdcd6cfd627a70878984","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-22T11:27:10Z","title_canon_sha256":"6ac66dd7bed46f4d02df914c4d37eef8eaac488eb981c85ef5fa43e5d8b91a97"},"schema_version":"1.0","source":{"id":"1310.5882","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.5882","created_at":"2026-05-18T03:09:24Z"},{"alias_kind":"arxiv_version","alias_value":"1310.5882v1","created_at":"2026-05-18T03:09:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.5882","created_at":"2026-05-18T03:09:24Z"},{"alias_kind":"pith_short_12","alias_value":"RWGTGDEGJGP2","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"RWGTGDEGJGP26HQB","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"RWGTGDEG","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:8bc75c8bcc9221e99eb7ccd2800aab83e92ece582b43b4cb6872f758aef3bb65","target":"graph","created_at":"2026-05-18T03:09:24Z","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 paper is a contribution to the problem of counting geometric graphs on point sets. More concretely, we look at the maximum numbers of non-crossing spanning trees and forests. We show that the so-called double chain point configuration of N points has Omega(12.52^N) non-crossing spanning trees and Omega(13.61^N) non-crossing forests. This improves the previous lower bounds on the maximum number of non-crossing spanning trees and of non-crossing forests among all sets of N points in general position given by Dumitrescu, Schulz, Sheffer and T\\'oth. Our analysis relies on the tools of analyti","authors_text":"Anna de Mier, Clemens Huemer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-22T11:27:10Z","title":"Lower bounds on the maximum number of non-crossing acyclic graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.5882","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:f372fa4f090fba34a7ffaaf15f4a79b45908f822ccf99a34eb72ede4c79177bd","target":"record","created_at":"2026-05-18T03:09:24Z","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":"476b1de5c5d1374964af7f0493983b4149c8990f81fecdcd6cfd627a70878984","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-22T11:27:10Z","title_canon_sha256":"6ac66dd7bed46f4d02df914c4d37eef8eaac488eb981c85ef5fa43e5d8b91a97"},"schema_version":"1.0","source":{"id":"1310.5882","kind":"arxiv","version":1}},"canonical_sha256":"8d8d330c86499faf1e016b62ca1ca573a098a42a16affa7c9792ec32be7c6ffd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d8d330c86499faf1e016b62ca1ca573a098a42a16affa7c9792ec32be7c6ffd","first_computed_at":"2026-05-18T03:09:24.345776Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:09:24.345776Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L9omrWcXLcfTpS89/DNa7VjTAJwox12OeNAoj5lzOhtOcK84GeCXfxztnmVnhGaL2d6OVmiI5q3P7QAbh5yxBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:09:24.346420Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.5882","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f372fa4f090fba34a7ffaaf15f4a79b45908f822ccf99a34eb72ede4c79177bd","sha256:8bc75c8bcc9221e99eb7ccd2800aab83e92ece582b43b4cb6872f758aef3bb65"],"state_sha256":"9a0a47766b883531f0fcde7fcb26f30c41eb320ceb42240adf9d2b7333da3f9a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zXG8sch7CCqLiYZhx41QsBhja/WxhWcNQ6tqI4vnLGGltXIdcnZqv5cAMp8cNoQiFkoTjjY4r5FxB7MeP0hNCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T15:39:54.918026Z","bundle_sha256":"64eb67e9bfdd7b51b69706241448e00c70882be54f5b5f604746b4c579645dab"}}