{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:HMFAD5EJFHQYS2TCED6VYL7CSR","short_pith_number":"pith:HMFAD5EJ","canonical_record":{"source":{"id":"1403.5546","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-21T19:10:28Z","cross_cats_sorted":["cs.CG","cs.DM"],"title_canon_sha256":"f7a1980274f0c061ad4f3d45502b6b7aefd1973ab5cf2d95de9c63f451a8ffcd","abstract_canon_sha256":"82fcef478a652f3fe8c0e64f519b9639c0fe922f97ebc65ed01e777016b7a40f"},"schema_version":"1.0"},"canonical_sha256":"3b0a01f48929e1896a6220fd5c2fe294657e0ef2f6637d96f16e02adc53a5106","source":{"kind":"arxiv","id":"1403.5546","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.5546","created_at":"2026-05-18T02:55:50Z"},{"alias_kind":"arxiv_version","alias_value":"1403.5546v1","created_at":"2026-05-18T02:55:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.5546","created_at":"2026-05-18T02:55:50Z"},{"alias_kind":"pith_short_12","alias_value":"HMFAD5EJFHQY","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HMFAD5EJFHQYS2TC","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HMFAD5EJ","created_at":"2026-05-18T12:28:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:HMFAD5EJFHQYS2TCED6VYL7CSR","target":"record","payload":{"canonical_record":{"source":{"id":"1403.5546","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-21T19:10:28Z","cross_cats_sorted":["cs.CG","cs.DM"],"title_canon_sha256":"f7a1980274f0c061ad4f3d45502b6b7aefd1973ab5cf2d95de9c63f451a8ffcd","abstract_canon_sha256":"82fcef478a652f3fe8c0e64f519b9639c0fe922f97ebc65ed01e777016b7a40f"},"schema_version":"1.0"},"canonical_sha256":"3b0a01f48929e1896a6220fd5c2fe294657e0ef2f6637d96f16e02adc53a5106","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:55:50.272332Z","signature_b64":"0c6UMR2KNvv9NHy7Al0YEaH3X0VEvAPP0p/lPqyTzg/ph/FbEaGC+ooeioCB5cvW4q0u+dLSWLxhI4MlZTisBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b0a01f48929e1896a6220fd5c2fe294657e0ef2f6637d96f16e02adc53a5106","last_reissued_at":"2026-05-18T02:55:50.271619Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:55:50.271619Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.5546","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":"2026-05-18T02:55:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h/Yn4n6J3J9LbqkDhlqaBv+pKJIKKv3a5bGutXKww68t9SZV3cBwbPn3bK9BASrog5KdEW7QH04+lW1wjwNODA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T09:41:36.422149Z"},"content_sha256":"bb637024eccc6bed470d8fdc6eaad51ce43ee91d6455e7e456cf0e75df2d8d92","schema_version":"1.0","event_id":"sha256:bb637024eccc6bed470d8fdc6eaad51ce43ee91d6455e7e456cf0e75df2d8d92"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:HMFAD5EJFHQYS2TCED6VYL7CSR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Disjoint compatibility graph of non-crossing matchings of points in convex position","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","cs.DM"],"primary_cat":"math.CO","authors_text":"Andrei Asinowski, Oswin Aichholzer, Tillmann Miltzow","submitted_at":"2014-03-21T19:10:28Z","abstract_excerpt":"Let $X_{2k}$ be a set of $2k$ labeled points in convex position in the plane. We consider geometric non-intersecting straight-line perfect matchings of $X_{2k}$. Two such matchings, $M$ and $M'$, are disjoint compatible if they do not have common edges, and no edge of $M$ crosses an edge of $M'$. Denote by $\\mathrm{DCM}_k$ the graph whose vertices correspond to such matchings, and two vertices are adjacent if and only if the corresponding matchings are disjoint compatible. We show that for each $k \\geq 9$, the connected components of $\\mathrm{DCM}_k$ form exactly three isomorphism classes -- n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5546","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":"2026-05-18T02:55:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WsZjZYkVxgrdr063tBdVNt+OQDX5TMPi4Gd8oE14A+kqsEL/vEbSsQfRPZh1GXY1On3BvvSx3ItJSuc0HvLLBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T09:41:36.422878Z"},"content_sha256":"91c690784cfd930ca8fbf96255ae9421fb0d16d652ddb29e6dd1ed8be3aa5eb1","schema_version":"1.0","event_id":"sha256:91c690784cfd930ca8fbf96255ae9421fb0d16d652ddb29e6dd1ed8be3aa5eb1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HMFAD5EJFHQYS2TCED6VYL7CSR/bundle.json","state_url":"https://pith.science/pith/HMFAD5EJFHQYS2TCED6VYL7CSR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HMFAD5EJFHQYS2TCED6VYL7CSR/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":"2026-05-26T09:41:36Z","links":{"resolver":"https://pith.science/pith/HMFAD5EJFHQYS2TCED6VYL7CSR","bundle":"https://pith.science/pith/HMFAD5EJFHQYS2TCED6VYL7CSR/bundle.json","state":"https://pith.science/pith/HMFAD5EJFHQYS2TCED6VYL7CSR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HMFAD5EJFHQYS2TCED6VYL7CSR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:HMFAD5EJFHQYS2TCED6VYL7CSR","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":"82fcef478a652f3fe8c0e64f519b9639c0fe922f97ebc65ed01e777016b7a40f","cross_cats_sorted":["cs.CG","cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-21T19:10:28Z","title_canon_sha256":"f7a1980274f0c061ad4f3d45502b6b7aefd1973ab5cf2d95de9c63f451a8ffcd"},"schema_version":"1.0","source":{"id":"1403.5546","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.5546","created_at":"2026-05-18T02:55:50Z"},{"alias_kind":"arxiv_version","alias_value":"1403.5546v1","created_at":"2026-05-18T02:55:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.5546","created_at":"2026-05-18T02:55:50Z"},{"alias_kind":"pith_short_12","alias_value":"HMFAD5EJFHQY","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HMFAD5EJFHQYS2TC","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HMFAD5EJ","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:91c690784cfd930ca8fbf96255ae9421fb0d16d652ddb29e6dd1ed8be3aa5eb1","target":"graph","created_at":"2026-05-18T02:55:50Z","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":"Let $X_{2k}$ be a set of $2k$ labeled points in convex position in the plane. We consider geometric non-intersecting straight-line perfect matchings of $X_{2k}$. Two such matchings, $M$ and $M'$, are disjoint compatible if they do not have common edges, and no edge of $M$ crosses an edge of $M'$. Denote by $\\mathrm{DCM}_k$ the graph whose vertices correspond to such matchings, and two vertices are adjacent if and only if the corresponding matchings are disjoint compatible. We show that for each $k \\geq 9$, the connected components of $\\mathrm{DCM}_k$ form exactly three isomorphism classes -- n","authors_text":"Andrei Asinowski, Oswin Aichholzer, Tillmann Miltzow","cross_cats":["cs.CG","cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-21T19:10:28Z","title":"Disjoint compatibility graph of non-crossing matchings of points in convex position"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5546","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:bb637024eccc6bed470d8fdc6eaad51ce43ee91d6455e7e456cf0e75df2d8d92","target":"record","created_at":"2026-05-18T02:55:50Z","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":"82fcef478a652f3fe8c0e64f519b9639c0fe922f97ebc65ed01e777016b7a40f","cross_cats_sorted":["cs.CG","cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-21T19:10:28Z","title_canon_sha256":"f7a1980274f0c061ad4f3d45502b6b7aefd1973ab5cf2d95de9c63f451a8ffcd"},"schema_version":"1.0","source":{"id":"1403.5546","kind":"arxiv","version":1}},"canonical_sha256":"3b0a01f48929e1896a6220fd5c2fe294657e0ef2f6637d96f16e02adc53a5106","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b0a01f48929e1896a6220fd5c2fe294657e0ef2f6637d96f16e02adc53a5106","first_computed_at":"2026-05-18T02:55:50.271619Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:55:50.271619Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0c6UMR2KNvv9NHy7Al0YEaH3X0VEvAPP0p/lPqyTzg/ph/FbEaGC+ooeioCB5cvW4q0u+dLSWLxhI4MlZTisBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:55:50.272332Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.5546","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bb637024eccc6bed470d8fdc6eaad51ce43ee91d6455e7e456cf0e75df2d8d92","sha256:91c690784cfd930ca8fbf96255ae9421fb0d16d652ddb29e6dd1ed8be3aa5eb1"],"state_sha256":"6a0185af6ad80c0b5a76d25d8b2bd109bc970bff1c698be71da83fab7d7de1bf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0hCvtC4mGaPzf8C+8oOQdqjmd/rz/PzB7f/SkmdbnlmxA6g0iohKJSwPA3qPy/lIZZt4uPbTKlUQxlTemvx9AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T09:41:36.426518Z","bundle_sha256":"7c993155cb73e1f5c427aa6d1743fec4760d6a1a4f8405083a4ce21524333824"}}