{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:P6ZCDRRMTSNYMPZYNBX7KBIXKL","short_pith_number":"pith:P6ZCDRRM","canonical_record":{"source":{"id":"1102.3177","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-02-15T20:49:50Z","cross_cats_sorted":["q-bio.QM"],"title_canon_sha256":"3dfaca1db68760dc93b8909d969c4ea93b7d59c4f42fe700fd71fb7fa907bfdd","abstract_canon_sha256":"561211601de71a9ea435fe2a77ff540c8b913d17f41c05776385439d47775ffb"},"schema_version":"1.0"},"canonical_sha256":"7fb221c62c9c9b863f38686ff5051752dd7ef8da16ac63b2a362d40e654ad017","source":{"kind":"arxiv","id":"1102.3177","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.3177","created_at":"2026-05-18T04:27:17Z"},{"alias_kind":"arxiv_version","alias_value":"1102.3177v3","created_at":"2026-05-18T04:27:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.3177","created_at":"2026-05-18T04:27:17Z"},{"alias_kind":"pith_short_12","alias_value":"P6ZCDRRMTSNY","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"P6ZCDRRMTSNYMPZY","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"P6ZCDRRM","created_at":"2026-05-18T12:26:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:P6ZCDRRMTSNYMPZYNBX7KBIXKL","target":"record","payload":{"canonical_record":{"source":{"id":"1102.3177","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-02-15T20:49:50Z","cross_cats_sorted":["q-bio.QM"],"title_canon_sha256":"3dfaca1db68760dc93b8909d969c4ea93b7d59c4f42fe700fd71fb7fa907bfdd","abstract_canon_sha256":"561211601de71a9ea435fe2a77ff540c8b913d17f41c05776385439d47775ffb"},"schema_version":"1.0"},"canonical_sha256":"7fb221c62c9c9b863f38686ff5051752dd7ef8da16ac63b2a362d40e654ad017","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:27:17.508108Z","signature_b64":"uy7FTARUgZ209cenEJ7/tAJvI4fnTUOzRabQrsyzDNwAShoVFWNIAgesSCNxDO7viquNcqhbVN7WXQSobiZeCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7fb221c62c9c9b863f38686ff5051752dd7ef8da16ac63b2a362d40e654ad017","last_reissued_at":"2026-05-18T04:27:17.507469Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:27:17.507469Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.3177","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:27:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mpd2HiRZiH544lhIlyoT+XODGToepINX2S+KUstv8H4qkDHAeYIgrFvfJWcF9Z27uQ+KFHSaVTZRTvNZ+ICUBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T12:44:07.448549Z"},"content_sha256":"9f59eb9361f804143b97d1252baa0f73002888bdb9c0af1f491f6c4ff505227c","schema_version":"1.0","event_id":"sha256:9f59eb9361f804143b97d1252baa0f73002888bdb9c0af1f491f6c4ff505227c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:P6ZCDRRMTSNYMPZYNBX7KBIXKL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Kalmanson Complex","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-bio.QM"],"primary_cat":"math.CO","authors_text":"Jonathan Terhorst","submitted_at":"2011-02-15T20:49:50Z","abstract_excerpt":"Let X be a finite set of cardinality n. The Kalmanson complex K_n is the simplicial complex whose vertices are non-trivial X-splits, and whose facets are maximal circular split systems over X. In this paper we examine K_n from three perspectives. In addition to the T-theoretic description, we show that K_n has a geometric realization as the Kalmanson conditions on a finite metric. A third description arises in terms of binary matrices which possess the circular ones property. We prove the equivalence of these three definitions. This leads to a simplified proof of the well-known equivalence bet"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.3177","kind":"arxiv","version":3},"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":"2026-05-18T04:27:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HjUeyMs7iOHC9HvMs7eB3ZLB54yhF8XEDfm54kxXuja6g/vcfxytKsN4eO2Y9Z52IVaGPjfkj7omLo5WpttBAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T12:44:07.448904Z"},"content_sha256":"7ca6cb64797f6aa90ca70f66656b940252e3eca5db36db0d574a8de9e7db7aee","schema_version":"1.0","event_id":"sha256:7ca6cb64797f6aa90ca70f66656b940252e3eca5db36db0d574a8de9e7db7aee"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P6ZCDRRMTSNYMPZYNBX7KBIXKL/bundle.json","state_url":"https://pith.science/pith/P6ZCDRRMTSNYMPZYNBX7KBIXKL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P6ZCDRRMTSNYMPZYNBX7KBIXKL/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":"2026-06-08T12:44:07Z","links":{"resolver":"https://pith.science/pith/P6ZCDRRMTSNYMPZYNBX7KBIXKL","bundle":"https://pith.science/pith/P6ZCDRRMTSNYMPZYNBX7KBIXKL/bundle.json","state":"https://pith.science/pith/P6ZCDRRMTSNYMPZYNBX7KBIXKL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P6ZCDRRMTSNYMPZYNBX7KBIXKL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:P6ZCDRRMTSNYMPZYNBX7KBIXKL","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":"561211601de71a9ea435fe2a77ff540c8b913d17f41c05776385439d47775ffb","cross_cats_sorted":["q-bio.QM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-02-15T20:49:50Z","title_canon_sha256":"3dfaca1db68760dc93b8909d969c4ea93b7d59c4f42fe700fd71fb7fa907bfdd"},"schema_version":"1.0","source":{"id":"1102.3177","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.3177","created_at":"2026-05-18T04:27:17Z"},{"alias_kind":"arxiv_version","alias_value":"1102.3177v3","created_at":"2026-05-18T04:27:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.3177","created_at":"2026-05-18T04:27:17Z"},{"alias_kind":"pith_short_12","alias_value":"P6ZCDRRMTSNY","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"P6ZCDRRMTSNYMPZY","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"P6ZCDRRM","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:7ca6cb64797f6aa90ca70f66656b940252e3eca5db36db0d574a8de9e7db7aee","target":"graph","created_at":"2026-05-18T04:27:17Z","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 be a finite set of cardinality n. The Kalmanson complex K_n is the simplicial complex whose vertices are non-trivial X-splits, and whose facets are maximal circular split systems over X. In this paper we examine K_n from three perspectives. In addition to the T-theoretic description, we show that K_n has a geometric realization as the Kalmanson conditions on a finite metric. A third description arises in terms of binary matrices which possess the circular ones property. We prove the equivalence of these three definitions. This leads to a simplified proof of the well-known equivalence bet","authors_text":"Jonathan Terhorst","cross_cats":["q-bio.QM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-02-15T20:49:50Z","title":"The Kalmanson Complex"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.3177","kind":"arxiv","version":3},"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":"sha256:9f59eb9361f804143b97d1252baa0f73002888bdb9c0af1f491f6c4ff505227c","target":"record","created_at":"2026-05-18T04:27:17Z","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":"561211601de71a9ea435fe2a77ff540c8b913d17f41c05776385439d47775ffb","cross_cats_sorted":["q-bio.QM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-02-15T20:49:50Z","title_canon_sha256":"3dfaca1db68760dc93b8909d969c4ea93b7d59c4f42fe700fd71fb7fa907bfdd"},"schema_version":"1.0","source":{"id":"1102.3177","kind":"arxiv","version":3}},"canonical_sha256":"7fb221c62c9c9b863f38686ff5051752dd7ef8da16ac63b2a362d40e654ad017","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7fb221c62c9c9b863f38686ff5051752dd7ef8da16ac63b2a362d40e654ad017","first_computed_at":"2026-05-18T04:27:17.507469Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:27:17.507469Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uy7FTARUgZ209cenEJ7/tAJvI4fnTUOzRabQrsyzDNwAShoVFWNIAgesSCNxDO7viquNcqhbVN7WXQSobiZeCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:27:17.508108Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.3177","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9f59eb9361f804143b97d1252baa0f73002888bdb9c0af1f491f6c4ff505227c","sha256:7ca6cb64797f6aa90ca70f66656b940252e3eca5db36db0d574a8de9e7db7aee"],"state_sha256":"b566ca38833a609724628064e7ea6d80b7e26a77c8150cdf2adafff8dee3bedd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4Z+iGAhbYBB5DWLId9QOhy7B9J82N0xcNqncZxoE4OtHMaN6jY/iXJSO2mnNNh0BtgJ+u5u7t9DWlNjk8LHgAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T12:44:07.451404Z","bundle_sha256":"ee3a21235f6f192832b7c6878cf0b29f07d809699c3128ecfe218e63a0961b9f"}}