{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:43K6GO7X73RONN5EQPIV4GHQGJ","short_pith_number":"pith:43K6GO7X","canonical_record":{"source":{"id":"1311.7001","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-11-27T15:21:57Z","cross_cats_sorted":[],"title_canon_sha256":"fe271452eb1fc6318294d1545e9c71a3717d0bd1e0c595b1a47808a40776665b","abstract_canon_sha256":"96829f79b8de6506a9128588dc8c4b5bf967c087657401ee141f42ec4ace28d8"},"schema_version":"1.0"},"canonical_sha256":"e6d5e33bf7fee2e6b7a483d15e18f03263c6eedb6de5b72c4716435bc7195f70","source":{"kind":"arxiv","id":"1311.7001","version":6},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.7001","created_at":"2026-05-18T00:20:27Z"},{"alias_kind":"arxiv_version","alias_value":"1311.7001v6","created_at":"2026-05-18T00:20:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.7001","created_at":"2026-05-18T00:20:27Z"},{"alias_kind":"pith_short_12","alias_value":"43K6GO7X73RO","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"43K6GO7X73RONN5E","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"43K6GO7X","created_at":"2026-05-18T12:27:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:43K6GO7X73RONN5EQPIV4GHQGJ","target":"record","payload":{"canonical_record":{"source":{"id":"1311.7001","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-11-27T15:21:57Z","cross_cats_sorted":[],"title_canon_sha256":"fe271452eb1fc6318294d1545e9c71a3717d0bd1e0c595b1a47808a40776665b","abstract_canon_sha256":"96829f79b8de6506a9128588dc8c4b5bf967c087657401ee141f42ec4ace28d8"},"schema_version":"1.0"},"canonical_sha256":"e6d5e33bf7fee2e6b7a483d15e18f03263c6eedb6de5b72c4716435bc7195f70","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:27.952548Z","signature_b64":"wADI7JH1zh/YcxO324YeDGhZg37Z2Q85XG6FPdKAXKjp3Yvz1DzJrGLCv+tvIsjVC/OigrqZdpoqyNc69lj2DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e6d5e33bf7fee2e6b7a483d15e18f03263c6eedb6de5b72c4716435bc7195f70","last_reissued_at":"2026-05-18T00:20:27.951970Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:27.951970Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.7001","source_version":6,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:20:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pYOkDe1QuzC4r5iCXokeEZY9F4E7LGiMcgh39jiJqkTHDkk7l140xWKMyXegRDUMmw5aat87TLqeJcl6CfYHAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T05:49:31.552662Z"},"content_sha256":"657af916918d1d41f0b234659c0e4d487302c0ba17439c431c490661a545e2ff","schema_version":"1.0","event_id":"sha256:657af916918d1d41f0b234659c0e4d487302c0ba17439c431c490661a545e2ff"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:43K6GO7X73RONN5EQPIV4GHQGJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Clique trees of infinite locally finite chordal graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Christoph Hofer-Temmel, Florian Lehner","submitted_at":"2013-11-27T15:21:57Z","abstract_excerpt":"We investigate clique trees of infinite locally finite chordal graphs. Our main contribution is a bijection between the set of clique trees and the product of local finite families of finite trees. Even more, the edges of a clique tree are in bijection with the edges of the corresponding collection of finite trees. This allows us to enumerate the clique trees of a chordal graph and extend various classic characterisations of clique trees to the infinite setting."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.7001","kind":"arxiv","version":6},"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":"2026-05-18T00:20:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x/v/jvTvD7C7MnMn6aYiXPp59RfgMfJn6gzXeadQCW5/9qIXpj4tIiVALMOQIgkgn6CYakDA2VGg1S1RLdigAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T05:49:31.552990Z"},"content_sha256":"74a6cdeebabf35f2cbf83c52b54e44e0422d9cfaa6bd59fd88c94d1cec13b7be","schema_version":"1.0","event_id":"sha256:74a6cdeebabf35f2cbf83c52b54e44e0422d9cfaa6bd59fd88c94d1cec13b7be"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/43K6GO7X73RONN5EQPIV4GHQGJ/bundle.json","state_url":"https://pith.science/pith/43K6GO7X73RONN5EQPIV4GHQGJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/43K6GO7X73RONN5EQPIV4GHQGJ/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":"2026-06-24T05:49:31Z","links":{"resolver":"https://pith.science/pith/43K6GO7X73RONN5EQPIV4GHQGJ","bundle":"https://pith.science/pith/43K6GO7X73RONN5EQPIV4GHQGJ/bundle.json","state":"https://pith.science/pith/43K6GO7X73RONN5EQPIV4GHQGJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/43K6GO7X73RONN5EQPIV4GHQGJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:43K6GO7X73RONN5EQPIV4GHQGJ","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":"96829f79b8de6506a9128588dc8c4b5bf967c087657401ee141f42ec4ace28d8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-11-27T15:21:57Z","title_canon_sha256":"fe271452eb1fc6318294d1545e9c71a3717d0bd1e0c595b1a47808a40776665b"},"schema_version":"1.0","source":{"id":"1311.7001","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.7001","created_at":"2026-05-18T00:20:27Z"},{"alias_kind":"arxiv_version","alias_value":"1311.7001v6","created_at":"2026-05-18T00:20:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.7001","created_at":"2026-05-18T00:20:27Z"},{"alias_kind":"pith_short_12","alias_value":"43K6GO7X73RO","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"43K6GO7X73RONN5E","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"43K6GO7X","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:74a6cdeebabf35f2cbf83c52b54e44e0422d9cfaa6bd59fd88c94d1cec13b7be","target":"graph","created_at":"2026-05-18T00:20:27Z","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":"We investigate clique trees of infinite locally finite chordal graphs. Our main contribution is a bijection between the set of clique trees and the product of local finite families of finite trees. Even more, the edges of a clique tree are in bijection with the edges of the corresponding collection of finite trees. This allows us to enumerate the clique trees of a chordal graph and extend various classic characterisations of clique trees to the infinite setting.","authors_text":"Christoph Hofer-Temmel, Florian Lehner","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-11-27T15:21:57Z","title":"Clique trees of infinite locally finite chordal graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.7001","kind":"arxiv","version":6},"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":"sha256:657af916918d1d41f0b234659c0e4d487302c0ba17439c431c490661a545e2ff","target":"record","created_at":"2026-05-18T00:20:27Z","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":"96829f79b8de6506a9128588dc8c4b5bf967c087657401ee141f42ec4ace28d8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-11-27T15:21:57Z","title_canon_sha256":"fe271452eb1fc6318294d1545e9c71a3717d0bd1e0c595b1a47808a40776665b"},"schema_version":"1.0","source":{"id":"1311.7001","kind":"arxiv","version":6}},"canonical_sha256":"e6d5e33bf7fee2e6b7a483d15e18f03263c6eedb6de5b72c4716435bc7195f70","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e6d5e33bf7fee2e6b7a483d15e18f03263c6eedb6de5b72c4716435bc7195f70","first_computed_at":"2026-05-18T00:20:27.951970Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:27.951970Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wADI7JH1zh/YcxO324YeDGhZg37Z2Q85XG6FPdKAXKjp3Yvz1DzJrGLCv+tvIsjVC/OigrqZdpoqyNc69lj2DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:27.952548Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.7001","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:657af916918d1d41f0b234659c0e4d487302c0ba17439c431c490661a545e2ff","sha256:74a6cdeebabf35f2cbf83c52b54e44e0422d9cfaa6bd59fd88c94d1cec13b7be"],"state_sha256":"75364234a6d13436b739cefc887d68598aa0f1b6c0b45d594786a1ad9a72cda7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EZCzCSU3UbAkzEnVcjXIX8I29YZHg3eL70GGQsAnkvro0xA/SoLCojm0QhBwAyt6nXmAe2JstJsoxVaTyUxzBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T05:49:31.554865Z","bundle_sha256":"3738b75e0072745d70acf7e3a18caf918b1c5e76208f6e95e5234dfc2d6bf710"}}