{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:ALP5GADM47LMHPX747HWRLAAV5","short_pith_number":"pith:ALP5GADM","canonical_record":{"source":{"id":"1309.4266","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-09-17T11:43:03Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"eec4ac9c3123190784615a0d6ea6a92bbe86ed36809b1228d10e85cb8e97d78f","abstract_canon_sha256":"1ce9ee8f6e9f5830331957635e87f31d10ad03587ddfae77c0ddf506f4c4550e"},"schema_version":"1.0"},"canonical_sha256":"02dfd3006ce7d6c3beffe7cf68ac00af7822cf92a35e62f7ac03983b9d8db9a0","source":{"kind":"arxiv","id":"1309.4266","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.4266","created_at":"2026-05-18T03:13:09Z"},{"alias_kind":"arxiv_version","alias_value":"1309.4266v1","created_at":"2026-05-18T03:13:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.4266","created_at":"2026-05-18T03:13:09Z"},{"alias_kind":"pith_short_12","alias_value":"ALP5GADM47LM","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"ALP5GADM47LMHPX7","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"ALP5GADM","created_at":"2026-05-18T12:27:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:ALP5GADM47LMHPX747HWRLAAV5","target":"record","payload":{"canonical_record":{"source":{"id":"1309.4266","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-09-17T11:43:03Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"eec4ac9c3123190784615a0d6ea6a92bbe86ed36809b1228d10e85cb8e97d78f","abstract_canon_sha256":"1ce9ee8f6e9f5830331957635e87f31d10ad03587ddfae77c0ddf506f4c4550e"},"schema_version":"1.0"},"canonical_sha256":"02dfd3006ce7d6c3beffe7cf68ac00af7822cf92a35e62f7ac03983b9d8db9a0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:13:09.158515Z","signature_b64":"42HNtGbdL90jvHXsm1TfFvkF5LEzvEZoj6mTr52OvfGS/zO4rX51PtzNBM2YGY/TDOr1IStf1W/N3GEBj9dHCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"02dfd3006ce7d6c3beffe7cf68ac00af7822cf92a35e62f7ac03983b9d8db9a0","last_reissued_at":"2026-05-18T03:13:09.157710Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:13:09.157710Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.4266","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":"2026-05-18T03:13:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QdTRUvR/lVKr/oys8RFQlayaPMcbKIQxvJjAhcydVsZHcaTiaS7p98sbXuxOAqBigNsnUa0XgsJOdqZ+FzePDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T14:22:38.054867Z"},"content_sha256":"6efd7ea08d397f49c20b9734cfdb94c0af7bd7f43739c72035ab0171927b7fd1","schema_version":"1.0","event_id":"sha256:6efd7ea08d397f49c20b9734cfdb94c0af7bd7f43739c72035ab0171927b7fd1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:ALP5GADM47LMHPX747HWRLAAV5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Complexities of relational structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"math.CO","authors_text":"David Hartman, Jan Hubicka, Jaroslav Nesetril","submitted_at":"2013-09-17T11:43:03Z","abstract_excerpt":"The relational complexity, introduced by G. Cherlin, G. Martin, and D. Saracino, is a measure of ultrahomogeneity of a relational structure. It provides an information on minimal arity of additional invariant relations needed to turn given structure into an ultrahomogeneous one. The original motivation was group theory. This work focuses more on structures and provides an alternative approach. Our study is motivated by related concept of lift complexity studied by Hubicka and Nesetril."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4266","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":"2026-05-18T03:13:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oPU12zDf6V3QN5i1KwpdBll/s1NrY4yJH1eXp04TXwhebC32pfmVsYHS9ffZ10s6ZlaVKiCofyGXiJfqjMvHCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T14:22:38.055594Z"},"content_sha256":"6a239c45d14e3f6f897e20d66f3d16765e3623c056e3c5c852d00796171e242b","schema_version":"1.0","event_id":"sha256:6a239c45d14e3f6f897e20d66f3d16765e3623c056e3c5c852d00796171e242b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ALP5GADM47LMHPX747HWRLAAV5/bundle.json","state_url":"https://pith.science/pith/ALP5GADM47LMHPX747HWRLAAV5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ALP5GADM47LMHPX747HWRLAAV5/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":"2026-06-06T14:22:38Z","links":{"resolver":"https://pith.science/pith/ALP5GADM47LMHPX747HWRLAAV5","bundle":"https://pith.science/pith/ALP5GADM47LMHPX747HWRLAAV5/bundle.json","state":"https://pith.science/pith/ALP5GADM47LMHPX747HWRLAAV5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ALP5GADM47LMHPX747HWRLAAV5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ALP5GADM47LMHPX747HWRLAAV5","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":"1ce9ee8f6e9f5830331957635e87f31d10ad03587ddfae77c0ddf506f4c4550e","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-09-17T11:43:03Z","title_canon_sha256":"eec4ac9c3123190784615a0d6ea6a92bbe86ed36809b1228d10e85cb8e97d78f"},"schema_version":"1.0","source":{"id":"1309.4266","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.4266","created_at":"2026-05-18T03:13:09Z"},{"alias_kind":"arxiv_version","alias_value":"1309.4266v1","created_at":"2026-05-18T03:13:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.4266","created_at":"2026-05-18T03:13:09Z"},{"alias_kind":"pith_short_12","alias_value":"ALP5GADM47LM","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"ALP5GADM47LMHPX7","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"ALP5GADM","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:6a239c45d14e3f6f897e20d66f3d16765e3623c056e3c5c852d00796171e242b","target":"graph","created_at":"2026-05-18T03:13:09Z","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":"The relational complexity, introduced by G. Cherlin, G. Martin, and D. Saracino, is a measure of ultrahomogeneity of a relational structure. It provides an information on minimal arity of additional invariant relations needed to turn given structure into an ultrahomogeneous one. The original motivation was group theory. This work focuses more on structures and provides an alternative approach. Our study is motivated by related concept of lift complexity studied by Hubicka and Nesetril.","authors_text":"David Hartman, Jan Hubicka, Jaroslav Nesetril","cross_cats":["cs.CC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-09-17T11:43:03Z","title":"Complexities of relational structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4266","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":"sha256:6efd7ea08d397f49c20b9734cfdb94c0af7bd7f43739c72035ab0171927b7fd1","target":"record","created_at":"2026-05-18T03:13:09Z","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":"1ce9ee8f6e9f5830331957635e87f31d10ad03587ddfae77c0ddf506f4c4550e","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-09-17T11:43:03Z","title_canon_sha256":"eec4ac9c3123190784615a0d6ea6a92bbe86ed36809b1228d10e85cb8e97d78f"},"schema_version":"1.0","source":{"id":"1309.4266","kind":"arxiv","version":1}},"canonical_sha256":"02dfd3006ce7d6c3beffe7cf68ac00af7822cf92a35e62f7ac03983b9d8db9a0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"02dfd3006ce7d6c3beffe7cf68ac00af7822cf92a35e62f7ac03983b9d8db9a0","first_computed_at":"2026-05-18T03:13:09.157710Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:13:09.157710Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"42HNtGbdL90jvHXsm1TfFvkF5LEzvEZoj6mTr52OvfGS/zO4rX51PtzNBM2YGY/TDOr1IStf1W/N3GEBj9dHCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:13:09.158515Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.4266","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6efd7ea08d397f49c20b9734cfdb94c0af7bd7f43739c72035ab0171927b7fd1","sha256:6a239c45d14e3f6f897e20d66f3d16765e3623c056e3c5c852d00796171e242b"],"state_sha256":"be8ae104a3285a7048f410dae3b41528d90bd38133516ef6876f42bd098e77b9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hRMfBONwXvgCoVI7ZCqX26psa26jUBel6LO8t0j3eDOiWu1icCMP1pqdw+PuFiCvxgoIYfXzS+q76deQvMm8DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T14:22:38.059664Z","bundle_sha256":"2f4fc256422aaf6c2b5d9978b8dccebc998b5c855e7c8e775e34ddc349347710"}}