{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:I4Y7XGXBS2XQ7BM3BXKUP6I7TD","short_pith_number":"pith:I4Y7XGXB","canonical_record":{"source":{"id":"1403.7916","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-31T09:02:56Z","cross_cats_sorted":[],"title_canon_sha256":"571164f34ca582a3c51f57cf5e2d9c89e73491c563fb3778308b70d37083ff6d","abstract_canon_sha256":"00a1c492bd7780e6dfd331b01efb615bd1188a9b84e5b4b2a0a1c4c13f1e6096"},"schema_version":"1.0"},"canonical_sha256":"4731fb9ae196af0f859b0dd547f91f98f66a03ff8d165475eceb027776297eef","source":{"kind":"arxiv","id":"1403.7916","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.7916","created_at":"2026-05-18T02:00:59Z"},{"alias_kind":"arxiv_version","alias_value":"1403.7916v3","created_at":"2026-05-18T02:00:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.7916","created_at":"2026-05-18T02:00:59Z"},{"alias_kind":"pith_short_12","alias_value":"I4Y7XGXBS2XQ","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"I4Y7XGXBS2XQ7BM3","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"I4Y7XGXB","created_at":"2026-05-18T12:28:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:I4Y7XGXBS2XQ7BM3BXKUP6I7TD","target":"record","payload":{"canonical_record":{"source":{"id":"1403.7916","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-31T09:02:56Z","cross_cats_sorted":[],"title_canon_sha256":"571164f34ca582a3c51f57cf5e2d9c89e73491c563fb3778308b70d37083ff6d","abstract_canon_sha256":"00a1c492bd7780e6dfd331b01efb615bd1188a9b84e5b4b2a0a1c4c13f1e6096"},"schema_version":"1.0"},"canonical_sha256":"4731fb9ae196af0f859b0dd547f91f98f66a03ff8d165475eceb027776297eef","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:00:59.086089Z","signature_b64":"KZFLJTeBddf4Dxq32Zj/t6fn/2cn6qzaDxr7qHleb2mx4Q2MEyU9zepZKmlo0f/3hS+357tjwwxhLQO8AXXoAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4731fb9ae196af0f859b0dd547f91f98f66a03ff8d165475eceb027776297eef","last_reissued_at":"2026-05-18T02:00:59.085581Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:00:59.085581Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.7916","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":"2026-05-18T02:00:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AFM1wNDUTVZ35WtLcZo4Bo4bjeQ7ZZh3Sn2nKcJOCv/Pq7WsynA4c7JcJzMHnLRQh0D3Nywz9YAML4Hz79lNDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T03:12:02.194537Z"},"content_sha256":"66e5a0b9414bfb82e03a57660d08b0f034d73b51abdcbe411dc0b04b084ae726","schema_version":"1.0","event_id":"sha256:66e5a0b9414bfb82e03a57660d08b0f034d73b51abdcbe411dc0b04b084ae726"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:I4Y7XGXBS2XQ7BM3BXKUP6I7TD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Study on Ornated Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Johan Kok, Sudev Naduvath, Vivian Mukungunugwa","submitted_at":"2014-03-31T09:02:56Z","abstract_excerpt":"In this paper, we introduce the notion of a finite non-simple directed graph, called an ornated graph and initiate a study on ornated graphs. An ornated graph is a directed graph on $n$ vertices, denoted by $O_n(s_l)$, whose vertices are consecutively labeled clockwise on the circumference of a circle and constructed from an ordered string $s_l$ joining them in such a way that for an odd indexed entry $a_t$ of the string, a tail $v_i$ has clockwise heads $v_j$ if and only if $(i+a_t) \\ge j$ and for an even indexed entry $a_s$ of the string a tail $v_i$ has anticlockwise heads $v_j$ if and only"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7916","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":"2026-05-18T02:00:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SYV+/TDyPABrN2mkauOEuZgRhYAZ5JreowFuCxRwN5P3GAy136FjfCe5dk4MZonY4d1CRrTXQH/ZRqoeQKHUCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T03:12:02.195266Z"},"content_sha256":"d0dff2d24854bb4dc378820dbcc63ebec3b72155193aea20e98cbb4c51b5da60","schema_version":"1.0","event_id":"sha256:d0dff2d24854bb4dc378820dbcc63ebec3b72155193aea20e98cbb4c51b5da60"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I4Y7XGXBS2XQ7BM3BXKUP6I7TD/bundle.json","state_url":"https://pith.science/pith/I4Y7XGXBS2XQ7BM3BXKUP6I7TD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I4Y7XGXBS2XQ7BM3BXKUP6I7TD/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":"2026-06-11T03:12:02Z","links":{"resolver":"https://pith.science/pith/I4Y7XGXBS2XQ7BM3BXKUP6I7TD","bundle":"https://pith.science/pith/I4Y7XGXBS2XQ7BM3BXKUP6I7TD/bundle.json","state":"https://pith.science/pith/I4Y7XGXBS2XQ7BM3BXKUP6I7TD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I4Y7XGXBS2XQ7BM3BXKUP6I7TD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:I4Y7XGXBS2XQ7BM3BXKUP6I7TD","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":"00a1c492bd7780e6dfd331b01efb615bd1188a9b84e5b4b2a0a1c4c13f1e6096","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-31T09:02:56Z","title_canon_sha256":"571164f34ca582a3c51f57cf5e2d9c89e73491c563fb3778308b70d37083ff6d"},"schema_version":"1.0","source":{"id":"1403.7916","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.7916","created_at":"2026-05-18T02:00:59Z"},{"alias_kind":"arxiv_version","alias_value":"1403.7916v3","created_at":"2026-05-18T02:00:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.7916","created_at":"2026-05-18T02:00:59Z"},{"alias_kind":"pith_short_12","alias_value":"I4Y7XGXBS2XQ","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"I4Y7XGXBS2XQ7BM3","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"I4Y7XGXB","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:d0dff2d24854bb4dc378820dbcc63ebec3b72155193aea20e98cbb4c51b5da60","target":"graph","created_at":"2026-05-18T02:00:59Z","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":"In this paper, we introduce the notion of a finite non-simple directed graph, called an ornated graph and initiate a study on ornated graphs. An ornated graph is a directed graph on $n$ vertices, denoted by $O_n(s_l)$, whose vertices are consecutively labeled clockwise on the circumference of a circle and constructed from an ordered string $s_l$ joining them in such a way that for an odd indexed entry $a_t$ of the string, a tail $v_i$ has clockwise heads $v_j$ if and only if $(i+a_t) \\ge j$ and for an even indexed entry $a_s$ of the string a tail $v_i$ has anticlockwise heads $v_j$ if and only","authors_text":"Johan Kok, Sudev Naduvath, Vivian Mukungunugwa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-31T09:02:56Z","title":"A Study on Ornated Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7916","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":"sha256:66e5a0b9414bfb82e03a57660d08b0f034d73b51abdcbe411dc0b04b084ae726","target":"record","created_at":"2026-05-18T02:00:59Z","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":"00a1c492bd7780e6dfd331b01efb615bd1188a9b84e5b4b2a0a1c4c13f1e6096","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-31T09:02:56Z","title_canon_sha256":"571164f34ca582a3c51f57cf5e2d9c89e73491c563fb3778308b70d37083ff6d"},"schema_version":"1.0","source":{"id":"1403.7916","kind":"arxiv","version":3}},"canonical_sha256":"4731fb9ae196af0f859b0dd547f91f98f66a03ff8d165475eceb027776297eef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4731fb9ae196af0f859b0dd547f91f98f66a03ff8d165475eceb027776297eef","first_computed_at":"2026-05-18T02:00:59.085581Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:00:59.085581Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KZFLJTeBddf4Dxq32Zj/t6fn/2cn6qzaDxr7qHleb2mx4Q2MEyU9zepZKmlo0f/3hS+357tjwwxhLQO8AXXoAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:00:59.086089Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.7916","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:66e5a0b9414bfb82e03a57660d08b0f034d73b51abdcbe411dc0b04b084ae726","sha256:d0dff2d24854bb4dc378820dbcc63ebec3b72155193aea20e98cbb4c51b5da60"],"state_sha256":"09ce33c2529e68641074eaca21be364d659e30a5c8778e5bb74f158e7e425b98"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UMbtrts6VCkaCPKJU8EqcHC4gHcaybNypyDCEBNApr2yaP+sRpCSeae5PhR0T0ZdZHNH7ZVy6OBdHyhLJKIDAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T03:12:02.199597Z","bundle_sha256":"35f7104a2f050ea15f4f625e3466ff5ad47d2477228b5b862400aaa6351716dd"}}