{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:YLQV642FFP366JCWTNG4SUB7JF","short_pith_number":"pith:YLQV642F","canonical_record":{"source":{"id":"1404.1714","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CO","submitted_at":"2014-04-07T09:55:31Z","cross_cats_sorted":[],"title_canon_sha256":"aab6213459e258ed922684588012147915b9a20684169364e2a95c01b38b4894","abstract_canon_sha256":"33d3425b379138f6df79821fca7464db3b313d4c82e5a1124cdf903aad821278"},"schema_version":"1.0"},"canonical_sha256":"c2e15f73452bf7ef24569b4dc9503f494791b5452c321d56257898984ebaa71f","source":{"kind":"arxiv","id":"1404.1714","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.1714","created_at":"2026-05-18T02:54:40Z"},{"alias_kind":"arxiv_version","alias_value":"1404.1714v1","created_at":"2026-05-18T02:54:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.1714","created_at":"2026-05-18T02:54:40Z"},{"alias_kind":"pith_short_12","alias_value":"YLQV642FFP36","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"YLQV642FFP366JCW","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"YLQV642F","created_at":"2026-05-18T12:28:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:YLQV642FFP366JCWTNG4SUB7JF","target":"record","payload":{"canonical_record":{"source":{"id":"1404.1714","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CO","submitted_at":"2014-04-07T09:55:31Z","cross_cats_sorted":[],"title_canon_sha256":"aab6213459e258ed922684588012147915b9a20684169364e2a95c01b38b4894","abstract_canon_sha256":"33d3425b379138f6df79821fca7464db3b313d4c82e5a1124cdf903aad821278"},"schema_version":"1.0"},"canonical_sha256":"c2e15f73452bf7ef24569b4dc9503f494791b5452c321d56257898984ebaa71f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:40.316325Z","signature_b64":"ggQdGTDxYwPyXyChP0dBf7St89oC5VShA/EqvG0kAyYOLFdfyGSVOj3tVGu/SqV5T2CuTb2YtTCV1UGK2PgIAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c2e15f73452bf7ef24569b4dc9503f494791b5452c321d56257898984ebaa71f","last_reissued_at":"2026-05-18T02:54:40.315902Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:40.315902Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.1714","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":"2026-05-18T02:54:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A5JMYx/67UjHPp0KuBf/LNti4Cv4dzvEs1+L0yvXpScl7GKiVm8KBr4dpVJktMyJxRxlh7Fj6q9JirDdC1U2Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T18:37:10.468884Z"},"content_sha256":"cc12dd506240fcf94ff2c58c43ba55d3581cc208a2cfdca45584325398b46719","schema_version":"1.0","event_id":"sha256:cc12dd506240fcf94ff2c58c43ba55d3581cc208a2cfdca45584325398b46719"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:YLQV642FFP366JCWTNG4SUB7JF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Characteristics of Jaco Graphs, $J_\\infty(a), a \\in \\Bbb N$","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bettina Wilkens, Johan Kok, Mokhwetha Mabula, Paul Fisher, Vivian Mukungunugwa","submitted_at":"2014-04-07T09:55:31Z","abstract_excerpt":"We introduce the concept of a family of finite directed graphs (order a) which are directed graphs derived from an infinite directed graph (order a), called the a-root digraph. The a-root digraph has four fundamental properties which are; $V(J_\\infty(a)) = \\{v_i|i \\in \\Bbb N\\}$ and, if $v_j$ is the head of an edge (arc) then the tail is always a vertex $v_i, i<j$ and, if$v_k$ for smallest $k \\in \\Bbb N$ is a tail vertex then all vertices $v_\\ell, k< \\ell < j$ are tails of arcs to $v_j$ and finally, the degree of vertex $k$ is $d(v_k) = ak.$ The family of finite directed graphs are those limite"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1714","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":"2026-05-18T02:54:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"psXUMxkFb5D+OvLBwCrV5YTKNC1z1V/4XUq2wAQiNs6kI/XRIX90+06VNxZ/27Ey343T4dZahBATyNhAw1+iCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T18:37:10.469232Z"},"content_sha256":"1750335d00045f888c4ae0ebae0d04a906df61490a54cdab58673f76c1816197","schema_version":"1.0","event_id":"sha256:1750335d00045f888c4ae0ebae0d04a906df61490a54cdab58673f76c1816197"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YLQV642FFP366JCWTNG4SUB7JF/bundle.json","state_url":"https://pith.science/pith/YLQV642FFP366JCWTNG4SUB7JF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YLQV642FFP366JCWTNG4SUB7JF/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":"2026-06-03T18:37:10Z","links":{"resolver":"https://pith.science/pith/YLQV642FFP366JCWTNG4SUB7JF","bundle":"https://pith.science/pith/YLQV642FFP366JCWTNG4SUB7JF/bundle.json","state":"https://pith.science/pith/YLQV642FFP366JCWTNG4SUB7JF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YLQV642FFP366JCWTNG4SUB7JF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:YLQV642FFP366JCWTNG4SUB7JF","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":"33d3425b379138f6df79821fca7464db3b313d4c82e5a1124cdf903aad821278","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CO","submitted_at":"2014-04-07T09:55:31Z","title_canon_sha256":"aab6213459e258ed922684588012147915b9a20684169364e2a95c01b38b4894"},"schema_version":"1.0","source":{"id":"1404.1714","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.1714","created_at":"2026-05-18T02:54:40Z"},{"alias_kind":"arxiv_version","alias_value":"1404.1714v1","created_at":"2026-05-18T02:54:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.1714","created_at":"2026-05-18T02:54:40Z"},{"alias_kind":"pith_short_12","alias_value":"YLQV642FFP36","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"YLQV642FFP366JCW","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"YLQV642F","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:1750335d00045f888c4ae0ebae0d04a906df61490a54cdab58673f76c1816197","target":"graph","created_at":"2026-05-18T02:54:40Z","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 introduce the concept of a family of finite directed graphs (order a) which are directed graphs derived from an infinite directed graph (order a), called the a-root digraph. The a-root digraph has four fundamental properties which are; $V(J_\\infty(a)) = \\{v_i|i \\in \\Bbb N\\}$ and, if $v_j$ is the head of an edge (arc) then the tail is always a vertex $v_i, i<j$ and, if$v_k$ for smallest $k \\in \\Bbb N$ is a tail vertex then all vertices $v_\\ell, k< \\ell < j$ are tails of arcs to $v_j$ and finally, the degree of vertex $k$ is $d(v_k) = ak.$ The family of finite directed graphs are those limite","authors_text":"Bettina Wilkens, Johan Kok, Mokhwetha Mabula, Paul Fisher, Vivian Mukungunugwa","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CO","submitted_at":"2014-04-07T09:55:31Z","title":"Characteristics of Jaco Graphs, $J_\\infty(a), a \\in \\Bbb N$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1714","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:cc12dd506240fcf94ff2c58c43ba55d3581cc208a2cfdca45584325398b46719","target":"record","created_at":"2026-05-18T02:54:40Z","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":"33d3425b379138f6df79821fca7464db3b313d4c82e5a1124cdf903aad821278","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CO","submitted_at":"2014-04-07T09:55:31Z","title_canon_sha256":"aab6213459e258ed922684588012147915b9a20684169364e2a95c01b38b4894"},"schema_version":"1.0","source":{"id":"1404.1714","kind":"arxiv","version":1}},"canonical_sha256":"c2e15f73452bf7ef24569b4dc9503f494791b5452c321d56257898984ebaa71f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c2e15f73452bf7ef24569b4dc9503f494791b5452c321d56257898984ebaa71f","first_computed_at":"2026-05-18T02:54:40.315902Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:40.315902Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ggQdGTDxYwPyXyChP0dBf7St89oC5VShA/EqvG0kAyYOLFdfyGSVOj3tVGu/SqV5T2CuTb2YtTCV1UGK2PgIAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:40.316325Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.1714","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cc12dd506240fcf94ff2c58c43ba55d3581cc208a2cfdca45584325398b46719","sha256:1750335d00045f888c4ae0ebae0d04a906df61490a54cdab58673f76c1816197"],"state_sha256":"6e66e1bacc67a6ab7bdf3688c07eae27658ae94a0bdaef9a4e3dc007fd7a22f0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fK3eQDlAvx4XQA3NuEqakyhuir4Kl5hdid4EdDbkcc4/Bj5a4fNPcxGNEvM5PrXoO0u+9+rjSEtxMvmccC80BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T18:37:10.471130Z","bundle_sha256":"39452d98e5f676a335b28891eed7765d6a67821e22cd321ac1a634613d98c27e"}}