{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:DRIEAHI2Q5HEE2EFB7XSX77HKH","short_pith_number":"pith:DRIEAHI2","canonical_record":{"source":{"id":"1409.0656","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CO","submitted_at":"2014-09-02T10:26:13Z","cross_cats_sorted":[],"title_canon_sha256":"e6489a6e94b972e578ca4cf61602d16f3f8cff716630735a724e6c71c7226c05","abstract_canon_sha256":"f1c6b8a234b6a409d4bcb0e2e936a6efc8eccb4512679461d1f4eed860b37e03"},"schema_version":"1.0"},"canonical_sha256":"1c50401d1a874e4268850fef2bffe751d125f378ea7f0fde3d2fb8540546b30f","source":{"kind":"arxiv","id":"1409.0656","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.0656","created_at":"2026-05-18T02:43:46Z"},{"alias_kind":"arxiv_version","alias_value":"1409.0656v1","created_at":"2026-05-18T02:43:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.0656","created_at":"2026-05-18T02:43:46Z"},{"alias_kind":"pith_short_12","alias_value":"DRIEAHI2Q5HE","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DRIEAHI2Q5HEE2EF","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DRIEAHI2","created_at":"2026-05-18T12:28:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:DRIEAHI2Q5HEE2EFB7XSX77HKH","target":"record","payload":{"canonical_record":{"source":{"id":"1409.0656","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CO","submitted_at":"2014-09-02T10:26:13Z","cross_cats_sorted":[],"title_canon_sha256":"e6489a6e94b972e578ca4cf61602d16f3f8cff716630735a724e6c71c7226c05","abstract_canon_sha256":"f1c6b8a234b6a409d4bcb0e2e936a6efc8eccb4512679461d1f4eed860b37e03"},"schema_version":"1.0"},"canonical_sha256":"1c50401d1a874e4268850fef2bffe751d125f378ea7f0fde3d2fb8540546b30f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:43:46.391846Z","signature_b64":"PtFS/LEh7EbDY0oKZD55J4wsZjkEA9e/jepxgCTThz+KG+aaX2w9H1NHeec5pKfbADBbPGLpjaXKb0yJFED4Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1c50401d1a874e4268850fef2bffe751d125f378ea7f0fde3d2fb8540546b30f","last_reissued_at":"2026-05-18T02:43:46.391483Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:43:46.391483Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.0656","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":"2026-05-18T02:43:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HsUzyaS3/Vv3QOMNtdpmew/WE2OHrxLL4+YNe1fJRSvSB8uTLPpQTDIByQxL321D1KikBGwPHT8Kp81w/XpwDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T00:34:14.791165Z"},"content_sha256":"eb27056d163a57986d752f9737def83c4df4b370231d4b8009f44e82b0a4b761","schema_version":"1.0","event_id":"sha256:eb27056d163a57986d752f9737def83c4df4b370231d4b8009f44e82b0a4b761"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:DRIEAHI2Q5HEE2EFB7XSX77HKH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A note on the number of edges of the Jaco Graph, $J_n(1), n \\in \\Bbb N","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Johan Kok, Vivian Mukungunugwa","submitted_at":"2014-09-02T10:26:13Z","abstract_excerpt":"Kok et.al. [3] introduced Jaco Graphs \\emph{(order 1)}. It is hoped that as a special case, a closed formula can be found for the number of edges of a finite Jaco Graph $J_n(1)$. However, the algorithms discussed in Ahlbach et.al. [1] suggest this might not be possible. Finding a closed formula for the number of edges of a Jaco Graph $J_n(1), n \\in \\Bbb N$ remains an interesting open problem. In this note we present three alternative, \\emph{formula}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.0656","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":"2026-05-18T02:43:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6L+cYFS8TT/WtwYUn/cYv6/n6Io5lfs0zGjNaptFtXsRUK2T+lLAAt2ZPVmFhe1iNQk6f6ERw9jH3ryLhfWaAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T00:34:14.791803Z"},"content_sha256":"5cfdaec7676ca3f467c1ae628a10da043dc210dacb1ef343693a9443894f7112","schema_version":"1.0","event_id":"sha256:5cfdaec7676ca3f467c1ae628a10da043dc210dacb1ef343693a9443894f7112"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DRIEAHI2Q5HEE2EFB7XSX77HKH/bundle.json","state_url":"https://pith.science/pith/DRIEAHI2Q5HEE2EFB7XSX77HKH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DRIEAHI2Q5HEE2EFB7XSX77HKH/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":"2026-06-04T00:34:14Z","links":{"resolver":"https://pith.science/pith/DRIEAHI2Q5HEE2EFB7XSX77HKH","bundle":"https://pith.science/pith/DRIEAHI2Q5HEE2EFB7XSX77HKH/bundle.json","state":"https://pith.science/pith/DRIEAHI2Q5HEE2EFB7XSX77HKH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DRIEAHI2Q5HEE2EFB7XSX77HKH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:DRIEAHI2Q5HEE2EFB7XSX77HKH","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":"f1c6b8a234b6a409d4bcb0e2e936a6efc8eccb4512679461d1f4eed860b37e03","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CO","submitted_at":"2014-09-02T10:26:13Z","title_canon_sha256":"e6489a6e94b972e578ca4cf61602d16f3f8cff716630735a724e6c71c7226c05"},"schema_version":"1.0","source":{"id":"1409.0656","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.0656","created_at":"2026-05-18T02:43:46Z"},{"alias_kind":"arxiv_version","alias_value":"1409.0656v1","created_at":"2026-05-18T02:43:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.0656","created_at":"2026-05-18T02:43:46Z"},{"alias_kind":"pith_short_12","alias_value":"DRIEAHI2Q5HE","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DRIEAHI2Q5HEE2EF","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DRIEAHI2","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:5cfdaec7676ca3f467c1ae628a10da043dc210dacb1ef343693a9443894f7112","target":"graph","created_at":"2026-05-18T02:43:46Z","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":"Kok et.al. [3] introduced Jaco Graphs \\emph{(order 1)}. It is hoped that as a special case, a closed formula can be found for the number of edges of a finite Jaco Graph $J_n(1)$. However, the algorithms discussed in Ahlbach et.al. [1] suggest this might not be possible. Finding a closed formula for the number of edges of a Jaco Graph $J_n(1), n \\in \\Bbb N$ remains an interesting open problem. In this note we present three alternative, \\emph{formula}.","authors_text":"Johan Kok, Vivian Mukungunugwa","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CO","submitted_at":"2014-09-02T10:26:13Z","title":"A note on the number of edges of the Jaco Graph, $J_n(1), n \\in \\Bbb N"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.0656","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:eb27056d163a57986d752f9737def83c4df4b370231d4b8009f44e82b0a4b761","target":"record","created_at":"2026-05-18T02:43:46Z","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":"f1c6b8a234b6a409d4bcb0e2e936a6efc8eccb4512679461d1f4eed860b37e03","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CO","submitted_at":"2014-09-02T10:26:13Z","title_canon_sha256":"e6489a6e94b972e578ca4cf61602d16f3f8cff716630735a724e6c71c7226c05"},"schema_version":"1.0","source":{"id":"1409.0656","kind":"arxiv","version":1}},"canonical_sha256":"1c50401d1a874e4268850fef2bffe751d125f378ea7f0fde3d2fb8540546b30f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c50401d1a874e4268850fef2bffe751d125f378ea7f0fde3d2fb8540546b30f","first_computed_at":"2026-05-18T02:43:46.391483Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:43:46.391483Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PtFS/LEh7EbDY0oKZD55J4wsZjkEA9e/jepxgCTThz+KG+aaX2w9H1NHeec5pKfbADBbPGLpjaXKb0yJFED4Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:43:46.391846Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.0656","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eb27056d163a57986d752f9737def83c4df4b370231d4b8009f44e82b0a4b761","sha256:5cfdaec7676ca3f467c1ae628a10da043dc210dacb1ef343693a9443894f7112"],"state_sha256":"264350851295cfdc7f846df2981fb97761b79e84ce3043f320da7d2cb3e4a24e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JnumkQZQhmZU+NB8GW9of65eunQFNdd7cGWJeFQB5SPknCd7teUStu25Zemifc9jQxL9kIM5l/PuYAia+iFjDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T00:34:14.794822Z","bundle_sha256":"bef1a0d96fb39453c98d6148d45a7a7ebc9b85d99f23b12a311fc3921c34b8f8"}}