{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:E5QDB3YEI5UOFXKFAIW7OEGXOM","short_pith_number":"pith:E5QDB3YE","canonical_record":{"source":{"id":"1608.00856","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2016-08-01T15:50:02Z","cross_cats_sorted":[],"title_canon_sha256":"effb539493d58cde6824534f0a786f3a64b8bfaf6b2f0aae8dff48616a1df554","abstract_canon_sha256":"648a9b09f9d5400638a9d0626120b3b74f37a64402ff6c004c6131afbf9b1258"},"schema_version":"1.0"},"canonical_sha256":"276030ef044768e2dd45022df710d773020b622fc2a64238e816e9723570260a","source":{"kind":"arxiv","id":"1608.00856","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.00856","created_at":"2026-05-18T01:10:00Z"},{"alias_kind":"arxiv_version","alias_value":"1608.00856v1","created_at":"2026-05-18T01:10:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.00856","created_at":"2026-05-18T01:10:00Z"},{"alias_kind":"pith_short_12","alias_value":"E5QDB3YEI5UO","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"E5QDB3YEI5UOFXKF","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"E5QDB3YE","created_at":"2026-05-18T12:30:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:E5QDB3YEI5UOFXKFAIW7OEGXOM","target":"record","payload":{"canonical_record":{"source":{"id":"1608.00856","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2016-08-01T15:50:02Z","cross_cats_sorted":[],"title_canon_sha256":"effb539493d58cde6824534f0a786f3a64b8bfaf6b2f0aae8dff48616a1df554","abstract_canon_sha256":"648a9b09f9d5400638a9d0626120b3b74f37a64402ff6c004c6131afbf9b1258"},"schema_version":"1.0"},"canonical_sha256":"276030ef044768e2dd45022df710d773020b622fc2a64238e816e9723570260a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:00.716601Z","signature_b64":"CGcE/lrofdv9EveN7s+sFKRL4hVe6KtuC7AWriW4GFFV+ha8QI8bBVNf3kEI6LGOZYFUag3adRC/zEFAX99yDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"276030ef044768e2dd45022df710d773020b622fc2a64238e816e9723570260a","last_reissued_at":"2026-05-18T01:10:00.715905Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:00.715905Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.00856","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":"2026-05-18T01:10:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2J/9/MDXeSMf9pj99sbT65C7wI/GQLGYJ7Aw7YSPFBzARtZcFrmufGWGZg+fHGwbpbpY9fKWIrm6dYhWppYbAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T13:04:43.936667Z"},"content_sha256":"0436944b998783f475cab548d7409c42cb9360ec564ac8e190a2256fdb904ea7","schema_version":"1.0","event_id":"sha256:0436944b998783f475cab548d7409c42cb9360ec564ac8e190a2256fdb904ea7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:E5QDB3YEI5UOFXKFAIW7OEGXOM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Vertex In-Degrees of Certain Jaco-Type Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Johan Kok, K. A. Germina, K. P. Chithra, N. K. Sudev, U. Mary","submitted_at":"2016-08-01T15:50:02Z","abstract_excerpt":"The concepts of linear Jaco graphs and Jaco-type graphs have been introduced as certain types of directed graphs with specifically defined adjacency conditions. The distinct difference between a pure Jaco graph and a Jaco-type graph is that for a pure Jaco graph, the total vertex degree $d(v)$ is well-defined, while for a Jaco-type graph the vertex out-degree $d^+(v)$ is well-defined. Hence, in the case of pure Jaco graphs a challenge is to determine $d^-(v)$ and $d^+(v)$ respectively and for Jaco-type graphs a challenge is to determine $d^-(v)$. In this paper, the vertex in-degrees for Fibona"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.00856","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":"2026-05-18T01:10:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"txOWt6zG8vm4XKyKeaNjocgjtK503D/B2VrB6FfzrCvCXPwCvYiVYauuXZVau+d5XpQbW0z6v0v9OQQBle1ABA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T13:04:43.937037Z"},"content_sha256":"cee1895d4220635f6c570deac9c1d424b61bb0f151ba818e146e03a2ec742371","schema_version":"1.0","event_id":"sha256:cee1895d4220635f6c570deac9c1d424b61bb0f151ba818e146e03a2ec742371"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E5QDB3YEI5UOFXKFAIW7OEGXOM/bundle.json","state_url":"https://pith.science/pith/E5QDB3YEI5UOFXKFAIW7OEGXOM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E5QDB3YEI5UOFXKFAIW7OEGXOM/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":"2026-06-05T13:04:43Z","links":{"resolver":"https://pith.science/pith/E5QDB3YEI5UOFXKFAIW7OEGXOM","bundle":"https://pith.science/pith/E5QDB3YEI5UOFXKFAIW7OEGXOM/bundle.json","state":"https://pith.science/pith/E5QDB3YEI5UOFXKFAIW7OEGXOM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E5QDB3YEI5UOFXKFAIW7OEGXOM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:E5QDB3YEI5UOFXKFAIW7OEGXOM","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":"648a9b09f9d5400638a9d0626120b3b74f37a64402ff6c004c6131afbf9b1258","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2016-08-01T15:50:02Z","title_canon_sha256":"effb539493d58cde6824534f0a786f3a64b8bfaf6b2f0aae8dff48616a1df554"},"schema_version":"1.0","source":{"id":"1608.00856","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.00856","created_at":"2026-05-18T01:10:00Z"},{"alias_kind":"arxiv_version","alias_value":"1608.00856v1","created_at":"2026-05-18T01:10:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.00856","created_at":"2026-05-18T01:10:00Z"},{"alias_kind":"pith_short_12","alias_value":"E5QDB3YEI5UO","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"E5QDB3YEI5UOFXKF","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"E5QDB3YE","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:cee1895d4220635f6c570deac9c1d424b61bb0f151ba818e146e03a2ec742371","target":"graph","created_at":"2026-05-18T01:10:00Z","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 concepts of linear Jaco graphs and Jaco-type graphs have been introduced as certain types of directed graphs with specifically defined adjacency conditions. The distinct difference between a pure Jaco graph and a Jaco-type graph is that for a pure Jaco graph, the total vertex degree $d(v)$ is well-defined, while for a Jaco-type graph the vertex out-degree $d^+(v)$ is well-defined. Hence, in the case of pure Jaco graphs a challenge is to determine $d^-(v)$ and $d^+(v)$ respectively and for Jaco-type graphs a challenge is to determine $d^-(v)$. In this paper, the vertex in-degrees for Fibona","authors_text":"Johan Kok, K. A. Germina, K. P. Chithra, N. K. Sudev, U. Mary","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2016-08-01T15:50:02Z","title":"On the Vertex In-Degrees of Certain Jaco-Type Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.00856","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":"sha256:0436944b998783f475cab548d7409c42cb9360ec564ac8e190a2256fdb904ea7","target":"record","created_at":"2026-05-18T01:10:00Z","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":"648a9b09f9d5400638a9d0626120b3b74f37a64402ff6c004c6131afbf9b1258","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2016-08-01T15:50:02Z","title_canon_sha256":"effb539493d58cde6824534f0a786f3a64b8bfaf6b2f0aae8dff48616a1df554"},"schema_version":"1.0","source":{"id":"1608.00856","kind":"arxiv","version":1}},"canonical_sha256":"276030ef044768e2dd45022df710d773020b622fc2a64238e816e9723570260a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"276030ef044768e2dd45022df710d773020b622fc2a64238e816e9723570260a","first_computed_at":"2026-05-18T01:10:00.715905Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:00.715905Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CGcE/lrofdv9EveN7s+sFKRL4hVe6KtuC7AWriW4GFFV+ha8QI8bBVNf3kEI6LGOZYFUag3adRC/zEFAX99yDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:00.716601Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.00856","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0436944b998783f475cab548d7409c42cb9360ec564ac8e190a2256fdb904ea7","sha256:cee1895d4220635f6c570deac9c1d424b61bb0f151ba818e146e03a2ec742371"],"state_sha256":"50fbb3f9aabf6ece75174f4c9f28921af0ed0d5abce463a30bbfedf5150035d2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LhqU1ossN3fRbHIN0bxtFC6vWJi2GJhaSZd7cpKOb3Cdio4AXFwa0LcQDb4ZzS89iwGxf8B7txkbTuwoTRJ/BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T13:04:43.939027Z","bundle_sha256":"25414eb468d559fa6a20be6b7fafbc1e5d906c84281afeee525b30e24ae82c61"}}