{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:N6YTPFQHWXCD6GFQDQXFNIHLG4","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":"a979d8581ec866af79b692feb6306e48af39a0b8a2546f1cac79cb9cff61d50a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2022-07-27T22:38:04Z","title_canon_sha256":"d45e27b0fbf5cd8ab998cadc76e2bde373795000961321bef86f6c66b64f8aa9"},"schema_version":"1.0","source":{"id":"2209.03730","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.03730","created_at":"2026-07-05T04:55:45Z"},{"alias_kind":"arxiv_version","alias_value":"2209.03730v1","created_at":"2026-07-05T04:55:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.03730","created_at":"2026-07-05T04:55:45Z"},{"alias_kind":"pith_short_12","alias_value":"N6YTPFQHWXCD","created_at":"2026-07-05T04:55:45Z"},{"alias_kind":"pith_short_16","alias_value":"N6YTPFQHWXCD6GFQ","created_at":"2026-07-05T04:55:45Z"},{"alias_kind":"pith_short_8","alias_value":"N6YTPFQH","created_at":"2026-07-05T04:55:45Z"}],"graph_snapshots":[{"event_id":"sha256:453d134a18b4b791885be4c650493b9d65669dffc034df8819922f4df0d2b4bb","target":"graph","created_at":"2026-07-05T04:55:45Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2209.03730/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The present work deals with the characterization of parity vectors of Collatz sequences (of finite and infinite length). Such a characterization leads to the determination of several numbers (integers or non-integers) that we call the characteristic numbers of a given parity vector. Some characteristic numbers are linked together by equations that can be called characteristic equations of the considered parity vector. If a parity vector v of finite length n contains the first n terms of a parity vector V of infinite length then all the characteristic numbers of v are considered as characterist","authors_text":"Raouf Rajab","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2022-07-27T22:38:04Z","title":"Characteristic numbers and characteristic equations of parity vectors of Collatz sequences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.03730","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:f7a73cf91b10c0497cf48e76f3a74a6aa45d6abc358aa94d112693801941dbde","target":"record","created_at":"2026-07-05T04:55:45Z","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":"a979d8581ec866af79b692feb6306e48af39a0b8a2546f1cac79cb9cff61d50a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2022-07-27T22:38:04Z","title_canon_sha256":"d45e27b0fbf5cd8ab998cadc76e2bde373795000961321bef86f6c66b64f8aa9"},"schema_version":"1.0","source":{"id":"2209.03730","kind":"arxiv","version":1}},"canonical_sha256":"6fb1379607b5c43f18b01c2e56a0eb372727e9f6b163d0b78e09109ddc48bf01","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6fb1379607b5c43f18b01c2e56a0eb372727e9f6b163d0b78e09109ddc48bf01","first_computed_at":"2026-07-05T04:55:45.236939Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:55:45.236939Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"15tjqINJaI8a/OMGujAWM2ngJTA90AmZEp5BlAcCoB8eFKqjUrsK1O/lfD3As2l9KGsyovF0/4AREc6XUzGoCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:55:45.237357Z","signed_message":"canonical_sha256_bytes"},"source_id":"2209.03730","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f7a73cf91b10c0497cf48e76f3a74a6aa45d6abc358aa94d112693801941dbde","sha256:453d134a18b4b791885be4c650493b9d65669dffc034df8819922f4df0d2b4bb"],"state_sha256":"db949593262b8d52e12322b71f1ccfab0ee20aa5b1601e7b5550f6d1b3b68a59"}