{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:CKXFRFKY5ZAXJ5R3XPBPMAEIAA","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":"f2812270189b4b5d12c7f60745ea0333947dc11acce473cb2fd46d19e7a91e33","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-12-03T14:15:51Z","title_canon_sha256":"c1bac59ee49ec1de0acaa8d5f95d3fbbd9733bdeb032599bb4d4b1ae0a5a0316"},"schema_version":"1.0","source":{"id":"1612.00970","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.00970","created_at":"2026-05-18T00:55:53Z"},{"alias_kind":"arxiv_version","alias_value":"1612.00970v1","created_at":"2026-05-18T00:55:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.00970","created_at":"2026-05-18T00:55:53Z"},{"alias_kind":"pith_short_12","alias_value":"CKXFRFKY5ZAX","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CKXFRFKY5ZAXJ5R3","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CKXFRFKY","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:018ef4ee8621e21739223b9a0928f5dba450dabc11dbe485485cf95e5a14757a","target":"graph","created_at":"2026-05-18T00:55:53Z","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":"Set of generalized Pascal matrices whose elements are generalized binomial coefficients is considered as an integral object. The special system of generalized Pascal matrices, based on which we are building fractal generalized Pascal matrices, is introduced. Pascal matrix (Pascal triangle) is the Hadamard product of the fractal generalized Pascal matrices. The concept of zero generalized Pascal matrices, an example of which is the Pascal triangle modulo 2, arise in connection with the system of matrices introduced.","authors_text":"E. Burlachenko","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-12-03T14:15:51Z","title":"Fractal generalized Pascal matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.00970","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:f7fb69131fcf67fbcd918b5b3cd77879fbe50e9cc4c57218c43a02dee7551b9b","target":"record","created_at":"2026-05-18T00:55:53Z","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":"f2812270189b4b5d12c7f60745ea0333947dc11acce473cb2fd46d19e7a91e33","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-12-03T14:15:51Z","title_canon_sha256":"c1bac59ee49ec1de0acaa8d5f95d3fbbd9733bdeb032599bb4d4b1ae0a5a0316"},"schema_version":"1.0","source":{"id":"1612.00970","kind":"arxiv","version":1}},"canonical_sha256":"12ae589558ee4174f63bbbc2f600880034dfad93daa54b6db3381bfaff8194d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"12ae589558ee4174f63bbbc2f600880034dfad93daa54b6db3381bfaff8194d2","first_computed_at":"2026-05-18T00:55:53.700351Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:53.700351Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"upBasfmosJP0E+gUv8YXoEjxt7y1ggQzpjHdpvlQA5BY2nZCDooGbVDbcNOR8Ussc9owi1hksXXBWESibO+xCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:53.700773Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.00970","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f7fb69131fcf67fbcd918b5b3cd77879fbe50e9cc4c57218c43a02dee7551b9b","sha256:018ef4ee8621e21739223b9a0928f5dba450dabc11dbe485485cf95e5a14757a"],"state_sha256":"e732a7ae7e64cda05c97e4b929e96a365e8ac3d4829b4a1e5162c758876ccd8b"}