{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:Z4LCA4JKYGBCBXWMYNHS7ZPVLB","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":"43d6fdd9c5fa944a87148959f23cd75e34c7923f89146d1ac6d0cbbe0d9628b4","cross_cats_sorted":["cs.HC","cs.SC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2025-06-12T11:21:58Z","title_canon_sha256":"fe91bc8ae13c5dc41acac882d70b7af887e7ffdbd54e81337feb85cec9e25727"},"schema_version":"1.0","source":{"id":"2506.10585","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.10585","created_at":"2026-07-05T11:20:26Z"},{"alias_kind":"arxiv_version","alias_value":"2506.10585v1","created_at":"2026-07-05T11:20:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.10585","created_at":"2026-07-05T11:20:26Z"},{"alias_kind":"pith_short_12","alias_value":"Z4LCA4JKYGBC","created_at":"2026-07-05T11:20:26Z"},{"alias_kind":"pith_short_16","alias_value":"Z4LCA4JKYGBCBXWM","created_at":"2026-07-05T11:20:26Z"},{"alias_kind":"pith_short_8","alias_value":"Z4LCA4JK","created_at":"2026-07-05T11:20:26Z"}],"graph_snapshots":[{"event_id":"sha256:62d3c9ad36f9a6e5a05702b9bba22af63952f3a5fd3929d93ca4681d0d136542","target":"graph","created_at":"2026-07-05T11:20:26Z","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/2506.10585/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper introduces the Primender sequence, a novel integer sequence defined by a hybrid rule that combines classical primality with modular digit-based conditions. Specifically, a number n is included in the sequence if it is prime or ends with a prime number of unit digit or any length. In other words, numbers which are primes or have at least one prime suffix. The resulting sequence exhibits a deterministic yet non-trivial structure, blending number-theoretic properties with symbolic patterning. We propose the Primender sequence as a benchmark for evaluating the symbolic reasoning capabil","authors_text":"Mohd Anwar Jamal Faiz","cross_cats":["cs.HC","cs.SC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2025-06-12T11:21:58Z","title":"Primender Sequence: A Novel Mathematical Construct for Testing Symbolic Inference and AI Reasoning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.10585","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":"sha256:54daaf59d6acd879d2186c9bd7d2340a8c330e523c08e5796c391f98ca291f17","target":"record","created_at":"2026-07-05T11:20:26Z","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":"43d6fdd9c5fa944a87148959f23cd75e34c7923f89146d1ac6d0cbbe0d9628b4","cross_cats_sorted":["cs.HC","cs.SC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2025-06-12T11:21:58Z","title_canon_sha256":"fe91bc8ae13c5dc41acac882d70b7af887e7ffdbd54e81337feb85cec9e25727"},"schema_version":"1.0","source":{"id":"2506.10585","kind":"arxiv","version":1}},"canonical_sha256":"cf1620712ac18220deccc34f2fe5f558645dd71dbeaeb0f859f11aee4b44b117","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf1620712ac18220deccc34f2fe5f558645dd71dbeaeb0f859f11aee4b44b117","first_computed_at":"2026-07-05T11:20:26.802105Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:20:26.802105Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hEoyT6dee0OzrfSfGUs0j95ZmLxvmTPUf6NHr6SH8wU1p/oVl4L6sgPeJifLRoicvT2G0EyST79t3Yig0GWbCA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:20:26.802598Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.10585","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:54daaf59d6acd879d2186c9bd7d2340a8c330e523c08e5796c391f98ca291f17","sha256:62d3c9ad36f9a6e5a05702b9bba22af63952f3a5fd3929d93ca4681d0d136542"],"state_sha256":"48bbdcda792e7f817c9ae7f1e1e4c8359246a6ea3773ed50b33aa5dab29a37ec"}