{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:HIIWCCOC3737KX5I74LFDR5SS2","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":"fed4a789fcefc86275ed4c5b96c354bea45784b40fcb0a74295bacfde42c8352","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-06-25T13:53:57Z","title_canon_sha256":"20bc1e4c4c43383c1e857d4fc0722b448ab916513b1c9112036288944b318138"},"schema_version":"1.0","source":{"id":"1606.07915","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.07915","created_at":"2026-07-05T06:23:17Z"},{"alias_kind":"arxiv_version","alias_value":"1606.07915v3","created_at":"2026-07-05T06:23:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.07915","created_at":"2026-07-05T06:23:17Z"},{"alias_kind":"pith_short_12","alias_value":"HIIWCCOC3737","created_at":"2026-07-05T06:23:17Z"},{"alias_kind":"pith_short_16","alias_value":"HIIWCCOC3737KX5I","created_at":"2026-07-05T06:23:17Z"},{"alias_kind":"pith_short_8","alias_value":"HIIWCCOC","created_at":"2026-07-05T06:23:17Z"}],"graph_snapshots":[{"event_id":"sha256:79031b913ed5eba11f54e82cab33319258f899a4e23a8d3687d7d578f805b2f1","target":"graph","created_at":"2026-07-05T06:23:17Z","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/1606.07915/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"An S-restricted composition of a positive integer n is an ordered partition of n where each summand is drawn from a given subset S of positive integers. There are various problems regarding such compositions which have received attention in recent years. This paper is an attempt at finding a closed- form formula for the number of S-restricted compositions of n. To do so, we reduce the problem to finding solutions to corresponding so-called interpreters which are linear homogeneous recurrence relations with constant coefficients. Then, we reduce interpreters to Diophantine equations. Such equat","authors_text":"Behrouz Zolfaghari, Mehdi Sedighi, Mehran S. Fallah","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-06-25T13:53:57Z","title":"S-Restricted Compositions Revisited"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.07915","kind":"arxiv","version":3},"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":"sha256:13245478020362b01bc4700106d19f6eba85f073fb6ef4d1027e3356bf7f1bad","target":"record","created_at":"2026-07-05T06:23:17Z","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":"fed4a789fcefc86275ed4c5b96c354bea45784b40fcb0a74295bacfde42c8352","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-06-25T13:53:57Z","title_canon_sha256":"20bc1e4c4c43383c1e857d4fc0722b448ab916513b1c9112036288944b318138"},"schema_version":"1.0","source":{"id":"1606.07915","kind":"arxiv","version":3}},"canonical_sha256":"3a116109c2dff7f55fa8ff1651c7b29689776f9c8a1fa584a7816c7ff9a21c99","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3a116109c2dff7f55fa8ff1651c7b29689776f9c8a1fa584a7816c7ff9a21c99","first_computed_at":"2026-07-05T06:23:17.147758Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:23:17.147758Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FQizVhQD6zA64cvJ2zBSawtlAB1uUjumRHop1EoKKukPlKhXPw+p5eZEgFxlCf8YM4OT4KfZD+IXrYywRhbfDA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:23:17.148177Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.07915","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:13245478020362b01bc4700106d19f6eba85f073fb6ef4d1027e3356bf7f1bad","sha256:79031b913ed5eba11f54e82cab33319258f899a4e23a8d3687d7d578f805b2f1"],"state_sha256":"ecd667e02888cf7272b86b3dcc6cebf22d77249f9039aede090dd4423c646961"}