{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:JNMABT7Q443ZKZXGGFXIQGAWHT","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":"21bff420b66e3ff9877376c46a7a1d0d23d4d36893cbc4f24993a8e07dcfc9cc","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-10-19T23:12:59Z","title_canon_sha256":"24590b615549d8b64159332d4a1597bd997020c2f5647b1fc8d89078e5f1950e"},"schema_version":"1.0","source":{"id":"1210.5561","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.5561","created_at":"2026-05-18T03:42:43Z"},{"alias_kind":"arxiv_version","alias_value":"1210.5561v1","created_at":"2026-05-18T03:42:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.5561","created_at":"2026-05-18T03:42:43Z"},{"alias_kind":"pith_short_12","alias_value":"JNMABT7Q443Z","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JNMABT7Q443ZKZXG","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JNMABT7Q","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:d032e354b2490fffeb269b6286a6b92bf21d10fc972b1e29e0c5631f7d7045e3","target":"graph","created_at":"2026-05-18T03:42:43Z","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":"In the first part of this work we provide a formula for the number of edges of the Hasse diagram of the independent subsets of the h-th power of a path ordered by inclusion. For h=1 such a value is the number of edges of a Fibonacci cube. We show that, in general, the number of edges of the diagram is obtained by convolution of a Fibonacci-like sequence with itself.\n  In the second part we consider the case of cycles. We evaluate the number of edges of the Hasse diagram of the independent subsets of the h-th power of a cycle ordered by inclusion. For h=1, and n>1, such a value is the number of","authors_text":"Ottavio M. D'Antona, Pietro Codara","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-10-19T23:12:59Z","title":"On the independent subsets of powers of paths and cycles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5561","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:be52af5e7c11b213618e5550efe290a56785fb3c26a489355092ad6c1f4daf11","target":"record","created_at":"2026-05-18T03:42:43Z","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":"21bff420b66e3ff9877376c46a7a1d0d23d4d36893cbc4f24993a8e07dcfc9cc","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-10-19T23:12:59Z","title_canon_sha256":"24590b615549d8b64159332d4a1597bd997020c2f5647b1fc8d89078e5f1950e"},"schema_version":"1.0","source":{"id":"1210.5561","kind":"arxiv","version":1}},"canonical_sha256":"4b5800cff0e7379566e6316e8818163cce9c17cdc12784f7752e8c2e720049d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b5800cff0e7379566e6316e8818163cce9c17cdc12784f7752e8c2e720049d7","first_computed_at":"2026-05-18T03:42:43.638049Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:42:43.638049Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gy7LE537DQXiB72GVw59vWeoO92FchgyzAyLK/y8OIRgpslwcgnbfB9z+tNIOhHDGhoe5bNjyF3zeEbeKln5Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T03:42:43.638555Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.5561","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:be52af5e7c11b213618e5550efe290a56785fb3c26a489355092ad6c1f4daf11","sha256:d032e354b2490fffeb269b6286a6b92bf21d10fc972b1e29e0c5631f7d7045e3"],"state_sha256":"b31b84bf6d457794929f5e56cd4e935c34b1b5a9d8a3f3298d21dc1c203bf839"}