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(Domination with exponential decay, Discrete Math. 309 (2009) 5877-5883) define $S$ to be an exponential dominating set of $G$ if $w_{(G,S)}(u)\\geq 1$ for every vertex $u$ in $V(G)\\setminus S$, where $w_{(G,S)}(u)=\\sum\\limits_{v\\in S}\\left(\\frac{1}{2}\\right)^{{\\rm dist}_{(G,S)}(u,v)-1}$. Inspired by this notion, we define $S$ to be an exponential independent set of $G$ if $w_{(G"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1605.05991","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-05-19T15:14:52Z","cross_cats_sorted":[],"title_canon_sha256":"d400f667f46ae426f9f44c4f198715c86bec6ab7a7bc0426e2c30c61d9c29503","abstract_canon_sha256":"b0d70a46dbed478ad0a91a0b0ea1d855abfb6065b37429044adfc9063488bd7c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:14:26.787756Z","signature_b64":"Tf+d4qhnYmNfAroG0C6H3xx6H+8NyDBZ7tiImu/kcMgg+Y6Gh6toDuRx7+Bzi6oE8IJIao/wpl+0Ly9Wyq9sBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a6e89203be17db2d455970e092ebbf61256c89cb92d47659d7cac8c26db911bd","last_reissued_at":"2026-05-18T01:14:26.787149Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:14:26.787149Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exponential Independence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dieter Rautenbach, Simon J\\\"ager","submitted_at":"2016-05-19T15:14:52Z","abstract_excerpt":"For a set $S$ of vertices of a graph $G$, a vertex $u$ in $V(G)\\setminus S$, and a vertex $v$ in $S$, let ${\\rm dist}_{(G,S)}(u,v)$ be the distance of $u$ and $v$ in the graph $G-(S\\setminus \\{ v\\})$. Dankelmann et al. (Domination with exponential decay, Discrete Math. 309 (2009) 5877-5883) define $S$ to be an exponential dominating set of $G$ if $w_{(G,S)}(u)\\geq 1$ for every vertex $u$ in $V(G)\\setminus S$, where $w_{(G,S)}(u)=\\sum\\limits_{v\\in S}\\left(\\frac{1}{2}\\right)^{{\\rm dist}_{(G,S)}(u,v)-1}$. Inspired by this notion, we define $S$ to be an exponential independent set of $G$ if $w_{(G"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.05991","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1605.05991","created_at":"2026-05-18T01:14:26.787237+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.05991v1","created_at":"2026-05-18T01:14:26.787237+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.05991","created_at":"2026-05-18T01:14:26.787237+00:00"},{"alias_kind":"pith_short_12","alias_value":"U3UJEA56C7NS","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_16","alias_value":"U3UJEA56C7NS2RKZ","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_8","alias_value":"U3UJEA56","created_at":"2026-05-18T12:30:46.583412+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/U3UJEA56C7NS2RKZODQJF257ME","json":"https://pith.science/pith/U3UJEA56C7NS2RKZODQJF257ME.json","graph_json":"https://pith.science/api/pith-number/U3UJEA56C7NS2RKZODQJF257ME/graph.json","events_json":"https://pith.science/api/pith-number/U3UJEA56C7NS2RKZODQJF257ME/events.json","paper":"https://pith.science/paper/U3UJEA56"},"agent_actions":{"view_html":"https://pith.science/pith/U3UJEA56C7NS2RKZODQJF257ME","download_json":"https://pith.science/pith/U3UJEA56C7NS2RKZODQJF257ME.json","view_paper":"https://pith.science/paper/U3UJEA56","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.05991&json=true","fetch_graph":"https://pith.science/api/pith-number/U3UJEA56C7NS2RKZODQJF257ME/graph.json","fetch_events":"https://pith.science/api/pith-number/U3UJEA56C7NS2RKZODQJF257ME/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/U3UJEA56C7NS2RKZODQJF257ME/action/timestamp_anchor","attest_storage":"https://pith.science/pith/U3UJEA56C7NS2RKZODQJF257ME/action/storage_attestation","attest_author":"https://pith.science/pith/U3UJEA56C7NS2RKZODQJF257ME/action/author_attestation","sign_citation":"https://pith.science/pith/U3UJEA56C7NS2RKZODQJF257ME/action/citation_signature","submit_replication":"https://pith.science/pith/U3UJEA56C7NS2RKZODQJF257ME/action/replication_record"}},"created_at":"2026-05-18T01:14:26.787237+00:00","updated_at":"2026-05-18T01:14:26.787237+00:00"}