{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:6IS63KKUUBGHCSP5KWXH76D7QF","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":"5d287ad90ebe0176326aa580047509652855922fda2902c0091ada9afd65d65f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-28T18:38:23Z","title_canon_sha256":"3c34d92d0cdbe13c0ebf5f2c7d09257cead7a383d4a95f5124ccb28b0a7ce7b3"},"schema_version":"1.0","source":{"id":"1410.7726","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.7726","created_at":"2026-05-18T02:39:09Z"},{"alias_kind":"arxiv_version","alias_value":"1410.7726v1","created_at":"2026-05-18T02:39:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.7726","created_at":"2026-05-18T02:39:09Z"},{"alias_kind":"pith_short_12","alias_value":"6IS63KKUUBGH","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6IS63KKUUBGHCSP5","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6IS63KKU","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:ceeccc56e92548220231f26951d2a18f5a1870d87118f0391bd0a8ee3a6a48f2","target":"graph","created_at":"2026-05-18T02:39:09Z","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":"The independence polynomial $I(G;x)$ of a graph $G$ is $I(G;x)=\\sum_{k=1}^{\\alpha(G)} s_k x^k$, where $s_k$ is the number of independent sets in $G$ of size $k$. The decycling number of a graph $G$, denoted $\\phi(G)$, is the minimum size of a set $S\\subseteq V(G)$ such that $G-S$ is acyclic. Engstr\\\"om proved that the independence polynomial satisfies $|I(G;-1)| \\leq 2^{\\phi(G)}$ for any graph $G$, and this bound is best possible. Levit and Mandrescu provided an elementary proof of the bound, and in addition conjectured that for every positive integer $k$ and integer $q$ with $|q|\\leq 2^k$, th","authors_text":"Jonathan Cutler, Nathan Kahl","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-28T18:38:23Z","title":"A note on the values of independence polynomials at $-1$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7726","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:caf6157390149c863a0f3f11e23a91ffa002d5b14ee527654b0b1a6f816e303b","target":"record","created_at":"2026-05-18T02:39:09Z","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":"5d287ad90ebe0176326aa580047509652855922fda2902c0091ada9afd65d65f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-28T18:38:23Z","title_canon_sha256":"3c34d92d0cdbe13c0ebf5f2c7d09257cead7a383d4a95f5124ccb28b0a7ce7b3"},"schema_version":"1.0","source":{"id":"1410.7726","kind":"arxiv","version":1}},"canonical_sha256":"f225eda954a04c7149fd55ae7ff87f816b7add3c0afb55930cc504cd93e451f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f225eda954a04c7149fd55ae7ff87f816b7add3c0afb55930cc504cd93e451f2","first_computed_at":"2026-05-18T02:39:09.613888Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:09.613888Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G3vg2C+wVuS3tR1L2dcAJkFQHVJblR1V6GntkUFDcNgc43vmY/LRJ8wcVwaUgFSW0vp6ZBbguzrdfQVWSWn+AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:09.614429Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.7726","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:caf6157390149c863a0f3f11e23a91ffa002d5b14ee527654b0b1a6f816e303b","sha256:ceeccc56e92548220231f26951d2a18f5a1870d87118f0391bd0a8ee3a6a48f2"],"state_sha256":"730fec60efa743eebe7c44fa1ac5424c38aff62b615308c0ba592ff40fcc2f19"}