{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:G3XFFLDCJB7J73PEPDNXYS2FDE","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":"b71f092324a211f0939ab430df4990f566d87c8e458546bf9bf8d4b285cac98a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-07-26T13:59:28Z","title_canon_sha256":"e926e1b666a10a0c2a32db138b5a250fa096e1b2806252e37475acf98ca5da21"},"schema_version":"1.0","source":{"id":"2607.23664","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.23664","created_at":"2026-07-28T01:23:04Z"},{"alias_kind":"arxiv_version","alias_value":"2607.23664v1","created_at":"2026-07-28T01:23:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.23664","created_at":"2026-07-28T01:23:04Z"},{"alias_kind":"pith_short_12","alias_value":"G3XFFLDCJB7J","created_at":"2026-07-28T01:23:04Z"},{"alias_kind":"pith_short_16","alias_value":"G3XFFLDCJB7J73PE","created_at":"2026-07-28T01:23:04Z"},{"alias_kind":"pith_short_8","alias_value":"G3XFFLDC","created_at":"2026-07-28T01:23:04Z"}],"graph_snapshots":[{"event_id":"sha256:1b204dd58023d756ffef7bf79f20c5227b8dc608af8df38deae4d5f60cc3a936","target":"graph","created_at":"2026-07-28T01:23:04Z","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/2607.23664/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We exhibit a connected graph on 24 vertices with maximum degree 3, independence number 9 and zero forcing number 11, refuting a 2017 conjecture of TxGraffiti recorded as Conjecture 2 of the survey of Davila, Brimkov and Pepper. The same construction with a different gadget gives a connected cubic graph on 36 vertices with independence number 15 and zero forcing number 17; the conjecture therefore fails also in the cubic form in which the survey's Lean 4 appendix states it. In particular Z <= alpha + 1 is not a universal bound for connected cubic graphs, and the value Z = alpha + 2 is attained.","authors_text":"Mikko Fischer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-07-26T13:59:28Z","title":"A counterexample to the zero forcing versus independence conjecture for cubic and subcubic graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.23664","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:e1d615bd170d43dad265156c2bd63d878f789c8cc43956013f29f70fdfca34c7","target":"record","created_at":"2026-07-28T01:23:04Z","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":"b71f092324a211f0939ab430df4990f566d87c8e458546bf9bf8d4b285cac98a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-07-26T13:59:28Z","title_canon_sha256":"e926e1b666a10a0c2a32db138b5a250fa096e1b2806252e37475acf98ca5da21"},"schema_version":"1.0","source":{"id":"2607.23664","kind":"arxiv","version":1}},"canonical_sha256":"36ee52ac62487e9fede478db7c4b451929794f0f1c2accf24c5de7987861f1f8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"36ee52ac62487e9fede478db7c4b451929794f0f1c2accf24c5de7987861f1f8","first_computed_at":"2026-07-28T01:23:04.321779Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-28T01:23:04.321779Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fatmtG4Dk5nWGMzvHIZVKA/rOr9dBs1MRfd515xmc0tBjkhpyxZOCEH4HhqUvUtyZNIDfS/m8G0FpsV1kUR2Dg==","signature_status":"signed_v1","signed_at":"2026-07-28T01:23:04.322524Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.23664","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e1d615bd170d43dad265156c2bd63d878f789c8cc43956013f29f70fdfca34c7","sha256:1b204dd58023d756ffef7bf79f20c5227b8dc608af8df38deae4d5f60cc3a936"],"state_sha256":"5023ea5e914da13570f7388c31822b55a019336e65edb9aaeed49f32fa3aa555"}