{"paper":{"title":"Highly connected non-formal Milnor fibers via polyhedral products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Milnor fibers of weighted-homogeneous polynomials can be made arbitrarily highly connected while remaining non-formal.","cross_cats":["math.AG","math.CO"],"primary_cat":"math.AT","authors_text":"Alexander I. Suciu","submitted_at":"2026-05-10T01:48:37Z","abstract_excerpt":"We show that the realization theorem of Fern\\'andez de Bobadilla, which identifies the Milnor fiber of a weighted-homogeneous polynomial with the complement of a germ of analytic set, can be combined with the systematic Massey product constructions of Grbi\\'c-Linton for moment-angle complexes $\\mathcal{Z}_K = \\mathcal{Z}_K(D^2, S^1)$ to produce weighted-homogeneous polynomials whose Milnor fibers are arbitrarily highly connected and non-formal. The original application of this strategy, due to Fern\\'andez de Bobadilla, used the Denham-Suciu classification of lowest-degree triple Massey product"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"the realization theorem of Fernández de Bobadilla, which identifies the Milnor fiber of a weighted-homogeneous polynomial with the complement of a germ of analytic set, can be combined with the systematic Massey product constructions of Grbić-Linton for moment-angle complexes Z_K = Z_K(D^2, S^1) to produce weighted-homogeneous polynomials whose Milnor fibers are arbitrarily highly connected and non-formal.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the Grbić-Linton Massey product constructions on moment-angle complexes can be transferred via the Fernández de Bobadilla realization theorem without destroying the non-formality or reducing the connectivity of the resulting Milnor fiber.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Combining a realization theorem for Milnor fibers with arbitrary n-fold Massey product constructions in polyhedral products yields weighted-homogeneous polynomials whose Milnor fibers are arbitrarily highly connected and non-formal.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Milnor fibers of weighted-homogeneous polynomials can be made arbitrarily highly connected while remaining non-formal.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"2799e38f679f111165775bf3ac381d1b27e9c453f35f2c8d8df816ab0a781b97"},"source":{"id":"2605.09254","kind":"arxiv","version":2},"verdict":{"id":"bda105c6-b97d-4453-9c4a-1a0db402349c","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-12T02:19:24.619700Z","strongest_claim":"the realization theorem of Fernández de Bobadilla, which identifies the Milnor fiber of a weighted-homogeneous polynomial with the complement of a germ of analytic set, can be combined with the systematic Massey product constructions of Grbić-Linton for moment-angle complexes Z_K = Z_K(D^2, S^1) to produce weighted-homogeneous polynomials whose Milnor fibers are arbitrarily highly connected and non-formal.","one_line_summary":"Combining a realization theorem for Milnor fibers with arbitrary n-fold Massey product constructions in polyhedral products yields weighted-homogeneous polynomials whose Milnor fibers are arbitrarily highly connected and non-formal.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the Grbić-Linton Massey product constructions on moment-angle complexes can be transferred via the Fernández de Bobadilla realization theorem without destroying the non-formality or reducing the connectivity of the resulting Milnor fiber.","pith_extraction_headline":"Milnor fibers of weighted-homogeneous polynomials can be made arbitrarily highly connected while remaining non-formal."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.09254/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-20T08:02:09.150168Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T20:34:42.267798Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T13:31:17.950669Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T10:22:46.240959Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"4f2a17223b3fcc1e476eda6ce7ffa06afa00d5f6cdd44d6a5f917782691a6225"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":1,"snapshot_sha256":"acea27c5442c201f547873ed43409710ac2098d851c770f7056c0d558dc0b5c1"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}