{"id":"palomar/PALOMAR-2026-10-27-000019","url":"https://github.com/Arthur742Ramos/Math-Formalization/tree/906804093ffc4f35224b35ae3bff6536bd56a372/algebraic-hodge/ddbar-pilot","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-27-000019-v1.json","repo":"https://github.com/Arthur742Ramos/Math-Formalization","tags":["math.AT","msc:18G40","msc:55T05"],"score":0,"title":"Algebraic E1 degeneration from explicit d′d″ identities","trust":"high","domain":"math.AT","source":"palomar","authors":["Arthur Freitas Ramos","Ruy Jose Guerra Barretto de Queiroz","David Barros Hulak"],"reviews":0,"subject":"math.AT","summary":"For actual commuting integer-indexed double complexes over a field, componentwise image/kernel identities imply biclosed representatives of vertical cohomology classes and vanishing of every higher differential of the column-filtered signed total complex. The genuine first quotient page identifies with vertical cohomology; canonical recurrence agrees on actual representatives and covers all next-page classes. Finite rectangular support gives actual quotient stabilization and a canonical identification with the associated graded of total cohomology with its finite, exhaustive, separated…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-27","reactions":{},"formalized":true,"formalizes":[{"title":"Real homotopy theory of Kähler manifolds, Inventiones Mathematicae 29 (1975), §§5.15–5.17","identifier":"https://www.math.stonybrook.edu/~dennis/publications/PDF/DS-pub-0024.pdf","relationship":"formalizes"}]}