Manuscript index
Papers & notes
7 manuscript lines, with 6 reading copies available. These are working manuscripts and technical reports, not journal publications or claims of external peer review.
Choose a reading format: Read online for a reflowing manuscript with equations and section links. PDF and extracted text are also available.
Versions, formats, and accessibility
About these versions: Reading-copy numbers identify fixed PDF versions selected for this site. The October 3 copies corrected author attribution or metadata; the October 5 copies add the minor source clarifications and copyedits from the internal audit. The stated mathematical results are unchanged. Each entry also names its source manuscript revision. For questions or an unavailable copy, email Brian@B-Theory.com.
Reading formats: Online manuscripts use HTML + MathML with navigable headings, structured equations, and text descriptions of diagrams. They use the same audited manuscript sources; screen-reader behavior still needs specialist testing. The original PDFs are not tagged for assistive technology. Extracted-text companions have transcription limitations, particularly in equations. You can also request an accessible format.
Current manuscript lines
ManuscriptCorrespondence and Logical Matrices: A Typed Boolean Operator Calculus
Contribution: Defines a typed symbolic and numeric Boolean operator calculus and states compatibility identities connecting the two representations.
Research status, version, and suggested sections
Where to look: See “Formula-valued logical matrices” and “Compatibility identities” in the September 2026 revision.
Research status: Foundations and synthesis manuscript; current revised version, September 2026.
Source revision: September 27 revised manuscript; earlier September 22 and September 27 revisions retained in the collection.
Site release: Reading copy 1 · PDF byline: Brian Theory
Observation Topologies for Finite Propositional Semantics: Distinguishability, Distance, and Inference
Contribution: Shows how chosen propositional observations induce truth-signature partitions, finite observation spaces, and tests of distinguishability.
Research status, version, and suggested sections
Where to look: See “Valuations, truth regions, and partitions” and “Observation-generated spaces” in v0.9.
Research status: Expository synthesis of standard finite constructions; current v0.9 manuscript.
Source revision: v0.9; sentence-fragment and truth-pattern example copyedits October 5, 2026. Earlier v0.6, v0.8, and v0.8.1 records retained in the collection.
Site release: Reading copy 2 · PDF byline: Brian Theory
Binary Order Thinning of Finite Posets: Homology, Collapses, and Sharp Limits
Contribution: Gives a rooted-forest criterion for vanishing relative homology and collapse under one Boolean bit in height-at-most-two finite orders.
Research status, version, and suggested sections
Where to look: See “The exact forest/collapse theorem” and the two “Sharpness” sections in local v3.
Research status: Focused research manuscript; internally reviewed local v3. Vertex minimality through six states is computer-assisted.
Source revision: Reviewed local v3, September 27, 2026; editorial domain, program-description, and supplement-access polish October 5, 2026. Stated results unchanged.
Site release: Reading copy 3 · PDF byline: Brian Theory
Successive Concept Differentiation as Observation Refinement
Contribution: Separates signature refinement, carrier splitting, and order thinning, then studies the topology and homology of finite refinement constructions.
Research status, version, and suggested sections
Where to look: See “Observation systems and three kinds of refinement” and “Carrier splitting under a new Boolean observation” in v0.5.
Research status: Integrated MIND research draft v0.5, with internal referee repairs; priority and external review remain open.
Source revision: Referee-repair draft v0.5, September 29, 2026; author corrected October 3, 2026; layer, nerve, and skeleton-proof polish October 5, 2026. Earlier revisions retained in the collection.
Site release: Reading copy 3 · PDF byline: Brian Theory
Hierarchical Concepts Under Finite Resolution: Observation Quotients and Adaptive Symmetry
Contribution: Defines observation quotients and resolution towers for ultrametric hierarchies while distinguishing symmetry measures from information gain.
Research status, version, and suggested sections
Where to look: See “A coordinate-free observation quotient” and “Information gain is not a symmetry index” in v0.3.
Research status: Short synthesis and correction note; current v0.3 research copy.
Source revision: Internal fresh-referee v0.3, September 29, 2026; author corrected October 3, 2026. Original PDF retained in the local history.
Site release: Reading copy 2 · PDF byline: Brian Theory
Vtree Alignment and Higher-Order Four-Corner Defects in Exact Boolean Factorization
Contribution: Analyzes how vtree alignment and higher-order defect support constrain exact Boolean factorization; later Phase 5B work remains separate.
Reading copy: Pending integration of later results and a named author line.
Research status, version, and suggested sections
Where to look: See “Setup” and “Defect support” in the Phase 5 theorem note.
Research status: Phase 5 theorem-note draft; later Phase 5B results await manuscript integration.
Source revision: Phase 5 theorem note, dated September 29, 2026; later Phase 5B corrections and results are not integrated.
From Observable States to Acquirable Predictive Models
Contribution: Characterizes reportable targets in a restricted finite ordered model, compares attainable distinctions with predictive equivalence, and treats alternating queries and known actions under an explicit finite-horizon contract.
Research status, version, and suggested sections
Where to look: Start with Section 1; see Theorem 2 and Corollaries 3 and 5 for fixed-state acquisition, Example 8 for query orientation, and Section 7 for actions and timing.
Research status: Consolidated technical report, revised October 7, 2026. Internal AI audits are not external peer review; priority of the specialized classification remains unresolved.
Source revision: Revised technical report, October 7, 2026; site PDF adds metadata and reference-line wrapping without changing mathematical content.
Site release: Reading copy 1 · PDF byline: Brian Theory
Supporting research records
Measurement and RF-IDENT has a linked theorem, model, and internal AI review for a least and greatest element around an antichain of middle states. The Acquirable Predictive Models report consolidates this branch's classification and connects it to prediction. The supporting records preserve the earlier work; neither they nor the report establish the general height-two case.
Research provenance
How these pages were prepared
The research programme and manuscripts are led by Brian Theory (Brian Droncheff). AI tools have assisted with drafting, organization, computation, and review in parts of the work. Each mathematical claim should be read at the scope stated in its manuscript; AI-assisted checks are distinct from external specialist review.
All current reading copies name Brian Theory as author. Historical references retain the names under which the cited works appeared. The version labels distinguish site reading copies from the internal revisions of each manuscript; they do not imply journal acceptance.
