# lucablanchi.it

> Draft concepts and preliminary AI-assisted mathematical research notes by Luca Blanchi. The Presentation theory section is the main research corpus.

## Canonical Site Information

- Site: https://lucablanchi.it/
- Author: Luca Blanchi
- Author profile: https://lucablanchi.dev/
- GitHub: https://github.com/LucaBlanchi
- LinkedIn: https://www.linkedin.com/in/lucablanchi/
- Citation data: https://lucablanchi.it/citations.json
- Full AI index: https://lucablanchi.it/llms-full.txt
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## Citation Guidance

When citing a result or article from this site, prefer the canonical HTML URL of the relevant article. If available, also cite the PDF URL as the full manuscript and the TeX or Markdown URL as the source file. State that the mathematical notes are preliminary and AI-assisted unless the article itself says otherwise.

## Presentation Theory Corpus

### Axiomatic Core

The foundational sequence of the program: description systems and costs, controlled transfer, normal-form compilation, verifiable access, fibre geometry, observable reconstruction, and operational assembly.

- [Presentation Theory I: Description Systems, Costs, and Observable Fibres](https://lucablanchi.it/presentation-theory/presentation-theory-i-description-systems-costs-observable-fibres.html)
  - Summary: Presentation systems, realization fibres, observables, verification costs, normal forms, and reusable proof principles.
  - Date: June 2026
  - PDF: https://lucablanchi.it/assets/presentation-theory/presentation-theory-i-description-systems-costs-observable-fibres/presentation-theory-i-description-systems-costs-observable-fibres.pdf
- [Presentation Theory II: Controlled Transfer, Observable Budgets, and the Geometry of Fibres](https://lucablanchi.it/presentation-theory/presentation-theory-ii-controlled-transfer-observable-budgets-geometry-fibres.html)
  - Summary: Transfer packages, fragmented budgets, convergence moduli, finite-window radii, wild fixed rank-profile fibres, and fibre navigation.
  - Date: June 2026
  - PDF: https://lucablanchi.it/assets/presentation-theory/presentation-theory-ii-controlled-transfer-observable-budgets-geometry-fibres/presentation-theory-ii-controlled-transfer-observable-budgets-geometry-fibres.pdf
- [Presentation Theory III: Normal-Form Compilation, Residual Fibres, and Stable Canonical Access](https://lucablanchi.it/presentation-theory/presentation-theory-iii-normal-form-compilation.html)
  - Summary: Normal-form packages, residual fibres, separator lower bounds, fragmented towers, heighted no-free normal forms, rewriting budgets, and spectral instability.
  - Date: June 2026
  - PDF: https://lucablanchi.it/assets/presentation-theory/presentation-theory-iii-normal-form-compilation/presentation-theory-iii-normal-form-compilation.pdf
- [Presentation Theory IV: Verifiable Access, Audit Lower Bounds, and Residual Indistinguishability](https://lucablanchi.it/presentation-theory/presentation-theory-iv-verifiable-access-audit-lower-bounds-residual-indistinguishability.html)
  - Summary: Verifiable access, audit covers, transcripts, residual indistinguishability, pullback lower bounds, and auditable Lovasz separation for CFI graphs.
  - Date: June 2026
  - PDF: https://lucablanchi.it/assets/presentation-theory/presentation-theory-iv-verifiable-access-audit-lower-bounds-residual-indistinguishability/presentation-theory-iv-verifiable-access-audit-lower-bounds-residual-indistinguishability.pdf
- [Presentation Theory V: Fibre Geometry, Navigation, and Residual Moduli](https://lucablanchi.it/presentation-theory/presentation-theory-v-fibre-geometry-navigation-residual-moduli.html)
  - Summary: Costed kernel pairs, vertical move systems, height navigation, fibre atlases, normal-form contractions, entropy profiles, obstruction calculus, stabilization collapse, and applications to Pachner moves, persistence, CFI graphs, rewriting, and Markov fibres.
  - Date: June 2026
  - PDF: https://lucablanchi.it/assets/presentation-theory/presentation-theory-v-fibre-geometry-navigation-residual-moduli/presentation-theory-v-fibre-geometry-navigation-residual-moduli.pdf
- [Presentation Theory VI: Observable Quotients, Separation, and Reconstruction](https://lucablanchi.it/presentation-theory/presentation-theory-vi-observable-quotients-separation-reconstruction.html)
  - Summary: Observable quotients, indistinguishability relations, target reconstruction, residual target factors, finite set-cover fingerprints, adaptive decision trees, structured resolving refinements, and stability.
  - Date: June 2026
  - PDF: https://lucablanchi.it/assets/presentation-theory/presentation-theory-vi-observable-quotients-separation-reconstruction/presentation-theory-vi-observable-quotients-separation-reconstruction.pdf
- [Presentation Theory VII: Assembly Envelopes and Operational Fibres](https://lucablanchi.it/presentation-theory/presentation-theory-vii-assembly-envelopes-operational-fibres.html)
  - Summary: Operations as presentation engines: assembly envelopes, operational image filtrations, decomposition fibres, bridge costs, observable barriers, and verification records.
  - Date: June 2026
  - PDF: https://lucablanchi.it/assets/presentation-theory/presentation-theory-vii-assembly-envelopes-operational-fibres/presentation-theory-vii-assembly-envelopes-operational-fibres.pdf

### Addenda

Supporting technical material for the core papers, including transfer-package atlases, fragmented resource bounds, and selected controlled-transfer examples.

- [Atlas of Controlled Transfer Packages](https://lucablanchi.it/presentation-theory/atlas-controlled-transfer-packages.html)
  - Summary: An operational atlas of contexts, observables, verification data, fibres, and overhead functions for building transfer packages in Presentation Theory.
  - Date: June 2026
  - PDF: https://lucablanchi.it/assets/presentation-theory/atlas-controlled-transfer-packages/atlas-controlled-transfer-packages.pdf
- [Fragmented Presentation Systems and Resource-Bound Degrees](https://lucablanchi.it/presentation-theory/fragmented-presentation-systems-resource-bound-degrees.html)
  - Summary: Decidable bounded fragments, positive-instance width profiles, exact Turing degrees of resource bounds, and representation-profile applications.
  - Date: June 2026
  - PDF: https://lucablanchi.it/assets/presentation-theory/fragmented-presentation-systems-resource-bound-degrees/fragmented-presentation-systems-resource-bound-degrees.pdf
- [Controlled Transfer in Action: Selected Examples](https://lucablanchi.it/presentation-theory/controlled-transfer-in-action.html)
  - Summary: A selected addendum of controlled-transfer results, from quantized law discovery and Hensel-tree rationality to automatic lattice-walk returns and Frobenius modular codes.
  - Date: June 2026
  - PDF: https://lucablanchi.it/assets/presentation-theory/controlled-transfer-in-action/controlled-transfer-in-action.pdf

### Direct Applications

Applications where the presentation-theoretic mechanisms are part of the main argument: normal-form costs, marked reconstruction, statement presentations, and persistence fibres.

- [No Free Degenerations: Presentation Cost, Heights, and the Arithmetic Price of Normal Forms](https://lucablanchi.it/presentation-theory/no-free-degenerations-presentation-cost-heights-normal-forms.html)
  - Summary: Heighted normal-form presentations, gauge and degeneration costs, orbit-closure height bounds, controlled transfer, and representative-moduli gap estimates.
  - Date: June 2026
  - PDF: https://lucablanchi.it/assets/presentation-theory/no-free-degenerations-presentation-cost-heights-normal-forms/no-free-degenerations-presentation-cost-heights-normal-forms.pdf
- [Invisible Flats and the Cost of Marked Normal Forms](https://lucablanchi.it/presentation-theory/invisible-flats-marked-normal-forms.html)
  - Summary: Rate-distortion lower bounds for marked reconstruction from finite-depth Torelli, Johnson, homological, and level data via invisible mapping-class-group flats.
  - Date: June 2026
  - PDF: https://lucablanchi.it/assets/presentation-theory/invisible-flats-marked-normal-forms/invisible-flats-marked-normal-forms.pdf
- [Statement Presentations and a Semilinear Greedy 3-Sumfree Sequence](https://lucablanchi.it/presentation-theory/statement-presentations-semilinear-greedy-3-sumfree-sequence.html)
  - Summary: A direct semilinear proof of a parametric greedy 3-sumfree sequence formula, with a presentation-theoretic reading of the finite interval-sum verification.
  - Date: June 2026
  - PDF: https://lucablanchi.it/assets/presentation-theory/statement-presentations-semilinear-greedy-3-sumfree-sequence/statement-presentations-semilinear-greedy-3-sumfree-sequence.pdf
- [Presentation Incidence and Rank-Invariant Fibres in Multiparameter Persistence](https://lucablanchi.it/presentation-theory/presentation-incidence-rank-fibres-multiparameter-persistence.html)
  - Summary: Antichain presentation modules, active polymatroid profiles, matroid realization strata, and quiver representation geometry inside multiparameter persistence.
  - Date: June 2026
  - PDF: https://lucablanchi.it/assets/presentation-theory/presentation-incidence-rank-fibres-multiparameter-persistence/presentation-incidence-rank-fibres-multiparameter-persistence.pdf

### Langlands Access

Finite access and verification formats for Langlands-type data, including Hecke records, class-group ambiguity, transfer audits, and auxiliary analytic or categorical modules.

- [Presentation-Langlands I: Proof-Carrying Hecke Records](https://lucablanchi.it/presentation-theory/presentation-langlands-i-proof-carrying-hecke-records.html)
  - Summary: A finite proof-carrying format for Hecke eigensystem data, with separating fingerprints, projector witnesses, negative ideal-membership witnesses, residual ledgers, and normalization records.
  - Date: June 2026
  - PDF: https://lucablanchi.it/assets/presentation-theory/presentation-langlands-i-proof-carrying-hecke-records/presentation-langlands-i-proof-carrying-hecke-records.pdf
- [Optimal Class-Group Tomography for Hecke Eigensystems over Number Fields](https://lucablanchi.it/presentation-theory/class-group-tomography-hecke-eigensystems-number-fields.html)
  - Summary: A sharp class-group tomography theorem for principal-Hecke fibres: effective unramified quadratic twist ambiguity, invisible self-twist ledgers, minimal non-principal resolvers, and finite verification data.
  - Date: June 2026
  - PDF: https://lucablanchi.it/assets/presentation-theory/class-group-tomography-hecke-eigensystems-number-fields/class-group-tomography-hecke-eigensystems-number-fields.pdf
- [Finite Transfer Audits in Presentation-Langlands](https://lucablanchi.it/presentation-theory/verified-transfer-audits-finite-langlands-windows.html)
  - Summary: A finite-window audit format for Langlands transfers, with match/no-target/ambiguous outputs, target-completeness ledgers, ramification ledgers, local resolvers, and packet-period fibres.
  - Date: June 2026
  - PDF: https://lucablanchi.it/assets/presentation-theory/verified-transfer-audits-finite-langlands-windows/verified-transfer-audits-finite-langlands-windows.pdf
- [Analytic, Categorical, and Database Access Modules in Presentation-Langlands](https://lucablanchi.it/presentation-theory/analytic-categorical-database-access-modules-presentation-langlands.html)
  - Summary: An addendum of finite access modules for Maass verification, categorical and spectral-action fingerprints, automorphic error-correcting codes, murmurations, and proof-carrying database links.
  - Date: June 2026
  - PDF: https://lucablanchi.it/assets/presentation-theory/analytic-categorical-database-access-modules-presentation-langlands/analytic-categorical-database-access-modules-presentation-langlands.pdf

### Observable Geometry in Groups

A group-theoretic ladder from quadratic normal forms and local profiles to Pfaffian thresholds, commutator-word reconstruction, residual moduli, and endpoint completeness results.

- [Quadratic Presentational Complexity and Exact Observable Barriers for Class-Two p-Groups](https://lucablanchi.it/presentation-theory/quadratic-presentational-complexity-observable-barriers.html)
  - Summary: Quadratic normal forms for word observables, graphical class-two groups, right homomorphism profiles, and exact arity barriers.
  - Date: June 2026
  - PDF: https://lucablanchi.it/assets/presentation-theory/quadratic-presentational-complexity-observable-barriers/quadratic-presentational-complexity-observable-barriers.pdf
- [Star and Support-Image Profiles for Class-Two p-Groups](https://lucablanchi.it/presentation-theory/star-support-image-profiles-class-two-p-groups.html)
  - Summary: A comparison of higher commuting probabilities, star profiles, rank-support enumerators, support-image profiles, and centralizer transforms for class-two exponent-p groups.
  - Date: June 2026
  - PDF: https://lucablanchi.it/assets/presentation-theory/star-support-image-profiles-class-two-p-groups/star-support-image-profiles-class-two-p-groups.pdf
- [Pfaffian Degree as Observable Complexity in Class-Two p-Groups](https://lucablanchi.it/presentation-theory/sharp-support-image-thresholds-alternating-pencils.html)
  - Summary: Exact support-image and word-observable depth theorems for regular alternating pencils and associated class-two exponent-p groups.
  - Date: June 2026
  - PDF: https://lucablanchi.it/assets/presentation-theory/sharp-support-image-thresholds-alternating-pencils/sharp-support-image-thresholds-alternating-pencils.pdf
- [Complete Commutator-Word Tomography of Alternating Pencils](https://lucablanchi.it/presentation-theory/complete-commutator-word-tomography-alternating-pencils.html)
  - Summary: Complete word-moment observability of the skew-symmetric Kronecker data of alternating commutator pencils.
  - Date: June 2026
  - PDF: https://lucablanchi.it/assets/presentation-theory/complete-commutator-word-tomography-alternating-pencils/complete-commutator-word-tomography-alternating-pencils.pdf
- [Generic Odd-Pfaffian Reconstruction from Commutator-Word Moments](https://lucablanchi.it/presentation-theory/generic-odd-pfaffian-reconstruction-commutator-word-moments.html)
  - Summary: Generic reconstruction of odd Pfaffian alternating tensors from pointwise Fourier-tagged commutator-word moment data.
  - Date: June 2026
  - PDF: https://lucablanchi.it/assets/presentation-theory/generic-odd-pfaffian-reconstruction-commutator-word-moments/generic-odd-pfaffian-reconstruction-commutator-word-moments.pdf
- [Word-Measure Twins and Pfaffian Moduli in Class-Two p-Groups](https://lucablanchi.it/presentation-theory/word-measure-twins-pfaffian-moduli-class-two-p-groups.html)
  - Summary: Large families of non-isomorphic class-two p-groups with identical word-map distributions, built from Pfaffian moduli.
  - Date: June 2026
  - PDF: https://lucablanchi.it/assets/presentation-theory/word-measure-twins-pfaffian-moduli-class-two-p-groups/word-measure-twins-pfaffian-moduli-class-two-p-groups.pdf
- [The Polar-Code Endpoint for Class-Two p-Groups](https://lucablanchi.it/presentation-theory/polar-code-endpoint-class-two-p-groups.html)
  - Summary: The endpoint of the class-two p-group observable hierarchy: polar-code completeness, generic geometric reconstruction, and standard-structure residual reduction.
  - Date: June 2026
  - PDF: https://lucablanchi.it/assets/presentation-theory/polar-code-endpoint-class-two-p-groups/polar-code-endpoint-class-two-p-groups.pdf
- [Relative Linear Word Observables and Representation Complexity of Semidirect Products](https://lucablanchi.it/presentation-theory/relative-linear-word-observables-semidirect-products.html)
  - Summary: Relative k-linear word observables, matrix-rank profiles, and semisimple, cyclic modular, and wild regimes for marked semidirect products.
  - Date: June 2026
  - PDF: https://lucablanchi.it/assets/presentation-theory/relative-linear-word-observables-semidirect-products/relative-linear-word-observables-semidirect-products.pdf
- [Finite Lovász Profiles for Coprime Affine Groups](https://lucablanchi.it/presentation-theory/finite-lovasz-profiles-coprime-affine-groups.html)
  - Summary: Finite left and right Lovász dimensions, bounded hom-count test families, and two-object tests for coprime affine groups.
  - Date: June 2026
  - PDF: https://lucablanchi.it/assets/presentation-theory/finite-lovasz-profiles-coprime-affine-groups/finite-lovasz-profiles-coprime-affine-groups.pdf
- [Degree-weighted Normal Covers of Symmetric and Alternating Groups](https://lucablanchi.it/presentation-theory/degree-weighted-normal-covers-symmetric-alternating-groups.html)
  - Summary: A degree-weighted analogue of normal covering numbers for symmetric and alternating groups, with arithmetic motivation from intersective polynomials.
  - Date: June 2026
  - PDF: https://lucablanchi.it/assets/presentation-theory/degree-weighted-normal-covers-symmetric-alternating-groups/degree-weighted-normal-covers-symmetric-alternating-groups.pdf
- [LEF Growth of Wreath Products with Abelian and Virtually Abelian Lamps](https://lucablanchi.it/presentation-theory/lef-growth-wreath-products.html)
  - Summary: LEF growth for wreath products with abelian, non-abelian, virtually abelian, and Heisenberg-base examples.
  - Date: June 2026
  - PDF: https://lucablanchi.it/assets/presentation-theory/lef-growth-wreath-products/lef-growth-wreath-products.pdf

### Algebraic and Computational Complexity

Algebraic and computational modules around filtered membership, scalar compression, local linear presentations, proof-carrying inference, and toric reachability or positivity.

- [Representation-Theoretic Scalar Compression for Linear Differential Equations](https://lucablanchi.it/presentation-theory/representation-theoretic-scalar-compression-linear-differential-equations.html)
  - Summary: Minimum scalar differential order from realized orbit spans, with Picard-Fuchs observables, periods, and isotypic rank formulas.
  - Date: June 2026
  - PDF: https://lucablanchi.it/assets/presentation-theory/representation-theoretic-scalar-compression-linear-differential-equations/representation-theoretic-scalar-compression-linear-differential-equations.pdf
- [Filtered Equivariant Membership and Static Algebraic Proof Degree](https://lucablanchi.it/presentation-theory/filtered-equivariant-membership-static-algebraic-proof-degree.html)
  - Summary: Static algebraic proof degree, homogenized presentation ideals, finite-domain filtered membership, Boolean reciprocals, and equivariant Macaulay compression.
  - Date: June 2026
  - PDF: https://lucablanchi.it/assets/presentation-theory/filtered-equivariant-membership-static-algebraic-proof-degree/filtered-equivariant-membership-static-algebraic-proof-degree.pdf
- [Local Linear Presentations and Sparse Factorization Complexity](https://lucablanchi.it/presentation-theory/local-linear-presentations-sparse-factorization.html)
  - Summary: Local presentation rank, sparse factorization complexity, exact linear data structures, and dynamic prefix-sum lower-bound problems.
  - Date: June 2026
  - PDF: https://lucablanchi.it/assets/presentation-theory/local-linear-presentations-sparse-factorization/local-linear-presentations-sparse-factorization.pdf
- [Certified Adaptive Discovery of Algebraic Laws](https://lucablanchi.it/presentation-theory/certified-adaptive-discovery-algebraic-laws.html)
  - Summary: A finite-sample inference layer for algebraic laws discovered after adaptive search, using volume certificates, e-values, and rational-data certificates.
  - Date: June 2026
  - PDF: https://lucablanchi.it/assets/presentation-theory/certified-adaptive-discovery-algebraic-laws/certified-adaptive-discovery-algebraic-laws.pdf
- [Toric Certificates for Effective Skolem Tails and Subspace Orbit Reachability](https://lucablanchi.it/presentation-theory/toric-certificates-effective-skolem-tails-subspace-orbit-reachability.html)
  - Summary: Toric lower-bound certificates, binomial-stratified certificate trees, and automatic effective zero-free tails for simultaneous Skolem and subspace orbit reachability.
  - Date: June 2026
  - PDF: https://lucablanchi.it/assets/presentation-theory/toric-certificates-effective-skolem-tails-subspace-orbit-reachability/toric-certificates-effective-skolem-tails-subspace-orbit-reachability.pdf
- [Proof-Carrying Toric Guard Certificates for Positivity of Linear Recurrence Sequences](https://lucablanchi.it/presentation-theory/proof-carrying-toric-guard-certificates-positivity-linear-recurrence-sequences.html)
  - Summary: Proof-carrying toric guard certificates for positivity of real algebraic linear recurrence sequences.
  - Date: June 2026
  - PDF: https://lucablanchi.it/assets/presentation-theory/proof-carrying-toric-guard-certificates-positivity-linear-recurrence-sequences/proof-carrying-toric-guard-certificates-positivity-linear-recurrence-sequences.pdf

### Arithmetic Dynamics and Geometry

Arithmetic and geometric applications where presentation costs or finite access data control preimage layers, p-adic traps, blow-up depth, and Rouquier-dimension bounds.

- [Exact Rational Preperiodic Portraits from Controlled p-adic Traps](https://lucablanchi.it/presentation-theory/exact-rational-preperiodic-portraits-controlled-p-adic-traps.html)
  - Summary: Exact rational preperiodic portraits for rational maps from controlled bad reduction and p-adic trap dynamics.
  - Date: June 2026
  - PDF: https://lucablanchi.it/assets/presentation-theory/exact-rational-preperiodic-portraits-controlled-p-adic-traps/exact-rational-preperiodic-portraits-controlled-p-adic-traps.pdf
- [Exact Preimage Layers and Effective Primitive Divisors for Rational Maps on P1](https://lucablanchi.it/presentation-theory/exact-preimage-layers-effective-primitive-divisors-rational-maps-p1.html)
  - Summary: Exact preimage layers and effective primitive divisor criteria for rational maps on the projective line.
  - Date: June 2026
  - PDF: https://lucablanchi.it/assets/presentation-theory/exact-preimage-layers-effective-primitive-divisors-rational-maps-p1/exact-preimage-layers-effective-primitive-divisors-rational-maps-p1.pdf
- [Blow-up Diagonal Depth and Wonderful Compactifications](https://lucablanchi.it/presentation-theory/blow-up-diagonal-depth-wonderful-compactifications.html)
  - Summary: Coherent product diagonal depth under smooth blow-ups, with applications to wonderful compactifications, Fulton-MacPherson spaces, and moduli spaces of pointed curves.
  - Date: June 2026
  - PDF: https://lucablanchi.it/assets/presentation-theory/blow-up-diagonal-depth-wonderful-compactifications/blow-up-diagonal-depth-wonderful-compactifications.pdf
- [Dependency Depth, Strict Product Diagonal Depth, and Rouquier Dimension of Odd Hassett Spaces](https://lucablanchi.it/presentation-theory/dependency-depth-odd-hassett-spaces.html)
  - Summary: Optimal Rouquier dimension bounds for odd-heavy Hassett spaces from dependency depth and strict product diagonal depth.
  - Date: June 2026
  - PDF: https://lucablanchi.it/assets/presentation-theory/dependency-depth-odd-hassett-spaces/dependency-depth-odd-hassett-spaces.pdf

### Compression, Boolean Lifts, and Finite Structures

Finite and symbolic compression problems, including previous-copy parsing, Boolean lift obstructions, random threshold models, relation lattices, and closure systems.

- [Previous-Copy Compression: Foundations and Algebraic Digit Expansions](https://lucablanchi.it/presentation-theory/previous-copy-compression-foundations.html)
  - Summary: Foundational papers on online previous-copy parsing, extremal and metric behaviour, and algebraic digit expansions.
  - Date: June 2026
  - PDF: https://lucablanchi.it/assets/presentation-theory/previous-copy-parsing/previous-copy-compression-algebraic-digit-expansions.pdf
- [Previous-Copy Compression: Quantitative Barriers](https://lucablanchi.it/presentation-theory/previous-copy-compression-quantitative-barriers.html)
  - Summary: Finite stammering profiles, exponential tube barriers, and conditional quantitative lower bounds for previous-copy compression.
  - Date: June 2026
  - PDF: https://lucablanchi.it/assets/presentation-theory/previous-copy-parsing/finite-stammering-profiles-tube-barriers.pdf
- [Lattice Obstructions and Coefficient Alphabets for Homogeneous Boolean Lifts](https://lucablanchi.it/presentation-theory/lattice-obstructions-coefficient-alphabets.html)
  - Summary: Exact notes on two-point encoding lattices, universal denominators, coefficient alphabets, and homogeneous Boolean lift criteria.
  - Date: June 2026
  - PDF: https://lucablanchi.it/assets/presentation-theory/lattice-obstructions-coefficient-alphabets/lattice-obstructions-coefficient-alphabets-homogeneous-boolean-lifts.pdf
- [Sharp Random Thresholds for Exact Ternary Homogeneous Boolean Lifts](https://lucablanchi.it/presentation-theory/sharp-random-thresholds-exact-ternary-lifts.html)
  - Summary: A sharp random threshold theorem for exact ternary homogeneous Boolean lifts in the expanded coefficient presentation.
  - Date: June 2026
  - PDF: https://lucablanchi.it/assets/presentation-theory/sharp-random-thresholds-exact-ternary-lifts/sharp-random-thresholds-exact-ternary-homogeneous-boolean-lifts.pdf
- [Random Saturation and Optimal Off-Origin Slack in Real Homogeneous Boolean Threshold Boxes](https://lucablanchi.it/presentation-theory/random-saturation-real-homogeneous-threshold-boxes.html)
  - Summary: A real-coefficient bounded-height model for homogeneous Boolean threshold boxes, random saturation, and optimal off-origin slack.
  - Date: June 2026
  - PDF: https://lucablanchi.it/assets/presentation-theory/random-saturation-real-homogeneous-threshold-boxes/random-saturation-optimal-off-origin-slack-real-homogeneous-boolean-threshold-boxes.pdf
- [Relation Lattices and Kolmogorov Deficiency of Rational Points](https://lucablanchi.it/presentation-theory/relation-lattices-kolmogorov-deficiency-rational-points.html)
  - Summary: A relation-lattice profile of rational points, random-lattice limits, and finite-height Kolmogorov deficiency from short arithmetic certificates.
  - Date: June 2026
  - PDF: https://lucablanchi.it/assets/presentation-theory/relation-lattices-kolmogorov-deficiency-rational-points/relation-lattices-kolmogorov-deficiency-rational-points.pdf
- [Representatives of Box-Closure Systems on Downsets of Products of Chains](https://lucablanchi.it/presentation-theory/box-closure-systems-downsets-products-of-chains.html)
  - Summary: A complete representative theorem for coordinate-mixture box-closure systems on finite downsets of products of chains, with matroidal and enumerative consequences.
  - Date: June 2026
  - PDF: https://lucablanchi.it/assets/presentation-theory/box-closure-systems-downsets-products-of-chains/box-closure-systems-downsets-products-of-chains.pdf

### Differential Equations and Analytic Geometry

Presentation-theoretic applications to differential equations and analytic geometry, including irregular connections, Stokes data, and controlled Riemann-Hilbert transfer.

- [Presentation Complexity of Irregular Connections and Stokes Data](https://lucablanchi.it/presentation-theory/presentation-complexity-irregular-connections-stokes-data.html)
  - Summary: Formal types, Stokes directions and factors, ordinary-monodromy fibres, local presentation lower bounds, and controlled irregular Riemann-Hilbert transfer.
  - Date: June 2026
  - PDF: https://lucablanchi.it/assets/presentation-theory/presentation-complexity-irregular-connections-stokes-data/presentation-complexity-irregular-connections-stokes-data.pdf
- [Stokes Geometry and Presentation Complexity: Four Applications](https://lucablanchi.it/presentation-theory/stokes-geometry-presentation-complexity-applications.html)
  - Summary: Turning-locus lower bounds, tame exponential direct images, finite curve restrictions, and bounded-presentation filtrations on wild character varieties.
  - Date: June 2026
  - PDF: https://lucablanchi.it/assets/presentation-theory/stokes-geometry-presentation-complexity-applications/stokes-geometry-presentation-complexity-applications.pdf

### Proof Strategies

Long-form conditional or strategic notes where the presentation-theoretic language organizes proof obligations, residual fibres, and remaining source blocks.

- [Predictive Fibres and Critical Oseen Transfer for Navier-Stokes: Conditional Proof Strategy](https://lucablanchi.it/presentation-theory/predictive-fibres-critical-oseen-transfer-navier-stokes.html)
  - Summary: An original presentation-theoretic conditional reduction for three-dimensional Navier-Stokes, with closed proof modules and a complete list of remaining source blocks.
  - Date: June 2026
  - PDF: https://lucablanchi.it/assets/presentation-theory/predictive-fibres-critical-oseen-transfer-navier-stokes/predictive-fibres-critical-oseen-transfer-navier-stokes.pdf
- [Switch Corridors and Boundary-Rigid Lenses in Even Dumbbell Thrackles: A Local Reduction and Minimal-Witness Strategy](https://lucablanchi.it/presentation-theory/conway-thrackle-proof-strategy.html)
  - Summary: A local reduction and minimal-witness strategy for the irreducible even-dumbbell step in Conway's thrackle program.
  - Date: June 2026
  - PDF: https://lucablanchi.it/assets/presentation-theory/conway-thrackle-proof-strategy/switch-corridors-boundary-rigid-lenses-conway.pdf

## Additional Resources

- Draft concepts index: https://lucablanchi.it/drafts.html
- Life simulation: https://lucablanchi.it/life-simulation.html
- Machine-readable citations: https://lucablanchi.it/citations.json