# lucablanchi.it Full AI Index

This file is an AI-readable index of lucablanchi.it. It is intended for search engines, retrieval systems, and AI assistants that need to cite Luca Blanchi's draft concepts and preliminary AI-assisted mathematical research notes accurately.

## Author

- Name: Luca Blanchi
- Canonical author id: https://lucablanchi.it/#luca-blanchi
- Research site: https://lucablanchi.it/
- Professional profile: https://lucablanchi.dev/
- Same as: https://lucablanchi.dev/, https://github.com/LucaBlanchi, https://www.linkedin.com/in/lucablanchi/
- Background: software engineer with a background in pure mathematics, associated publicly with Università degli Studi di Pisa on lucablanchi.dev.
- Public areas of expertise: presentation theory, AI-assisted mathematics, preliminary mathematical research notes, pure mathematics, software engineering, full-stack development, TypeScript, Java, Spring Boot, Node.js, React, Angular, generative AI, prompt engineering

## Site-Level Files

- Homepage: https://lucablanchi.it/
- Life simulation: https://lucablanchi.it/life-simulation.html
- Sitemap: https://lucablanchi.it/sitemap.xml
- Robots: https://lucablanchi.it/robots.txt
- Citation JSON: https://lucablanchi.it/citations.json
- Short LLM index: https://lucablanchi.it/llms.txt

## How To Cite

Use the canonical HTML page as the main source URL. For mathematical articles, include the PDF when referring to the full manuscript and include the TeX or Markdown source when discussing exact wording or formal structure. The articles in the Presentation theory corpus should be described as preliminary AI-assisted mathematical notes unless a later version says otherwise.

## Presentation Theory Articles

### 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

- Canonical URL: https://lucablanchi.it/presentation-theory/presentation-theory-i-description-systems-costs-observable-fibres.html
- Section: Axiomatic Core
- Date: June 2026
- Summary: Presentation systems, realization fibres, observables, verification costs, normal forms, and reusable proof principles.
- Suggested citation: Luca Blanchi. "Presentation Theory I: Description Systems, Costs, and Observable Fibres." lucablanchi.it, June 2026, https://lucablanchi.it/presentation-theory/presentation-theory-i-description-systems-costs-observable-fibres.html.
- Assets:
  - PDF: Presentation Theory I Description Systems Costs Observable Fibres: https://lucablanchi.it/assets/presentation-theory/presentation-theory-i-description-systems-costs-observable-fibres/presentation-theory-i-description-systems-costs-observable-fibres.pdf
  - TeX source: Presentation Theory I Description Systems Costs Observable Fibres: https://lucablanchi.it/assets/presentation-theory/presentation-theory-i-description-systems-costs-observable-fibres/presentation-theory-i-description-systems-costs-observable-fibres.tex

#### Presentation Theory II: Controlled Transfer, Observable Budgets, and the Geometry of Fibres

- Canonical URL: https://lucablanchi.it/presentation-theory/presentation-theory-ii-controlled-transfer-observable-budgets-geometry-fibres.html
- Section: Axiomatic Core
- Date: June 2026
- Summary: Transfer packages, fragmented budgets, convergence moduli, finite-window radii, wild fixed rank-profile fibres, and fibre navigation.
- Suggested citation: Luca Blanchi. "Presentation Theory II: Controlled Transfer, Observable Budgets, and the Geometry of Fibres." lucablanchi.it, June 2026, https://lucablanchi.it/presentation-theory/presentation-theory-ii-controlled-transfer-observable-budgets-geometry-fibres.html.
- Assets:
  - PDF: Presentation Theory Ii Controlled Transfer Observable Budgets Geometry Fibres: 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
  - TeX source: Presentation Theory Ii Controlled Transfer Observable Budgets Geometry Fibres: https://lucablanchi.it/assets/presentation-theory/presentation-theory-ii-controlled-transfer-observable-budgets-geometry-fibres/presentation-theory-ii-controlled-transfer-observable-budgets-geometry-fibres.tex

#### Presentation Theory III: Normal-Form Compilation, Residual Fibres, and Stable Canonical Access

- Canonical URL: https://lucablanchi.it/presentation-theory/presentation-theory-iii-normal-form-compilation.html
- Section: Axiomatic Core
- Date: June 2026
- Summary: Normal-form packages, residual fibres, separator lower bounds, fragmented towers, heighted no-free normal forms, rewriting budgets, and spectral instability.
- Suggested citation: Luca Blanchi. "Presentation Theory III: Normal-Form Compilation, Residual Fibres, and Stable Canonical Access." lucablanchi.it, June 2026, https://lucablanchi.it/presentation-theory/presentation-theory-iii-normal-form-compilation.html.
- Assets:
  - PDF: Presentation Theory Iii Normal Form Compilation: https://lucablanchi.it/assets/presentation-theory/presentation-theory-iii-normal-form-compilation/presentation-theory-iii-normal-form-compilation.pdf
  - TeX source: Presentation Theory Iii Normal Form Compilation: https://lucablanchi.it/assets/presentation-theory/presentation-theory-iii-normal-form-compilation/presentation-theory-iii-normal-form-compilation.tex

#### Presentation Theory IV: Verifiable Access, Audit Lower Bounds, and Residual Indistinguishability

- Canonical URL: https://lucablanchi.it/presentation-theory/presentation-theory-iv-verifiable-access-audit-lower-bounds-residual-indistinguishability.html
- Section: Axiomatic Core
- Date: June 2026
- Summary: Verifiable access, audit covers, transcripts, residual indistinguishability, pullback lower bounds, and auditable Lovasz separation for CFI graphs.
- Suggested citation: Luca Blanchi. "Presentation Theory IV: Verifiable Access, Audit Lower Bounds, and Residual Indistinguishability." lucablanchi.it, June 2026, https://lucablanchi.it/presentation-theory/presentation-theory-iv-verifiable-access-audit-lower-bounds-residual-indistinguishability.html.
- Assets:
  - PDF: Presentation Theory Iv Verifiable Access Audit Lower Bounds Residual Indistinguishability: 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
  - TeX source: Presentation Theory Iv Verifiable Access Audit Lower Bounds Residual Indistinguishability: 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.tex

#### Presentation Theory V: Fibre Geometry, Navigation, and Residual Moduli

- Canonical URL: https://lucablanchi.it/presentation-theory/presentation-theory-v-fibre-geometry-navigation-residual-moduli.html
- Section: Axiomatic Core
- Date: June 2026
- 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.
- Suggested citation: Luca Blanchi. "Presentation Theory V: Fibre Geometry, Navigation, and Residual Moduli." lucablanchi.it, June 2026, https://lucablanchi.it/presentation-theory/presentation-theory-v-fibre-geometry-navigation-residual-moduli.html.
- Assets:
  - PDF: Presentation Theory V Fibre Geometry Navigation Residual Moduli: https://lucablanchi.it/assets/presentation-theory/presentation-theory-v-fibre-geometry-navigation-residual-moduli/presentation-theory-v-fibre-geometry-navigation-residual-moduli.pdf
  - TeX source: Presentation Theory V Fibre Geometry Navigation Residual Moduli: https://lucablanchi.it/assets/presentation-theory/presentation-theory-v-fibre-geometry-navigation-residual-moduli/presentation-theory-v-fibre-geometry-navigation-residual-moduli.tex

#### Presentation Theory VI: Observable Quotients, Separation, and Reconstruction

- Canonical URL: https://lucablanchi.it/presentation-theory/presentation-theory-vi-observable-quotients-separation-reconstruction.html
- Section: Axiomatic Core
- Date: June 2026
- Summary: Observable quotients, indistinguishability relations, target reconstruction, residual target factors, finite set-cover fingerprints, adaptive decision trees, structured resolving refinements, and stability.
- Suggested citation: Luca Blanchi. "Presentation Theory VI: Observable Quotients, Separation, and Reconstruction." lucablanchi.it, June 2026, https://lucablanchi.it/presentation-theory/presentation-theory-vi-observable-quotients-separation-reconstruction.html.
- Assets:
  - PDF: Presentation Theory Vi Observable Quotients Separation Reconstruction: https://lucablanchi.it/assets/presentation-theory/presentation-theory-vi-observable-quotients-separation-reconstruction/presentation-theory-vi-observable-quotients-separation-reconstruction.pdf
  - TeX source: Presentation Theory Vi Observable Quotients Separation Reconstruction: https://lucablanchi.it/assets/presentation-theory/presentation-theory-vi-observable-quotients-separation-reconstruction/presentation-theory-vi-observable-quotients-separation-reconstruction.tex

#### Presentation Theory VII: Assembly Envelopes and Operational Fibres

- Canonical URL: https://lucablanchi.it/presentation-theory/presentation-theory-vii-assembly-envelopes-operational-fibres.html
- Section: Axiomatic Core
- Date: June 2026
- Summary: Operations as presentation engines: assembly envelopes, operational image filtrations, decomposition fibres, bridge costs, observable barriers, and verification records.
- Suggested citation: Luca Blanchi. "Presentation Theory VII: Assembly Envelopes and Operational Fibres." lucablanchi.it, June 2026, https://lucablanchi.it/presentation-theory/presentation-theory-vii-assembly-envelopes-operational-fibres.html.
- Assets:
  - PDF: Presentation Theory VII: Assembly Envelopes and Operational Fibres: https://lucablanchi.it/assets/presentation-theory/presentation-theory-vii-assembly-envelopes-operational-fibres/presentation-theory-vii-assembly-envelopes-operational-fibres.pdf
  - TeX source: Presentation Theory VII: Assembly Envelopes and Operational Fibres: https://lucablanchi.it/assets/presentation-theory/presentation-theory-vii-assembly-envelopes-operational-fibres/presentation-theory-vii-assembly-envelopes-operational-fibres.tex

### 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

- Canonical URL: https://lucablanchi.it/presentation-theory/atlas-controlled-transfer-packages.html
- Section: Addenda
- Date: June 2026
- Summary: An operational atlas of contexts, observables, verification data, fibres, and overhead functions for building transfer packages in Presentation Theory.
- Suggested citation: Luca Blanchi. "Atlas of Controlled Transfer Packages." lucablanchi.it, June 2026, https://lucablanchi.it/presentation-theory/atlas-controlled-transfer-packages.html.
- Assets:
  - PDF: Atlas Controlled Transfer Packages: https://lucablanchi.it/assets/presentation-theory/atlas-controlled-transfer-packages/atlas-controlled-transfer-packages.pdf
  - TeX source: Atlas Controlled Transfer Packages: https://lucablanchi.it/assets/presentation-theory/atlas-controlled-transfer-packages/atlas-controlled-transfer-packages.tex

#### Fragmented Presentation Systems and Resource-Bound Degrees

- Canonical URL: https://lucablanchi.it/presentation-theory/fragmented-presentation-systems-resource-bound-degrees.html
- Section: Addenda
- Date: June 2026
- Summary: Decidable bounded fragments, positive-instance width profiles, exact Turing degrees of resource bounds, and representation-profile applications.
- Suggested citation: Luca Blanchi. "Fragmented Presentation Systems and Resource-Bound Degrees." lucablanchi.it, June 2026, https://lucablanchi.it/presentation-theory/fragmented-presentation-systems-resource-bound-degrees.html.
- Assets:
  - PDF: Fragmented Presentation Systems Resource Bound Degrees: https://lucablanchi.it/assets/presentation-theory/fragmented-presentation-systems-resource-bound-degrees/fragmented-presentation-systems-resource-bound-degrees.pdf
  - TeX source: Fragmented Presentation Systems Resource Bound Degrees: https://lucablanchi.it/assets/presentation-theory/fragmented-presentation-systems-resource-bound-degrees/fragmented-presentation-systems-resource-bound-degrees.tex

#### Controlled Transfer in Action: Selected Examples

- Canonical URL: https://lucablanchi.it/presentation-theory/controlled-transfer-in-action.html
- Section: Addenda
- Date: June 2026
- 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.
- Suggested citation: Luca Blanchi. "Controlled Transfer in Action: Selected Examples." lucablanchi.it, June 2026, https://lucablanchi.it/presentation-theory/controlled-transfer-in-action.html.
- Assets:
  - PDF: Controlled Transfer In Action: https://lucablanchi.it/assets/presentation-theory/controlled-transfer-in-action/controlled-transfer-in-action.pdf
  - TeX source: Controlled Transfer In Action: https://lucablanchi.it/assets/presentation-theory/controlled-transfer-in-action/controlled-transfer-in-action.tex

### 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

- Canonical URL: https://lucablanchi.it/presentation-theory/no-free-degenerations-presentation-cost-heights-normal-forms.html
- Section: Direct Applications
- Date: June 2026
- Summary: Heighted normal-form presentations, gauge and degeneration costs, orbit-closure height bounds, controlled transfer, and representative-moduli gap estimates.
- Suggested citation: Luca Blanchi. "No Free Degenerations: Presentation Cost, Heights, and the Arithmetic Price of Normal Forms." lucablanchi.it, June 2026, https://lucablanchi.it/presentation-theory/no-free-degenerations-presentation-cost-heights-normal-forms.html.
- Assets:
  - PDF: No Free Degenerations Presentation Cost Heights Normal Forms: https://lucablanchi.it/assets/presentation-theory/no-free-degenerations-presentation-cost-heights-normal-forms/no-free-degenerations-presentation-cost-heights-normal-forms.pdf
  - TeX source: No Free Degenerations Presentation Cost Heights Normal Forms: https://lucablanchi.it/assets/presentation-theory/no-free-degenerations-presentation-cost-heights-normal-forms/no-free-degenerations-presentation-cost-heights-normal-forms.tex

#### Invisible Flats and the Cost of Marked Normal Forms

- Canonical URL: https://lucablanchi.it/presentation-theory/invisible-flats-marked-normal-forms.html
- Section: Direct Applications
- Date: June 2026
- Summary: Rate-distortion lower bounds for marked reconstruction from finite-depth Torelli, Johnson, homological, and level data via invisible mapping-class-group flats.
- Suggested citation: Luca Blanchi. "Invisible Flats and the Cost of Marked Normal Forms." lucablanchi.it, June 2026, https://lucablanchi.it/presentation-theory/invisible-flats-marked-normal-forms.html.
- Assets:
  - PDF: Invisible Flats Marked Normal Forms: https://lucablanchi.it/assets/presentation-theory/invisible-flats-marked-normal-forms/invisible-flats-marked-normal-forms.pdf
  - TeX source: Invisible Flats Marked Normal Forms: https://lucablanchi.it/assets/presentation-theory/invisible-flats-marked-normal-forms/invisible-flats-marked-normal-forms.tex

#### Statement Presentations and a Semilinear Greedy 3-Sumfree Sequence

- Canonical URL: https://lucablanchi.it/presentation-theory/statement-presentations-semilinear-greedy-3-sumfree-sequence.html
- Section: Direct Applications
- Date: June 2026
- Summary: A direct semilinear proof of a parametric greedy 3-sumfree sequence formula, with a presentation-theoretic reading of the finite interval-sum verification.
- Suggested citation: Luca Blanchi. "Statement Presentations and a Semilinear Greedy 3-Sumfree Sequence." lucablanchi.it, June 2026, https://lucablanchi.it/presentation-theory/statement-presentations-semilinear-greedy-3-sumfree-sequence.html.
- Assets:
  - PDF: Statement Presentations Semilinear Greedy 3 Sumfree Sequence: https://lucablanchi.it/assets/presentation-theory/statement-presentations-semilinear-greedy-3-sumfree-sequence/statement-presentations-semilinear-greedy-3-sumfree-sequence.pdf
  - TeX source: Statement Presentations Semilinear Greedy 3 Sumfree Sequence: https://lucablanchi.it/assets/presentation-theory/statement-presentations-semilinear-greedy-3-sumfree-sequence/statement-presentations-semilinear-greedy-3-sumfree-sequence.tex

#### Presentation Incidence and Rank-Invariant Fibres in Multiparameter Persistence

- Canonical URL: https://lucablanchi.it/presentation-theory/presentation-incidence-rank-fibres-multiparameter-persistence.html
- Section: Direct Applications
- Date: June 2026
- Summary: Antichain presentation modules, active polymatroid profiles, matroid realization strata, and quiver representation geometry inside multiparameter persistence.
- Suggested citation: Luca Blanchi. "Presentation Incidence and Rank-Invariant Fibres in Multiparameter Persistence." lucablanchi.it, June 2026, https://lucablanchi.it/presentation-theory/presentation-incidence-rank-fibres-multiparameter-persistence.html.
- Assets:
  - PDF: Presentation Incidence Rank Fibres Multiparameter Persistence: https://lucablanchi.it/assets/presentation-theory/presentation-incidence-rank-fibres-multiparameter-persistence/presentation-incidence-rank-fibres-multiparameter-persistence.pdf
  - TeX source: Presentation Incidence Rank Fibres Multiparameter Persistence: https://lucablanchi.it/assets/presentation-theory/presentation-incidence-rank-fibres-multiparameter-persistence/presentation-incidence-rank-fibres-multiparameter-persistence.tex

### 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

- Canonical URL: https://lucablanchi.it/presentation-theory/presentation-langlands-i-proof-carrying-hecke-records.html
- Section: Langlands Access
- Date: June 2026
- Summary: A finite proof-carrying format for Hecke eigensystem data, with separating fingerprints, projector witnesses, negative ideal-membership witnesses, residual ledgers, and normalization records.
- Suggested citation: Luca Blanchi. "Presentation-Langlands I: Proof-Carrying Hecke Records." lucablanchi.it, June 2026, https://lucablanchi.it/presentation-theory/presentation-langlands-i-proof-carrying-hecke-records.html.
- Assets:
  - PDF: Presentation Langlands I Proof Carrying Hecke Records: https://lucablanchi.it/assets/presentation-theory/presentation-langlands-i-proof-carrying-hecke-records/presentation-langlands-i-proof-carrying-hecke-records.pdf
  - TeX source: Presentation Langlands I Proof Carrying Hecke Records: https://lucablanchi.it/assets/presentation-theory/presentation-langlands-i-proof-carrying-hecke-records/presentation-langlands-i-proof-carrying-hecke-records.tex

#### Optimal Class-Group Tomography for Hecke Eigensystems over Number Fields

- Canonical URL: https://lucablanchi.it/presentation-theory/class-group-tomography-hecke-eigensystems-number-fields.html
- Section: Langlands Access
- Date: June 2026
- 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.
- Suggested citation: Luca Blanchi. "Optimal Class-Group Tomography for Hecke Eigensystems over Number Fields." lucablanchi.it, June 2026, https://lucablanchi.it/presentation-theory/class-group-tomography-hecke-eigensystems-number-fields.html.
- Assets:
  - PDF: Optimal Class Group Tomography Hecke Eigensystems Number Fields: https://lucablanchi.it/assets/presentation-theory/class-group-tomography-hecke-eigensystems-number-fields/class-group-tomography-hecke-eigensystems-number-fields.pdf
  - TeX source: Optimal Class Group Tomography Hecke Eigensystems Number Fields: https://lucablanchi.it/assets/presentation-theory/class-group-tomography-hecke-eigensystems-number-fields/class-group-tomography-hecke-eigensystems-number-fields.tex

#### Finite Transfer Audits in Presentation-Langlands

- Canonical URL: https://lucablanchi.it/presentation-theory/verified-transfer-audits-finite-langlands-windows.html
- Section: Langlands Access
- Date: June 2026
- 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.
- Suggested citation: Luca Blanchi. "Finite Transfer Audits in Presentation-Langlands." lucablanchi.it, June 2026, https://lucablanchi.it/presentation-theory/verified-transfer-audits-finite-langlands-windows.html.
- Assets:
  - PDF: Finite Transfer Audits Presentation Langlands: https://lucablanchi.it/assets/presentation-theory/verified-transfer-audits-finite-langlands-windows/verified-transfer-audits-finite-langlands-windows.pdf
  - TeX source: Finite Transfer Audits Presentation Langlands: https://lucablanchi.it/assets/presentation-theory/verified-transfer-audits-finite-langlands-windows/verified-transfer-audits-finite-langlands-windows.tex

#### Analytic, Categorical, and Database Access Modules in Presentation-Langlands

- Canonical URL: https://lucablanchi.it/presentation-theory/analytic-categorical-database-access-modules-presentation-langlands.html
- Section: Langlands Access
- Date: June 2026
- 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.
- Suggested citation: Luca Blanchi. "Analytic, Categorical, and Database Access Modules in Presentation-Langlands." lucablanchi.it, June 2026, https://lucablanchi.it/presentation-theory/analytic-categorical-database-access-modules-presentation-langlands.html.
- Assets:
  - PDF: Analytic Categorical Database Access Modules Presentation Langlands: https://lucablanchi.it/assets/presentation-theory/analytic-categorical-database-access-modules-presentation-langlands/analytic-categorical-database-access-modules-presentation-langlands.pdf
  - TeX source: Analytic Categorical Database Access Modules Presentation Langlands: https://lucablanchi.it/assets/presentation-theory/analytic-categorical-database-access-modules-presentation-langlands/analytic-categorical-database-access-modules-presentation-langlands.tex

### 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

- Canonical URL: https://lucablanchi.it/presentation-theory/quadratic-presentational-complexity-observable-barriers.html
- Section: Observable Geometry in Groups
- Date: June 2026
- Summary: Quadratic normal forms for word observables, graphical class-two groups, right homomorphism profiles, and exact arity barriers.
- Suggested citation: Luca Blanchi. "Quadratic Presentational Complexity and Exact Observable Barriers for Class-Two p-Groups." lucablanchi.it, June 2026, https://lucablanchi.it/presentation-theory/quadratic-presentational-complexity-observable-barriers.html.
- Assets:
  - PDF: Quadratic Presentational Complexity Observable Barriers: https://lucablanchi.it/assets/presentation-theory/quadratic-presentational-complexity-observable-barriers/quadratic-presentational-complexity-observable-barriers.pdf
  - TeX source: Quadratic Presentational Complexity Observable Barriers: https://lucablanchi.it/assets/presentation-theory/quadratic-presentational-complexity-observable-barriers/quadratic-presentational-complexity-observable-barriers.tex

#### Star and Support-Image Profiles for Class-Two p-Groups

- Canonical URL: https://lucablanchi.it/presentation-theory/star-support-image-profiles-class-two-p-groups.html
- Section: Observable Geometry in Groups
- Date: June 2026
- Summary: A comparison of higher commuting probabilities, star profiles, rank-support enumerators, support-image profiles, and centralizer transforms for class-two exponent-p groups.
- Suggested citation: Luca Blanchi. "Star and Support-Image Profiles for Class-Two p-Groups." lucablanchi.it, June 2026, https://lucablanchi.it/presentation-theory/star-support-image-profiles-class-two-p-groups.html.
- Assets:
  - PDF: Star Support Image Profiles Class Two P Groups: https://lucablanchi.it/assets/presentation-theory/star-support-image-profiles-class-two-p-groups/star-support-image-profiles-class-two-p-groups.pdf
  - TeX source: Star Support Image Profiles Class Two P Groups: https://lucablanchi.it/assets/presentation-theory/star-support-image-profiles-class-two-p-groups/star-support-image-profiles-class-two-p-groups.tex

#### Pfaffian Degree as Observable Complexity in Class-Two p-Groups

- Canonical URL: https://lucablanchi.it/presentation-theory/sharp-support-image-thresholds-alternating-pencils.html
- Section: Observable Geometry in Groups
- Date: June 2026
- Summary: Exact support-image and word-observable depth theorems for regular alternating pencils and associated class-two exponent-p groups.
- Suggested citation: Luca Blanchi. "Pfaffian Degree as Observable Complexity in Class-Two p-Groups." lucablanchi.it, June 2026, https://lucablanchi.it/presentation-theory/sharp-support-image-thresholds-alternating-pencils.html.
- Assets:
  - PDF: Sharp Support Image Thresholds Alternating Pencils: https://lucablanchi.it/assets/presentation-theory/sharp-support-image-thresholds-alternating-pencils/sharp-support-image-thresholds-alternating-pencils.pdf
  - TeX source: Sharp Support Image Thresholds Alternating Pencils: https://lucablanchi.it/assets/presentation-theory/sharp-support-image-thresholds-alternating-pencils/sharp-support-image-thresholds-alternating-pencils.tex

#### Complete Commutator-Word Tomography of Alternating Pencils

- Canonical URL: https://lucablanchi.it/presentation-theory/complete-commutator-word-tomography-alternating-pencils.html
- Section: Observable Geometry in Groups
- Date: June 2026
- Summary: Complete word-moment observability of the skew-symmetric Kronecker data of alternating commutator pencils.
- Suggested citation: Luca Blanchi. "Complete Commutator-Word Tomography of Alternating Pencils." lucablanchi.it, June 2026, https://lucablanchi.it/presentation-theory/complete-commutator-word-tomography-alternating-pencils.html.
- Assets:
  - PDF: Complete Commutator Word Tomography Alternating Pencils: https://lucablanchi.it/assets/presentation-theory/complete-commutator-word-tomography-alternating-pencils/complete-commutator-word-tomography-alternating-pencils.pdf
  - TeX source: Complete Commutator Word Tomography Alternating Pencils: https://lucablanchi.it/assets/presentation-theory/complete-commutator-word-tomography-alternating-pencils/complete-commutator-word-tomography-alternating-pencils.tex

#### Generic Odd-Pfaffian Reconstruction from Commutator-Word Moments

- Canonical URL: https://lucablanchi.it/presentation-theory/generic-odd-pfaffian-reconstruction-commutator-word-moments.html
- Section: Observable Geometry in Groups
- Date: June 2026
- Summary: Generic reconstruction of odd Pfaffian alternating tensors from pointwise Fourier-tagged commutator-word moment data.
- Suggested citation: Luca Blanchi. "Generic Odd-Pfaffian Reconstruction from Commutator-Word Moments." lucablanchi.it, June 2026, https://lucablanchi.it/presentation-theory/generic-odd-pfaffian-reconstruction-commutator-word-moments.html.
- Assets:
  - PDF: Generic Odd Pfaffian Reconstruction Commutator Word Moments: https://lucablanchi.it/assets/presentation-theory/generic-odd-pfaffian-reconstruction-commutator-word-moments/generic-odd-pfaffian-reconstruction-commutator-word-moments.pdf
  - TeX source: Generic Odd Pfaffian Reconstruction Commutator Word Moments: https://lucablanchi.it/assets/presentation-theory/generic-odd-pfaffian-reconstruction-commutator-word-moments/generic-odd-pfaffian-reconstruction-commutator-word-moments.tex

#### Word-Measure Twins and Pfaffian Moduli in Class-Two p-Groups

- Canonical URL: https://lucablanchi.it/presentation-theory/word-measure-twins-pfaffian-moduli-class-two-p-groups.html
- Section: Observable Geometry in Groups
- Date: June 2026
- Summary: Large families of non-isomorphic class-two p-groups with identical word-map distributions, built from Pfaffian moduli.
- Suggested citation: Luca Blanchi. "Word-Measure Twins and Pfaffian Moduli in Class-Two p-Groups." lucablanchi.it, June 2026, https://lucablanchi.it/presentation-theory/word-measure-twins-pfaffian-moduli-class-two-p-groups.html.
- Assets:
  - PDF: Word Measure Twins Pfaffian Moduli Class Two P Groups: 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
  - TeX source: Word Measure Twins Pfaffian Moduli Class Two P Groups: https://lucablanchi.it/assets/presentation-theory/word-measure-twins-pfaffian-moduli-class-two-p-groups/word-measure-twins-pfaffian-moduli-class-two-p-groups.tex

#### The Polar-Code Endpoint for Class-Two p-Groups

- Canonical URL: https://lucablanchi.it/presentation-theory/polar-code-endpoint-class-two-p-groups.html
- Section: Observable Geometry in Groups
- Date: June 2026
- Summary: The endpoint of the class-two p-group observable hierarchy: polar-code completeness, generic geometric reconstruction, and standard-structure residual reduction.
- Suggested citation: Luca Blanchi. "The Polar-Code Endpoint for Class-Two p-Groups." lucablanchi.it, June 2026, https://lucablanchi.it/presentation-theory/polar-code-endpoint-class-two-p-groups.html.
- Assets:
  - PDF: Polar Code Endpoint Class Two P Groups: https://lucablanchi.it/assets/presentation-theory/polar-code-endpoint-class-two-p-groups/polar-code-endpoint-class-two-p-groups.pdf
  - TeX source: Polar Code Endpoint Class Two P Groups: https://lucablanchi.it/assets/presentation-theory/polar-code-endpoint-class-two-p-groups/polar-code-endpoint-class-two-p-groups.tex

#### Relative Linear Word Observables and Representation Complexity of Semidirect Products

- Canonical URL: https://lucablanchi.it/presentation-theory/relative-linear-word-observables-semidirect-products.html
- Section: Observable Geometry in Groups
- Date: June 2026
- Summary: Relative k-linear word observables, matrix-rank profiles, and semisimple, cyclic modular, and wild regimes for marked semidirect products.
- Suggested citation: Luca Blanchi. "Relative Linear Word Observables and Representation Complexity of Semidirect Products." lucablanchi.it, June 2026, https://lucablanchi.it/presentation-theory/relative-linear-word-observables-semidirect-products.html.
- Assets:
  - PDF: Relative Linear Word Observables Semidirect Products: https://lucablanchi.it/assets/presentation-theory/relative-linear-word-observables-semidirect-products/relative-linear-word-observables-semidirect-products.pdf
  - TeX source: Relative Linear Word Observables Semidirect Products: https://lucablanchi.it/assets/presentation-theory/relative-linear-word-observables-semidirect-products/relative-linear-word-observables-semidirect-products.tex

#### Finite Lovász Profiles for Coprime Affine Groups

- Canonical URL: https://lucablanchi.it/presentation-theory/finite-lovasz-profiles-coprime-affine-groups.html
- Section: Observable Geometry in Groups
- Date: June 2026
- Summary: Finite left and right Lovász dimensions, bounded hom-count test families, and two-object tests for coprime affine groups.
- Suggested citation: Luca Blanchi. "Finite Lovász Profiles for Coprime Affine Groups." lucablanchi.it, June 2026, https://lucablanchi.it/presentation-theory/finite-lovasz-profiles-coprime-affine-groups.html.
- Assets:
  - PDF: Finite Lovasz Profiles Coprime Affine Groups: https://lucablanchi.it/assets/presentation-theory/finite-lovasz-profiles-coprime-affine-groups/finite-lovasz-profiles-coprime-affine-groups.pdf
  - TeX source: Finite Lovasz Profiles Coprime Affine Groups: https://lucablanchi.it/assets/presentation-theory/finite-lovasz-profiles-coprime-affine-groups/finite-lovasz-profiles-coprime-affine-groups.tex

#### Degree-weighted Normal Covers of Symmetric and Alternating Groups

- Canonical URL: https://lucablanchi.it/presentation-theory/degree-weighted-normal-covers-symmetric-alternating-groups.html
- Section: Observable Geometry in Groups
- Date: June 2026
- Summary: A degree-weighted analogue of normal covering numbers for symmetric and alternating groups, with arithmetic motivation from intersective polynomials.
- Suggested citation: Luca Blanchi. "Degree-weighted Normal Covers of Symmetric and Alternating Groups." lucablanchi.it, June 2026, https://lucablanchi.it/presentation-theory/degree-weighted-normal-covers-symmetric-alternating-groups.html.
- Assets:
  - PDF: Degree Weighted Normal Covers Symmetric Alternating Groups: https://lucablanchi.it/assets/presentation-theory/degree-weighted-normal-covers-symmetric-alternating-groups/degree-weighted-normal-covers-symmetric-alternating-groups.pdf
  - TeX source: Degree Weighted Normal Covers Symmetric Alternating Groups: https://lucablanchi.it/assets/presentation-theory/degree-weighted-normal-covers-symmetric-alternating-groups/degree-weighted-normal-covers-symmetric-alternating-groups.tex
  - Markdown source: Degree Weighted Normal Covers Symmetric Alternating Groups: https://lucablanchi.it/assets/presentation-theory/degree-weighted-normal-covers-symmetric-alternating-groups/degree-weighted-normal-covers-symmetric-alternating-groups.md

#### LEF Growth of Wreath Products with Abelian and Virtually Abelian Lamps

- Canonical URL: https://lucablanchi.it/presentation-theory/lef-growth-wreath-products.html
- Section: Observable Geometry in Groups
- Date: June 2026
- Summary: LEF growth for wreath products with abelian, non-abelian, virtually abelian, and Heisenberg-base examples.
- Suggested citation: Luca Blanchi. "LEF Growth of Wreath Products with Abelian and Virtually Abelian Lamps." lucablanchi.it, June 2026, https://lucablanchi.it/presentation-theory/lef-growth-wreath-products.html.
- Assets:
  - PDF: Lef Growth Wreath Products: https://lucablanchi.it/assets/presentation-theory/lef-growth-wreath-products/lef-growth-wreath-products.pdf
  - TeX source: Lef Growth Wreath Products: https://lucablanchi.it/assets/presentation-theory/lef-growth-wreath-products/lef-growth-wreath-products.tex

### 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

- Canonical URL: https://lucablanchi.it/presentation-theory/representation-theoretic-scalar-compression-linear-differential-equations.html
- Section: Algebraic and Computational Complexity
- Date: June 2026
- Summary: Minimum scalar differential order from realized orbit spans, with Picard-Fuchs observables, periods, and isotypic rank formulas.
- Suggested citation: Luca Blanchi. "Representation-Theoretic Scalar Compression for Linear Differential Equations." lucablanchi.it, June 2026, https://lucablanchi.it/presentation-theory/representation-theoretic-scalar-compression-linear-differential-equations.html.
- Assets:
  - PDF: Representation Theoretic Scalar Compression Linear Differential Equations: https://lucablanchi.it/assets/presentation-theory/representation-theoretic-scalar-compression-linear-differential-equations/representation-theoretic-scalar-compression-linear-differential-equations.pdf
  - TeX source: Representation Theoretic Scalar Compression Linear Differential Equations: https://lucablanchi.it/assets/presentation-theory/representation-theoretic-scalar-compression-linear-differential-equations/representation-theoretic-scalar-compression-linear-differential-equations.tex

#### Filtered Equivariant Membership and Static Algebraic Proof Degree

- Canonical URL: https://lucablanchi.it/presentation-theory/filtered-equivariant-membership-static-algebraic-proof-degree.html
- Section: Algebraic and Computational Complexity
- Date: June 2026
- Summary: Static algebraic proof degree, homogenized presentation ideals, finite-domain filtered membership, Boolean reciprocals, and equivariant Macaulay compression.
- Suggested citation: Luca Blanchi. "Filtered Equivariant Membership and Static Algebraic Proof Degree." lucablanchi.it, June 2026, https://lucablanchi.it/presentation-theory/filtered-equivariant-membership-static-algebraic-proof-degree.html.
- Assets:
  - PDF: Filtered Equivariant Membership Static Algebraic Proof Degree: https://lucablanchi.it/assets/presentation-theory/filtered-equivariant-membership-static-algebraic-proof-degree/filtered-equivariant-membership-static-algebraic-proof-degree.pdf
  - TeX source: Filtered Equivariant Membership Static Algebraic Proof Degree: https://lucablanchi.it/assets/presentation-theory/filtered-equivariant-membership-static-algebraic-proof-degree/filtered-equivariant-membership-static-algebraic-proof-degree.tex

#### Local Linear Presentations and Sparse Factorization Complexity

- Canonical URL: https://lucablanchi.it/presentation-theory/local-linear-presentations-sparse-factorization.html
- Section: Algebraic and Computational Complexity
- Date: June 2026
- Summary: Local presentation rank, sparse factorization complexity, exact linear data structures, and dynamic prefix-sum lower-bound problems.
- Suggested citation: Luca Blanchi. "Local Linear Presentations and Sparse Factorization Complexity." lucablanchi.it, June 2026, https://lucablanchi.it/presentation-theory/local-linear-presentations-sparse-factorization.html.
- Assets:
  - PDF: Local Linear Presentations Sparse Factorization: https://lucablanchi.it/assets/presentation-theory/local-linear-presentations-sparse-factorization/local-linear-presentations-sparse-factorization.pdf
  - TeX source: Local Linear Presentations Sparse Factorization: https://lucablanchi.it/assets/presentation-theory/local-linear-presentations-sparse-factorization/local-linear-presentations-sparse-factorization.tex

#### Certified Adaptive Discovery of Algebraic Laws

- Canonical URL: https://lucablanchi.it/presentation-theory/certified-adaptive-discovery-algebraic-laws.html
- Section: Algebraic and Computational Complexity
- Date: June 2026
- Summary: A finite-sample inference layer for algebraic laws discovered after adaptive search, using volume certificates, e-values, and rational-data certificates.
- Suggested citation: Luca Blanchi. "Certified Adaptive Discovery of Algebraic Laws." lucablanchi.it, June 2026, https://lucablanchi.it/presentation-theory/certified-adaptive-discovery-algebraic-laws.html.
- Assets:
  - PDF: Certified Adaptive Discovery Algebraic Laws: https://lucablanchi.it/assets/presentation-theory/certified-adaptive-discovery-algebraic-laws/certified-adaptive-discovery-algebraic-laws.pdf
  - TeX source: Certified Adaptive Discovery Algebraic Laws: https://lucablanchi.it/assets/presentation-theory/certified-adaptive-discovery-algebraic-laws/certified-adaptive-discovery-algebraic-laws.tex

#### Toric Certificates for Effective Skolem Tails and Subspace Orbit Reachability

- Canonical URL: https://lucablanchi.it/presentation-theory/toric-certificates-effective-skolem-tails-subspace-orbit-reachability.html
- Section: Algebraic and Computational Complexity
- Date: June 2026
- Summary: Toric lower-bound certificates, binomial-stratified certificate trees, and automatic effective zero-free tails for simultaneous Skolem and subspace orbit reachability.
- Suggested citation: Luca Blanchi. "Toric Certificates for Effective Skolem Tails and Subspace Orbit Reachability." lucablanchi.it, June 2026, https://lucablanchi.it/presentation-theory/toric-certificates-effective-skolem-tails-subspace-orbit-reachability.html.
- Assets:
  - PDF: Toric Certificates Effective Skolem Tails Subspace Orbit Reachability: https://lucablanchi.it/assets/presentation-theory/toric-certificates-effective-skolem-tails-subspace-orbit-reachability/toric-certificates-effective-skolem-tails-subspace-orbit-reachability.pdf
  - TeX source: Toric Certificates Effective Skolem Tails Subspace Orbit Reachability: https://lucablanchi.it/assets/presentation-theory/toric-certificates-effective-skolem-tails-subspace-orbit-reachability/toric-certificates-effective-skolem-tails-subspace-orbit-reachability.tex

#### Proof-Carrying Toric Guard Certificates for Positivity of Linear Recurrence Sequences

- Canonical URL: https://lucablanchi.it/presentation-theory/proof-carrying-toric-guard-certificates-positivity-linear-recurrence-sequences.html
- Section: Algebraic and Computational Complexity
- Date: June 2026
- Summary: Proof-carrying toric guard certificates for positivity of real algebraic linear recurrence sequences.
- Suggested citation: Luca Blanchi. "Proof-Carrying Toric Guard Certificates for Positivity of Linear Recurrence Sequences." lucablanchi.it, June 2026, https://lucablanchi.it/presentation-theory/proof-carrying-toric-guard-certificates-positivity-linear-recurrence-sequences.html.
- Assets:
  - PDF: Proof Carrying Toric Guard Certificates Positivity Linear Recurrence Sequences: 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
  - TeX source: Proof Carrying Toric Guard Certificates Positivity Linear Recurrence Sequences: https://lucablanchi.it/assets/presentation-theory/proof-carrying-toric-guard-certificates-positivity-linear-recurrence-sequences/proof-carrying-toric-guard-certificates-positivity-linear-recurrence-sequences.tex

### 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

- Canonical URL: https://lucablanchi.it/presentation-theory/exact-rational-preperiodic-portraits-controlled-p-adic-traps.html
- Section: Arithmetic Dynamics and Geometry
- Date: June 2026
- Summary: Exact rational preperiodic portraits for rational maps from controlled bad reduction and p-adic trap dynamics.
- Suggested citation: Luca Blanchi. "Exact Rational Preperiodic Portraits from Controlled p-adic Traps." lucablanchi.it, June 2026, https://lucablanchi.it/presentation-theory/exact-rational-preperiodic-portraits-controlled-p-adic-traps.html.
- Assets:
  - PDF: Exact Rational Preperiodic Portraits Controlled P Adic Traps: https://lucablanchi.it/assets/presentation-theory/exact-rational-preperiodic-portraits-controlled-p-adic-traps/exact-rational-preperiodic-portraits-controlled-p-adic-traps.pdf
  - TeX source: Exact Rational Preperiodic Portraits Controlled P Adic Traps: https://lucablanchi.it/assets/presentation-theory/exact-rational-preperiodic-portraits-controlled-p-adic-traps/exact-rational-preperiodic-portraits-controlled-p-adic-traps.tex

#### Exact Preimage Layers and Effective Primitive Divisors for Rational Maps on P1

- Canonical URL: https://lucablanchi.it/presentation-theory/exact-preimage-layers-effective-primitive-divisors-rational-maps-p1.html
- Section: Arithmetic Dynamics and Geometry
- Date: June 2026
- Summary: Exact preimage layers and effective primitive divisor criteria for rational maps on the projective line.
- Suggested citation: Luca Blanchi. "Exact Preimage Layers and Effective Primitive Divisors for Rational Maps on P1." lucablanchi.it, June 2026, https://lucablanchi.it/presentation-theory/exact-preimage-layers-effective-primitive-divisors-rational-maps-p1.html.
- Assets:
  - PDF: Exact Preimage Layers Effective Primitive Divisors Rational Maps P1: 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
  - TeX source: Exact Preimage Layers Effective Primitive Divisors Rational Maps P1: https://lucablanchi.it/assets/presentation-theory/exact-preimage-layers-effective-primitive-divisors-rational-maps-p1/exact-preimage-layers-effective-primitive-divisors-rational-maps-p1.tex

#### Blow-up Diagonal Depth and Wonderful Compactifications

- Canonical URL: https://lucablanchi.it/presentation-theory/blow-up-diagonal-depth-wonderful-compactifications.html
- Section: Arithmetic Dynamics and Geometry
- Date: June 2026
- Summary: Coherent product diagonal depth under smooth blow-ups, with applications to wonderful compactifications, Fulton-MacPherson spaces, and moduli spaces of pointed curves.
- Suggested citation: Luca Blanchi. "Blow-up Diagonal Depth and Wonderful Compactifications." lucablanchi.it, June 2026, https://lucablanchi.it/presentation-theory/blow-up-diagonal-depth-wonderful-compactifications.html.
- Assets:
  - PDF: Blow Up Diagonal Depth Wonderful Compactifications: https://lucablanchi.it/assets/presentation-theory/blow-up-diagonal-depth-wonderful-compactifications/blow-up-diagonal-depth-wonderful-compactifications.pdf
  - TeX source: Blow Up Diagonal Depth Wonderful Compactifications: https://lucablanchi.it/assets/presentation-theory/blow-up-diagonal-depth-wonderful-compactifications/blow-up-diagonal-depth-wonderful-compactifications.tex

#### Dependency Depth, Strict Product Diagonal Depth, and Rouquier Dimension of Odd Hassett Spaces

- Canonical URL: https://lucablanchi.it/presentation-theory/dependency-depth-odd-hassett-spaces.html
- Section: Arithmetic Dynamics and Geometry
- Date: June 2026
- Summary: Optimal Rouquier dimension bounds for odd-heavy Hassett spaces from dependency depth and strict product diagonal depth.
- Suggested citation: Luca Blanchi. "Dependency Depth, Strict Product Diagonal Depth, and Rouquier Dimension of Odd Hassett Spaces." lucablanchi.it, June 2026, https://lucablanchi.it/presentation-theory/dependency-depth-odd-hassett-spaces.html.
- Assets:
  - PDF: Dependency Depth Odd Hassett Spaces: https://lucablanchi.it/assets/presentation-theory/dependency-depth-odd-hassett-spaces/dependency-depth-odd-hassett-spaces.pdf
  - TeX source: Dependency Depth Odd Hassett Spaces: https://lucablanchi.it/assets/presentation-theory/dependency-depth-odd-hassett-spaces/dependency-depth-odd-hassett-spaces.tex

### 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

- Canonical URL: https://lucablanchi.it/presentation-theory/previous-copy-compression-foundations.html
- Section: Compression, Boolean Lifts, and Finite Structures
- Date: June 2026
- Summary: Foundational papers on online previous-copy parsing, extremal and metric behaviour, and algebraic digit expansions.
- Suggested citation: Luca Blanchi. "Previous-Copy Compression: Foundations and Algebraic Digit Expansions." lucablanchi.it, June 2026, https://lucablanchi.it/presentation-theory/previous-copy-compression-foundations.html.
- Assets:
  - PDF: Previous Copy Compression Algebraic Digit Expansions: https://lucablanchi.it/assets/presentation-theory/previous-copy-parsing/previous-copy-compression-algebraic-digit-expansions.pdf
  - TeX source: Previous Copy Compression Algebraic Digit Expansions: https://lucablanchi.it/assets/presentation-theory/previous-copy-parsing/previous-copy-compression-algebraic-digit-expansions.tex
  - PDF: Metric Extremal Online Previous Copy Compression: https://lucablanchi.it/assets/presentation-theory/previous-copy-parsing/metric-extremal-online-previous-copy-compression.pdf
  - TeX source: Metric Extremal Online Previous Copy Compression: https://lucablanchi.it/assets/presentation-theory/previous-copy-parsing/metric-extremal-online-previous-copy-compression.tex

#### Previous-Copy Compression: Quantitative Barriers

- Canonical URL: https://lucablanchi.it/presentation-theory/previous-copy-compression-quantitative-barriers.html
- Section: Compression, Boolean Lifts, and Finite Structures
- Date: June 2026
- Summary: Finite stammering profiles, exponential tube barriers, and conditional quantitative lower bounds for previous-copy compression.
- Suggested citation: Luca Blanchi. "Previous-Copy Compression: Quantitative Barriers." lucablanchi.it, June 2026, https://lucablanchi.it/presentation-theory/previous-copy-compression-quantitative-barriers.html.
- Assets:
  - PDF: Finite Stammering Profiles Tube Barriers: https://lucablanchi.it/assets/presentation-theory/previous-copy-parsing/finite-stammering-profiles-tube-barriers.pdf
  - TeX source: Finite Stammering Profiles Tube Barriers: https://lucablanchi.it/assets/presentation-theory/previous-copy-parsing/finite-stammering-profiles-tube-barriers.tex

#### Lattice Obstructions and Coefficient Alphabets for Homogeneous Boolean Lifts

- Canonical URL: https://lucablanchi.it/presentation-theory/lattice-obstructions-coefficient-alphabets.html
- Section: Compression, Boolean Lifts, and Finite Structures
- Date: June 2026
- Summary: Exact notes on two-point encoding lattices, universal denominators, coefficient alphabets, and homogeneous Boolean lift criteria.
- Suggested citation: Luca Blanchi. "Lattice Obstructions and Coefficient Alphabets for Homogeneous Boolean Lifts." lucablanchi.it, June 2026, https://lucablanchi.it/presentation-theory/lattice-obstructions-coefficient-alphabets.html.
- Assets:
  - PDF: Lattice Obstructions Coefficient Alphabets Homogeneous Boolean Lifts: https://lucablanchi.it/assets/presentation-theory/lattice-obstructions-coefficient-alphabets/lattice-obstructions-coefficient-alphabets-homogeneous-boolean-lifts.pdf
  - TeX source: Lattice Obstructions Coefficient Alphabets Homogeneous Boolean Lifts: https://lucablanchi.it/assets/presentation-theory/lattice-obstructions-coefficient-alphabets/lattice-obstructions-coefficient-alphabets-homogeneous-boolean-lifts.tex
  - Markdown source: Lattice Obstructions Coefficient Alphabets Homogeneous Boolean Lifts: https://lucablanchi.it/assets/presentation-theory/lattice-obstructions-coefficient-alphabets/lattice-obstructions-coefficient-alphabets-homogeneous-boolean-lifts.md

#### Sharp Random Thresholds for Exact Ternary Homogeneous Boolean Lifts

- Canonical URL: https://lucablanchi.it/presentation-theory/sharp-random-thresholds-exact-ternary-lifts.html
- Section: Compression, Boolean Lifts, and Finite Structures
- Date: June 2026
- Summary: A sharp random threshold theorem for exact ternary homogeneous Boolean lifts in the expanded coefficient presentation.
- Suggested citation: Luca Blanchi. "Sharp Random Thresholds for Exact Ternary Homogeneous Boolean Lifts." lucablanchi.it, June 2026, https://lucablanchi.it/presentation-theory/sharp-random-thresholds-exact-ternary-lifts.html.
- Assets:
  - PDF: Sharp Random Thresholds Exact Ternary Homogeneous Boolean Lifts: https://lucablanchi.it/assets/presentation-theory/sharp-random-thresholds-exact-ternary-lifts/sharp-random-thresholds-exact-ternary-homogeneous-boolean-lifts.pdf
  - TeX source: Sharp Random Thresholds Exact Ternary Homogeneous Boolean Lifts: https://lucablanchi.it/assets/presentation-theory/sharp-random-thresholds-exact-ternary-lifts/sharp-random-thresholds-exact-ternary-homogeneous-boolean-lifts.tex
  - Markdown source: Sharp Random Thresholds Exact Ternary Homogeneous Boolean Lifts: https://lucablanchi.it/assets/presentation-theory/sharp-random-thresholds-exact-ternary-lifts/sharp-random-thresholds-exact-ternary-homogeneous-boolean-lifts.md

#### Random Saturation and Optimal Off-Origin Slack in Real Homogeneous Boolean Threshold Boxes

- Canonical URL: https://lucablanchi.it/presentation-theory/random-saturation-real-homogeneous-threshold-boxes.html
- Section: Compression, Boolean Lifts, and Finite Structures
- Date: June 2026
- Summary: A real-coefficient bounded-height model for homogeneous Boolean threshold boxes, random saturation, and optimal off-origin slack.
- Suggested citation: Luca Blanchi. "Random Saturation and Optimal Off-Origin Slack in Real Homogeneous Boolean Threshold Boxes." lucablanchi.it, June 2026, https://lucablanchi.it/presentation-theory/random-saturation-real-homogeneous-threshold-boxes.html.
- Assets:
  - PDF: Random Saturation Optimal Off Origin Slack Real Homogeneous Boolean Threshold Boxes: https://lucablanchi.it/assets/presentation-theory/random-saturation-real-homogeneous-threshold-boxes/random-saturation-optimal-off-origin-slack-real-homogeneous-boolean-threshold-boxes.pdf
  - TeX source: Random Saturation Optimal Off Origin Slack Real Homogeneous Boolean Threshold Boxes: https://lucablanchi.it/assets/presentation-theory/random-saturation-real-homogeneous-threshold-boxes/random-saturation-optimal-off-origin-slack-real-homogeneous-boolean-threshold-boxes.tex
  - Markdown source: Random Saturation Optimal Off Origin Slack Real Homogeneous Boolean Threshold Boxes: https://lucablanchi.it/assets/presentation-theory/random-saturation-real-homogeneous-threshold-boxes/random-saturation-optimal-off-origin-slack-real-homogeneous-boolean-threshold-boxes.md

#### Relation Lattices and Kolmogorov Deficiency of Rational Points

- Canonical URL: https://lucablanchi.it/presentation-theory/relation-lattices-kolmogorov-deficiency-rational-points.html
- Section: Compression, Boolean Lifts, and Finite Structures
- Date: June 2026
- Summary: A relation-lattice profile of rational points, random-lattice limits, and finite-height Kolmogorov deficiency from short arithmetic certificates.
- Suggested citation: Luca Blanchi. "Relation Lattices and Kolmogorov Deficiency of Rational Points." lucablanchi.it, June 2026, https://lucablanchi.it/presentation-theory/relation-lattices-kolmogorov-deficiency-rational-points.html.
- Assets:
  - PDF: Relation Lattices Kolmogorov Deficiency Rational Points: https://lucablanchi.it/assets/presentation-theory/relation-lattices-kolmogorov-deficiency-rational-points/relation-lattices-kolmogorov-deficiency-rational-points.pdf
  - TeX source: Relation Lattices Kolmogorov Deficiency Rational Points: https://lucablanchi.it/assets/presentation-theory/relation-lattices-kolmogorov-deficiency-rational-points/relation-lattices-kolmogorov-deficiency-rational-points.tex
  - Markdown source: Relation Lattices Kolmogorov Deficiency Rational Points: https://lucablanchi.it/assets/presentation-theory/relation-lattices-kolmogorov-deficiency-rational-points/relation-lattices-kolmogorov-deficiency-rational-points.md

#### Representatives of Box-Closure Systems on Downsets of Products of Chains

- Canonical URL: https://lucablanchi.it/presentation-theory/box-closure-systems-downsets-products-of-chains.html
- Section: Compression, Boolean Lifts, and Finite Structures
- Date: June 2026
- Summary: A complete representative theorem for coordinate-mixture box-closure systems on finite downsets of products of chains, with matroidal and enumerative consequences.
- Suggested citation: Luca Blanchi. "Representatives of Box-Closure Systems on Downsets of Products of Chains." lucablanchi.it, June 2026, https://lucablanchi.it/presentation-theory/box-closure-systems-downsets-products-of-chains.html.
- Assets:
  - PDF: Box Closure Systems Downsets Products Of Chains: https://lucablanchi.it/assets/presentation-theory/box-closure-systems-downsets-products-of-chains/box-closure-systems-downsets-products-of-chains.pdf
  - TeX source: Box Closure Systems Downsets Products Of Chains: https://lucablanchi.it/assets/presentation-theory/box-closure-systems-downsets-products-of-chains/box-closure-systems-downsets-products-of-chains.tex

### 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

- Canonical URL: https://lucablanchi.it/presentation-theory/presentation-complexity-irregular-connections-stokes-data.html
- Section: Differential Equations and Analytic Geometry
- Date: June 2026
- Summary: Formal types, Stokes directions and factors, ordinary-monodromy fibres, local presentation lower bounds, and controlled irregular Riemann-Hilbert transfer.
- Suggested citation: Luca Blanchi. "Presentation Complexity of Irregular Connections and Stokes Data." lucablanchi.it, June 2026, https://lucablanchi.it/presentation-theory/presentation-complexity-irregular-connections-stokes-data.html.
- Assets:
  - PDF: Presentation Complexity Irregular Connections Stokes Data: https://lucablanchi.it/assets/presentation-theory/presentation-complexity-irregular-connections-stokes-data/presentation-complexity-irregular-connections-stokes-data.pdf
  - TeX source: Presentation Complexity Irregular Connections Stokes Data: https://lucablanchi.it/assets/presentation-theory/presentation-complexity-irregular-connections-stokes-data/presentation-complexity-irregular-connections-stokes-data.tex

#### Stokes Geometry and Presentation Complexity: Four Applications

- Canonical URL: https://lucablanchi.it/presentation-theory/stokes-geometry-presentation-complexity-applications.html
- Section: Differential Equations and Analytic Geometry
- Date: June 2026
- Summary: Turning-locus lower bounds, tame exponential direct images, finite curve restrictions, and bounded-presentation filtrations on wild character varieties.
- Suggested citation: Luca Blanchi. "Stokes Geometry and Presentation Complexity: Four Applications." lucablanchi.it, June 2026, https://lucablanchi.it/presentation-theory/stokes-geometry-presentation-complexity-applications.html.
- Assets:
  - PDF: Stokes Geometry Presentation Complexity Applications: https://lucablanchi.it/assets/presentation-theory/stokes-geometry-presentation-complexity-applications/stokes-geometry-presentation-complexity-applications.pdf
  - TeX source: Stokes Geometry Presentation Complexity Applications: https://lucablanchi.it/assets/presentation-theory/stokes-geometry-presentation-complexity-applications/stokes-geometry-presentation-complexity-applications.tex

### 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

- Canonical URL: https://lucablanchi.it/presentation-theory/predictive-fibres-critical-oseen-transfer-navier-stokes.html
- Section: Proof Strategies
- Date: June 2026
- Summary: An original presentation-theoretic conditional reduction for three-dimensional Navier-Stokes, with closed proof modules and a complete list of remaining source blocks.
- Suggested citation: Luca Blanchi. "Predictive Fibres and Critical Oseen Transfer for Navier-Stokes: Conditional Proof Strategy." lucablanchi.it, June 2026, https://lucablanchi.it/presentation-theory/predictive-fibres-critical-oseen-transfer-navier-stokes.html.
- Assets:
  - PDF: Predictive Fibres Critical Oseen Transfer Navier Stokes: https://lucablanchi.it/assets/presentation-theory/predictive-fibres-critical-oseen-transfer-navier-stokes/predictive-fibres-critical-oseen-transfer-navier-stokes.pdf
  - TeX source: Predictive Fibres Critical Oseen Transfer Navier Stokes: https://lucablanchi.it/assets/presentation-theory/predictive-fibres-critical-oseen-transfer-navier-stokes/predictive-fibres-critical-oseen-transfer-navier-stokes.tex
  - Markdown source: Predictive Fibres Critical Oseen Transfer Navier Stokes Proof Audit: https://lucablanchi.it/assets/presentation-theory/predictive-fibres-critical-oseen-transfer-navier-stokes/predictive-fibres-critical-oseen-transfer-navier-stokes-proof-audit.md

#### Switch Corridors and Boundary-Rigid Lenses in Even Dumbbell Thrackles: A Local Reduction and Minimal-Witness Strategy

- Canonical URL: https://lucablanchi.it/presentation-theory/conway-thrackle-proof-strategy.html
- Section: Proof Strategies
- Date: June 2026
- Summary: A local reduction and minimal-witness strategy for the irreducible even-dumbbell step in Conway's thrackle program.
- Suggested citation: Luca Blanchi. "Switch Corridors and Boundary-Rigid Lenses in Even Dumbbell Thrackles: A Local Reduction and Minimal-Witness Strategy." lucablanchi.it, June 2026, https://lucablanchi.it/presentation-theory/conway-thrackle-proof-strategy.html.
- Assets:
  - PDF: Switch Corridors Boundary Rigid Lenses Conway: https://lucablanchi.it/assets/presentation-theory/conway-thrackle-proof-strategy/switch-corridors-boundary-rigid-lenses-conway.pdf
  - TeX source: Switch Corridors Boundary Rigid Lenses Conway: https://lucablanchi.it/assets/presentation-theory/conway-thrackle-proof-strategy/switch-corridors-boundary-rigid-lenses-conway.tex
  - Markdown source: Switch Corridors Boundary Rigid Lenses Conway: https://lucablanchi.it/assets/presentation-theory/conway-thrackle-proof-strategy/switch-corridors-boundary-rigid-lenses-conway.md

## Draft Concepts

### Rock-paper-scissors with a disadvantage

- Canonical URL: https://lucablanchi.it/drafts/morra-cinese-con-svantaggio.html
- Italian title: Morra cinese con svantaggio
- Date: June 28, 2026
- Summary: A game-theoretic note on a rock-paper-scissors variant where one player cannot play scissors, reducing the game to guessing a positive integer.
- Italian summary: Una nota di teoria dei giochi su una variante della morra cinese in cui un giocatore non può giocare forbici, ridotta al problema di indovinare un intero positivo.
- Suggested citation: Luca Blanchi. "Rock-paper-scissors with a disadvantage." lucablanchi.it, June 28, 2026, https://lucablanchi.it/drafts/morra-cinese-con-svantaggio.html.

### Half bit storage

- Canonical URL: https://lucablanchi.it/drafts/half-bit-storage.html
- Italian title: Storage da mezzo bit
- Date: June 14, 2026
- Summary: A defective one-bit storage cell loses a continuous amount of useful information as read noise increases; Shannon entropy pinpoints the flip probability that leaves half a bit.
- Italian summary: Una cella di memoria difettosa perde una quantità continua di informazione utile al crescere del rumore di lettura; l'entropia di Shannon individua la probabilità di flip che lascia mezzo bit.
- Suggested citation: Luca Blanchi. "Half bit storage." lucablanchi.it, June 14, 2026, https://lucablanchi.it/drafts/half-bit-storage.html.

### Largest Number Game

- Canonical URL: https://lucablanchi.it/drafts/gioco-numero-piu-grande.html
- Italian title: Gioco del numero più grande
- Date: June 13, 2026
- Summary: A draft about short descriptions, enormous numbers, and Ackermann-style recursion.
- Italian summary: Una bozza su un gioco di descrizioni corte, numeri enormi e ricorsioni alla Ackermann.
- Suggested citation: Luca Blanchi. "Largest Number Game." lucablanchi.it, June 13, 2026, https://lucablanchi.it/drafts/gioco-numero-piu-grande.html.

### Game META theory

- Canonical URL: https://lucablanchi.it/drafts/meta-theory.html
- Italian title: Teoria del Meta
- Date: December 1, 2021
- Summary: A draft about populations of strategies, game graphs, simplex dynamics, and categorical operations.
- Italian summary: Una bozza su popolazioni di strategie, grafi di gioco, dinamiche nel simplesso e operazioni categoriali.
- Suggested citation: Luca Blanchi. "Game META theory." lucablanchi.it, December 1, 2021, https://lucablanchi.it/drafts/meta-theory.html.

### A cool formula with primes

- Canonical URL: https://lucablanchi.it/drafts/cool-prime-formula.html
- Italian title: Una formula carina con i numeri primi
- Date: June 12, 2026
- Summary: An informal heuristic about primes, written as a nested formula and compressed into an infinite product.
- Italian summary: Un'euristica informale sui numeri primi, scritta come formula annidata e poi compressa in una produttoria.
- Suggested citation: Luca Blanchi. "A cool formula with primes." lucablanchi.it, June 12, 2026, https://lucablanchi.it/drafts/cool-prime-formula.html.

### Chess encoding

- Canonical URL: https://lucablanchi.it/drafts/chess-encoding.html
- Italian title: Codifica degli scacchi
- Date: June 10, 2026
- Summary: Encoding chess moves, positions, games, and game graphs using as few bits as reasonably possible while keeping positions readable and reconstructible.
- Italian summary: Codificare mosse, posizioni, partite e grafi di partite di scacchi con il minor numero di bit ragionevole, senza perdere leggibilità e ricostruibilità.
- Suggested citation: Luca Blanchi. "Chess encoding." lucablanchi.it, June 10, 2026, https://lucablanchi.it/drafts/chess-encoding.html.