Presentation theory

Presentation systems, realization fibres, observables, verification costs, normal forms, and reusable proof principles.

Transfer packages, fragmented budgets, convergence moduli, finite-window radii, wild fixed rank-profile fibres, and fibre navigation.

Normal-form packages, residual fibres, separator lower bounds, fragmented towers, heighted no-free normal forms, rewriting budgets, and spectral instability.

Verifiable access, audit covers, transcripts, residual indistinguishability, pullback lower bounds, and auditable Lovasz separation for CFI graphs.

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.

Observable quotients, indistinguishability relations, target reconstruction, residual target factors, finite set-cover fingerprints, adaptive decision trees, structured resolving refinements, and stability.

Operations as presentation engines: assembly envelopes, operational image filtrations, decomposition fibres, bridge costs, observable barriers, and verification records.

An operational atlas of contexts, observables, verification data, fibres, and overhead functions for building transfer packages in Presentation Theory.

Decidable bounded fragments, positive-instance width profiles, exact Turing degrees of resource bounds, and representation-profile applications.

A selected addendum of controlled-transfer results, from quantized law discovery and Hensel-tree rationality to automatic lattice-walk returns and Frobenius modular codes.

Heighted normal-form presentations, gauge and degeneration costs, orbit-closure height bounds, controlled transfer, and representative-moduli gap estimates.

Rate-distortion lower bounds for marked reconstruction from finite-depth Torelli, Johnson, homological, and level data via invisible mapping-class-group flats.

A direct semilinear proof of a parametric greedy 3-sumfree sequence formula, with a presentation-theoretic reading of the finite interval-sum verification.

Antichain presentation modules, active polymatroid profiles, matroid realization strata, and quiver representation geometry inside multiparameter persistence.

A finite proof-carrying format for Hecke eigensystem data, with separating fingerprints, projector witnesses, negative ideal-membership witnesses, residual ledgers, and normalization records.

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.

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.

An addendum of finite access modules for Maass verification, categorical and spectral-action fingerprints, automorphic error-correcting codes, murmurations, and proof-carrying database links.

Quadratic normal forms for word observables, graphical class-two groups, right homomorphism profiles, and exact arity barriers.

A comparison of higher commuting probabilities, star profiles, rank-support enumerators, support-image profiles, and centralizer transforms for class-two exponent-p groups.

Exact support-image and word-observable depth theorems for regular alternating pencils and associated class-two exponent-p groups.

Complete word-moment observability of the skew-symmetric Kronecker data of alternating commutator pencils.

Generic reconstruction of odd Pfaffian alternating tensors from pointwise Fourier-tagged commutator-word moment data.

Large families of non-isomorphic class-two p-groups with identical word-map distributions, built from Pfaffian moduli.

The endpoint of the class-two p-group observable hierarchy: polar-code completeness, generic geometric reconstruction, and standard-structure residual reduction.

Relative k-linear word observables, matrix-rank profiles, and semisimple, cyclic modular, and wild regimes for marked semidirect products.

Finite left and right Lovász dimensions, bounded hom-count test families, and two-object tests for coprime affine groups.

A degree-weighted analogue of normal covering numbers for symmetric and alternating groups, with arithmetic motivation from intersective polynomials.

LEF growth for wreath products with abelian, non-abelian, virtually abelian, and Heisenberg-base examples.

Minimum scalar differential order from realized orbit spans, with Picard-Fuchs observables, periods, and isotypic rank formulas.

Static algebraic proof degree, homogenized presentation ideals, finite-domain filtered membership, Boolean reciprocals, and equivariant Macaulay compression.

Local presentation rank, sparse factorization complexity, exact linear data structures, and dynamic prefix-sum lower-bound problems.

A finite-sample inference layer for algebraic laws discovered after adaptive search, using volume certificates, e-values, and rational-data certificates.

Toric lower-bound certificates, binomial-stratified certificate trees, and automatic effective zero-free tails for simultaneous Skolem and subspace orbit reachability.

Proof-carrying toric guard certificates for positivity of real algebraic linear recurrence sequences.

Exact rational preperiodic portraits for rational maps from controlled bad reduction and p-adic trap dynamics.

Exact preimage layers and effective primitive divisor criteria for rational maps on the projective line.

Coherent product diagonal depth under smooth blow-ups, with applications to wonderful compactifications, Fulton-MacPherson spaces, and moduli spaces of pointed curves.

Optimal Rouquier dimension bounds for odd-heavy Hassett spaces from dependency depth and strict product diagonal depth.

Foundational papers on online previous-copy parsing, extremal and metric behaviour, and algebraic digit expansions.

Finite stammering profiles, exponential tube barriers, and conditional quantitative lower bounds for previous-copy compression.

Exact notes on two-point encoding lattices, universal denominators, coefficient alphabets, and homogeneous Boolean lift criteria.

A sharp random threshold theorem for exact ternary homogeneous Boolean lifts in the expanded coefficient presentation.

A real-coefficient bounded-height model for homogeneous Boolean threshold boxes, random saturation, and optimal off-origin slack.

A relation-lattice profile of rational points, random-lattice limits, and finite-height Kolmogorov deficiency from short arithmetic certificates.

A complete representative theorem for coordinate-mixture box-closure systems on finite downsets of products of chains, with matroidal and enumerative consequences.

Formal types, Stokes directions and factors, ordinary-monodromy fibres, local presentation lower bounds, and controlled irregular Riemann-Hilbert transfer.

Turning-locus lower bounds, tame exponential direct images, finite curve restrictions, and bounded-presentation filtrations on wild character varieties.

An original presentation-theoretic conditional reduction for three-dimensional Navier-Stokes, with closed proof modules and a complete list of remaining source blocks.

A local reduction and minimal-witness strategy for the irreducible even-dumbbell step in Conway's thrackle program.