navstokgap

Typeset papers

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Why the abelian theory has no gap, in the language of the target box: its coupling does not runnote
An action floor on transverse phase-space area produces the Yang–Mills quantum-mechanical gap, and a gap forces an action unitnote
action-gap-foundations—
Classical action scales: obstructions, conditional bounds and quantum premisesnote
A universal action floor needs a fixed action unit and no admitted similaritynote
The Agmon bound controls the global excess only: the local large-field estimate does not follownote
An Agmon bound for the Kogut–Susskind ground state: large fields are suppressed at rate 1/g² per plaquettenote
Why the ancients argued about the arrow and not the slingnote
The blocking criterion is monotonically worse in the block size: blocking gains nothing without a change of couplingnote
One blocking step: the obstruction is the variation, not the size, of the inter-block couplingnote
A sharp mechanical cost for a finite-duration reversalnote
One action scale, two rules for composing pathsnote
classical-action-field—
classical-spins-operational-closure—
collision-action-relaxation—
A shared action coefficient from classical compositionnote
The confinement scale in three bands, with published numbers, and the verification restated gauge-invariantlynote
A conservative receiver and the origin of a correlation scalenote
A surviving action defect and consistency under inserting cutsnote
Dobrushin's uniqueness condition for the Wilson action: a two-line strong-coupling gap at g² > 444, and the block criterion that is the finite verificationnote
Nonlinear feedback selects an action only while its energy source supplies powernote
Local entangling gates preserve an energy gap uniformly in chain lengthnote
The finiteness half of the mass gap is the nonvanishing of one smeared susceptibilitynote
Flowing before decimating leaves every norm-based criterion unchanged: what is needed is a statement about the statenote
Conjugation by the flow preserves the spectrum, so the renormalization step is a truncationnote
The flow Jacobian's growth factor is sharp: it is the Nielsen–Olesen mode, so the large-field region cannot be flowednote
The truncation error of a flow step is Gaussian times e2t\|G\|∞, so the renormalization step is small exactly on small-field configurationsnote
The flowed bound in free field theory: the coupling cancels, and the bound is informative only at the confinement scalenote
T2' is the absence of a zero-temperature phase transition, and the missing input is closedness of the gapped setnote
The ground-state measure is the time-slice marginal of the Euclidean measure, and that imports the local large-field estimatenote
Holography in the lowest dimensions: at d=0 it is the wave-function identity, at d=1 it is the Schwarziannote
A uniform relaxation gap with nearest-neighbour interactionsnote
The intermediate region as a finite verification: complete analyticity, the transfer matrix, and the two numbers whose meeting closes the proofnote
The Ising gap gives a conditional local parent Hamiltoniannote
Continuous-time expansion for Kogut–Susskind: SU(3) gapped for g² ≥ 388, gap approaching (8/3)g² ℏ c/anote
The large-field action lower bound is immediate in the natural variable, and the constant field saturates itnote
The large-field region costs more action than it has unstable directions, by the factor 2π²/g²note
The large-field region in the Hamiltonian route needs an operator inequality, and the measure statement is weaker than thatnote
Upper bounds on the lattice gap: the Feynman–Bijl inequality, the abelian structure factor and the non-abelian dressing obstructionnote
On the lattice one flow step has a uniformly bounded truncation error: the obstruction is decimationnote
A Lieb–Robinson bound for the Kogut–Susskind Hamiltonian, with velocity ∝ Nc/g²note
Independent monotone receivers cannot suppress coincidencesnote
A gap is a scale the classical theory lacks: solved low-dimensional mass gaps and the positive-action questionnote
Two exact identities for the magnetic energy, a ground-state sum rule, and why pointwise Gibbs domination fails as Agmon doesnote
The mark cost is exactly ℏ/2, and the worst-case theorem survives as a statistical onenote
The map as one conditional theorem: two hypotheses, both finite in kind, and an explicit lower bound m ≥ ℏ c γ'/a*note
The mass gap as a finite list of theorems: the Hamiltonian lattice routenote
The mass gap: current position of this programmenote
Mechanical interference measures phase without fixing an action unitnote
A monotone hierarchy of upper bounds from one flowed correlator, and why no bound of this kind can give m > 0note
Galileo's falling parabola, Newton's refinement and the Planck-scale questionnote
The cost of a mark: a Newton-age floor for the Galileo comparisonnote
A passive threshold creates events, but its scale belongs to the receivernote
A physical cut: elastic reversal, finite speed and memorynote
The Planck gap as a theorem: every marking protocol needs F²τ³ > 9mκnote
The cost of a mark: Newton's vanishing sagitta and a floor of order ℏnote
The probabilistic Planck gap: τΔE ≥ (1-2ε)²ℏ²/(4A), and why it is resource-relativenote
The gap is bounded by the variance of the averaged spatial Polyakov loop, with the small-volume scaling built innote
The two reasons to stop, as research problems: what a correlation inequality would buy, what a certified verification cannot, and where the research isnote
Reciprocal exchange fixes relative mechanical scalesnote
regulator-limits—
research-programme—
same-collisions-different-transport—
The Schur error of the small-volume reduction is an ultraviolet problem: a fixed-lattice theorem is available, the renormalized regime is notnote
Independent settings test shared readiness, while leaving action units freenote
A shared release produces exclusive fringe-weighted eventsnote
One small-field blocking step, part 1b: the decay rate and the shape of the threshold, and why the weak side's deficit is ten orders of magnitudenote
One small-field blocking step for SU(3), part 1: the Gaussian fluctuation integral with block averaging, with explicit constantsnote
Global spin phases quantize a ratio, not an absolute action scalenote
Stabilizing a topological radius exposes an action coefficientnote
The target box: the strong-coupling gap survives local perturbations, so the renormalization group has an explicit finish linenote
The strong-coupling threshold made explicit: Yarotsky's proof gives g₀²~10¹⁰⁰, and only a direct expansion can give g₀²~10²note
The strong-coupling gap of the Kogut–Susskind Hamiltonian is uniform in the volumenote
SU(3) in four dimensions: every constant of this programme, evaluatednote
When an action plateau controls a spectral gapnote
A finite-speed return bridge: cuts and midpoint crossovernote
Thermal reliability selects a detector cost, not a universal actionnote
In three dimensions the mass gap is the positivity of one function at infinitynote
time-refinement—
A topological energy floor survives shrinking while the action cost vanishesnote
The one-loop potential along the abelian valley of the torus is periodic, reproduces C133's linear term at the origin, and saturates at order 1/Lnote
On typical configurations the flow truncation is controlled at any coupling; the whole obstruction is the large-field tailnote
The weak-coupling gap in a small box reduces to three inequalities through the Schur complementnote
What would unblock the confinement-scale region, and what was checked and failsnote
An explicit strong-coupling gap for the Wilson transfer matrix: SU(3) is gapped for g² ≥ 176, with Δ ≥ (ℏ c/a) 4log(g²/176)note