navstokgap digests
What survives refinement: the most interesting results, condensed for a phone screen
The repository navstokgap is a research programme opened in September 2026 on two problems: whether the limit Newton takes in Book I of the Principia can be taken once the comparison has to be recorded, and the continuum mass gap of pure SU(3) Yang–Mills theory. Its notes are written by language-model agents under my direction. On 1 October 2026 Claude Opus 5.5 read all 175 notes in full and scored each from 1 to 10 for interestingness and for correctness of its own derivations; Claude Fable 5.1 then reviewed the condensed statements of the selected notes against the sources, removed false or superseded claims, and assembled two digests. The page size is 84 mm by 150 mm, so each page fills a phone screen without zooming.
The two digests
- The most interesting results26 notes scored 6 or more for interest, whatever their correctness; 46 pages, 180KB
- Interesting and correct results22 notes scored 6 or more for interest and 8 or more for correctness; 36 pages, 160KB
Every note scored
Interest (I) and correctness (C) as scored; status is the scorer's reading of the note's proof level. The last column says which volumes contain the note (A: most interesting; B: interesting and correct). Struck-through entries were removed by the final review because their main claim was found false or superseded. Each name links to the full note on the project site.
| Note | I | C | Status | In |
|---|---|---|---|---|
| mark-cost-and-statistical-floor The mark cost is exactly $\hbar/2$, and the worst-case theorem survives as a statistical one | 7 | 8 | proved | A B |
| planck-gap-probabilistic The probabilistic Planck gap: $F\tau(L+\tau P/2m)\ge\hbar\arcsin(1-2\epsilon)$, and why it is resource-relative | 7 | 8 | proved | A B |
| sed-closure-under-recording Shared radiation and closure under recording | 7 | 8 | mixed | A B |
| series-parallel-gauge-refinement Series and parallel: where the gauge insertion law stops closing | 7 | 8 | mixed | A B |
| planck-gap-paper The cost of a mark: Newton's vanishing sagitta and a floor of order $\hbar$ | 7 | 7 | mixed | A |
| cut-measure-newton Newton's cell action as a measure on cuts | 6 | 9 | proved | A B |
| galileo-two-path-interference # Galileo's comparison as two-path interference | 6 | 9 | conditional | A B |
| polygon-lift-phase Newton's inscribed polygon differs from the parabola by the phase of its segments | 6 | 9 | proved | A B |
| telegraph-return-bridge A finite-speed return bridge: cuts and midpoint crossover | 6 | 9 | proved | A B |
| villain-monopole-refinement Compact U(1) under refinement: an explicit total-variation bound in three dimensions, and why it fails in four | 6 | 9 | proved | A B |
| four-dimensional-parallel-log # Four-dimensional parallel insertions: one-loop shifts and the logarithm | 6 | 8 | conditional | A B |
| kogut-susskind-strong-coupling-explicit # Continuous-time expansion for Kogut--Susskind: $SU(3)$ gapped for $g^2\ge388$, gap approaching $(8/3)g^2\,\hbar c/a$ | 6 | 8 | proved | A B |
| lattice-gap-upper-bounds # Upper bounds on the lattice gap: the Feynman--Bijl inequality, the abelian structure factor and the non-abelian dressing obstruction | 6 | 8 | mixed | A B |
| leibniz-continuity-records # Leibniz's law of continuity, read on records, selects a positive action floor for motions | 6 | 8 | conditional | A B |
| low-dimensional-mass-gap # A gap is a scale the classical theory lacks: solved low-dimensional mass gaps and the positive-action question | 6 | 8 | mixed | A B |
| newton-indeterminacy-routes Newton indeterminacy routes: the physical premise a record floor needs | 6 | 8 | conditional | A B |
| principia-fifth-postulate A fifth postulate for the Principia: joint determinacy of place and motion | 6 | 8 | proved | A B |
| record-costs-disturbance The record costs disturbance: a floor for every instrument | 6 | 8 | proved | A B |
| record-costs-recoil The record costs recoil: a floor for every probe state | 6 | 8 | proved | A B |
| record-distance-path-length The record's distance is a path length | 6 | 8 | proved | A B |
| su2-midplane-order-t SU(2) on the full mid-plane: the relative-order-t halving defect | 6 | 8 | conditional | A B |
| sun-midpoint-centre The bridge midpoint on a compact group at any cut: windings and the centre | 6 | 8 | proved | A B |
| zero-spacing-any-action The zero-spacing limit for any plaquette action and any dimension | 6 | 8 | mixed | A B |
| four-dimensional-composition # Four-dimensional composition: exact Gaussian blocking and one-loop matching | 6 | 7 | mixed | A |
| su2-midplane-small-field The SU(2) mid-plane on its small-field set: bounds and the missing comparison | 6 | 7 | mixed | A |
| planck-gap-derivation The Planck gap as a theorem: every marking protocol needs $F^2\tau^3>9m\kappa$ | 6 | 6 | mixed | A |
| action-unit-dimensional-selection A universal action floor needs a fixed action unit and no admitted similarity | 5 | 9 | proved | |
| additive-noise-marks Every mark with body-independent noise is a momentum-transfer mark | 5 | 9 | proved | |
| autonomous-finite-readout A finite mechanical clock and four persistent readout records | 5 | 9 | proved | |
| dobrushin-uniqueness-wilson Dobrushin's uniqueness condition for the Wilson action: a two-line strong-coupling gap at $g^2>444$, and the block criterion that is the finite verification | 5 | 9 | proved | |
| fixed-force-small-circles # Fixed force ceiling: small bound circles and an excitation floor | 5 | 9 | proved | |
| fixed-preparation-ambiguity # Positive preparation width hides receiver states from exact records | 5 | 9 | proved | |
| full-apparatus-preparation-ambiguity # Full final apparatus records can hide the entire receiver energy shell | 5 | 9 | proved | |
| newton-insertion-action Galileo's falling parabola, Newton's refinement and the Planck-scale question | 5 | 9 | proved | |
| rivero-1998-conjecture-central-forces Rivero's consistency conjecture: quartic paths and central-force angles | 5 | 9 | proved | |
| stochastic-route-velocitas-ultima Brownian free motion: the velocitas ultima denied, one action constant, and the floor | 5 | 9 | conditional | |
| su2-midpoint-exact The SU(2) bridge midpoint in closed form: the curvature term is exact | 5 | 9 | proved | |
| agmon-global-not-local The Agmon bound controls the global excess only: the local large-field estimate does not follow | 5 | 8 | proved | |
| cut-paradox-two-faces The cut paradox in two signatures: sections of a solid and instants of a motion | 5 | 8 | proved | |
| necessity-unit-and-indeterminacy What a necessity argument for $h>0$ must supply: a unit and an indeterminacy | 5 | 8 | proved | |
| refinement-composition-and-limit Inserting a point, subdividing a cell: how the limit is built | 5 | 8 | proved | |
| score-constrained-ensemble Score-constrained ensembles and population transport | 5 | 8 | proved | |
| superdeterminism-floor Superdeterminism lives below every resolution; a floor gives it a lifetime | 5 | 8 | conditional | |
| torus-valley-potential 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/L | 5 | 8 | proved | |
| wilson-strong-coupling-explicit An explicit strong-coupling gap for the Wilson transfer matrix: $SU(3)$ is gapped for $g^2\ge176$, with $\Delta\ge(\hbar c/a)\,4\log(g^2/176)$ | 5 | 8 | proved | |
| blocking-criterion-monotone The blocking criterion is monotonically worse in the block size: blocking gains nothing without a change of coupling | 5 | 7 | proved | |
| dimension-ladder The dimension ladder: from 0+0 to 1+3, and what the action constant does on each rung | 5 | 7 | conjectural | |
| finiteness-half-flowed-susceptibility The finiteness half of the mass gap is the nonvanishing of one smeared susceptibility | 5 | 7 | conditional | |
| flow-conjugation-truncation # Conjugation by the flow preserves the spectrum, so the renormalization step is a truncation | 5 | 7 | mixed | |
| lieb-robinson-kogut-susskind # A Lieb--Robinson bound for the Kogut--Susskind Hamiltonian, with velocity $\propto Nc/g^2$ | 5 | 7 | proved | |
| mass-gap-openings Openings for the mass gap, and why it is not special to SU(3) | 5 | 7 | mixed | |
| newton-mark-floor The cost of a mark: a Newton-age floor for the Galileo comparison | 5 | 7 | mixed | |
| tangent-groupoid-trajectories The tangent groupoid, its zoom, and whole trajectories | 5 | 7 | mixed | |
| weak-coupling-feshbach-reduction The weak-coupling gap in a small box reduces to three inequalities through the Schur complement | 5 | 7 | conditional | |
| action-floor-yang-mills-gap An action floor on transverse phase-space area produces the Yang--Mills quantum-mechanical gap, and a gap forces an action unit | 5 | 6 | mixed | |
| confinement-scale-bands The confinement scale in three bands, with published numbers, and the verification restated gauge-invariantly | 5 | 6 | mixed | |
| flow-jacobian-truncation-error # The truncation error of a flow step is Gaussian times $e^{2t\|G\|_\infty}$, so the renormalization step is small exactly on small-field configurations | 5 | 6 | mixed | |
| intermediate-region-finite-verification # The intermediate region as a finite verification: complete analyticity, the transfer matrix, and the two numbers whose meeting closes the proof | 5 | 6 | conjectural | |
| large-field-operator-inequality # The large-field region in the Hamiltonian route needs an operator inequality, and the measure statement is weaker than that | 5 | 6 | mixed | |
| lattice-truncation-uniform # On the lattice one flow step has a uniformly bounded truncation error: the obstruction is decimation | 5 | 6 | mixed | |
| small-field-step-decay-and-threshold 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 magnitude | 5 | 6 | mixed | |
| strong-coupling-threshold-explicit The strong-coupling threshold made explicit: Yarotsky's proof gives $g_0^2\sim10^{100}$, and only a direct expansion can give $g_0^2\sim10^2$ | 5 | 6 | mixed | |
| strong-coupling-target-box The target box: the strong-coupling gap survives local perturbations, so the renormalization group has an explicit finish line | 5 | 5 | conditional | |
| flow-instability-large-field # The flow Jacobian's growth factor is sharp: it is the Nielsen--Olesen mode, so the large-field region cannot be flowed | 5 | 4 | mixed | |
| schur-error-ultraviolet The Schur error of the small-volume reduction is an ultraviolet problem: a fixed-lattice theorem is available, the renormalized regime is not | 5 | 4 | mixed | |
| action-scale-dilation Dilation closure and the action-selection obstruction | 4 | 9 | proved | |
| calibrated-displacement-ambiguity One calibrated displacement still leaves full receiver ambiguity | 4 | 9 | proved | |
| calibration-tolerance-recovery Calibration tolerance sets the recovery crossover | 4 | 9 | proved | |
| checkerboard-dynamics One action scale, two rules for composing paths | 4 | 9 | proved | |
| classical-cut-state What a classical cut must retain | 4 | 9 | proved | |
| classical-orientation-closure Finite operational closure does not select quantum composition | 4 | 9 | proved | |
| closed-orbit-force-action Closed trajectories: action from total turning and persistent excitation | 4 | 9 | proved | |
| composition-universality A shared action coefficient from classical composition | 4 | 9 | conditional | |
| cut-point-consistency A surviving action defect and consistency under inserting cuts | 4 | 9 | proved | |
| energy-depot-action-selection Nonlinear feedback selects an action only while its energy source supplies power | 4 | 9 | proved | |
| finite-horizon-minimax Exact finite-horizon phase recovery | 4 | 9 | proved | |
| flowed-bound-free-field # The flowed bound in free field theory: the coupling cancels, and the bound is informative only at the confinement scale | 4 | 9 | proved | |
| hamiltonian-finite-closure # The spin interaction admits no exact finite observable repair | 4 | 9 | proved | |
| hamiltonian-moment-descent # A reversible spin interaction separates identical operational states | 4 | 9 | proved | |
| hidden-clock-ambiguity # An unknown clock hides an exact fixed-energy receiver phase | 4 | 9 | proved | |
| indistinguishable-phase-bound # A sharp information bound from indistinguishable motions | 4 | 9 | proved | |
| local-detector-coincidences # Independent monotone receivers cannot suppress coincidences | 4 | 9 | proved | |
| mechanical-interference-action Mechanical interference measures phase without fixing an action unit | 4 | 9 | proved | |
| moment-hierarchy-upper-bounds A monotone hierarchy of upper bounds from one flowed correlator, and why no bound of this kind can give $m>0$ | 4 | 9 | conditional | |
| radiation-noise-action-selection Radiation balance selects a spectral shape, but leaves its action amplitude free | 4 | 9 | proved | |
| relativistic-kepler-threshold Relativistic Kepler: a singular-core angular-action threshold | 4 | 9 | proved | |
| thermal-receiver-reliability Thermal reliability selects a detector cost, not a universal action | 4 | 9 | proved | |
| three-body-cut-memory Tagged momentum and the memory of a third body | 4 | 9 | proved | |
| topological-sector-action-selection A topological energy floor survives shrinking while the action cost vanishes | 4 | 9 | proved | |
| action-scale-obstructions Classical action scales: obstructions, conditional bounds and quantum premises | 4 | 8 | mixed | |
| conservative-harmonic-receiver A conservative receiver and the origin of a correlation scale | 4 | 8 | mixed | |
| fixed-coupling-calibration # Fixed coupling permits precise calibrated readout | 4 | 8 | proved | |
| full-clock-phase-recovery # Complete final apparatus records replace the initial clock calibration | 4 | 8 | proved | |
| full-pointer-recovery # Full pointer records recover receiver and unknown probe positions | 4 | 8 | proved | |
| gaussian-blocking-coupling # Gaussian product blocking: the tree-level coupling never moves | 4 | 8 | proved | |
| global-clock-speed-ambiguity # Distinct clock speeds give identical full pointer records on the shell | 4 | 8 | proved | |
| halving-atlas # Atlas of halving: what one refinement step does, and what emerges, in each dimension | 4 | 8 | mixed | |
| magnetic-energy-identities # Two exact identities for the magnetic energy, a ground-state sum rule, and why pointwise Gibbs domination fails as Agmon does | 4 | 8 | proved | |
| minimax-composition Worst-case information scales under mechanical composition | 4 | 8 | proved | |
| polyakov-average-gap-bound The gap is bounded by the variance of the averaged spatial Polyakov loop, with the small-volume scaling built in | 4 | 8 | proved | |
| reasons-to-stop-as-research The two reasons to stop, as research problems: what a correlation inequality would buy, what a certified verification cannot, and where the research is | 4 | 8 | mixed | |
| refinement-results What survives refinement: results on Newton's vanishing sagitta and the halving of lattice gauge fields | 4 | 8 | mixed | |
| rotation-composition-universality One action constant from composition and spatial rotations | 4 | 8 | conditional | |
| sed-zeta-radiation-link A Lorentz-invariant background and the state-route constant: a conditional link to the radiation unit | 4 | 8 | conditional | |
| strong-coupling-uniform-gap The strong-coupling gap of the Kogut--Susskind Hamiltonian is uniform in the volume | 4 | 8 | proved | |
| thermodynamic-records-no-floor Thermodynamics of records gives a trade-off and no floor | 4 | 8 | proved | |
| three-continuum-limits What survives refinement: the pion, the Yang--Mills gap and Newton's action | 4 | 8 | mixed | |
| two-calibration-branches Two calibrated probe positions give local recovery and two global branches | 4 | 8 | proved | |
| arrow-not-sling Why the ancients argued about the arrow and not the sling | 4 | 7 | none | |
| mass-gap-obligations-lattice The mass gap as a finite list of theorems: the Hamiltonian lattice route | 4 | 7 | mixed | |
| small-field-step-gaussian One small-field blocking step for $SU(3)$, part 1: the Gaussian fluctuation integral with block averaging, with explicit constants | 4 | 7 | mixed | |
| three-calibration-global-recovery Three calibrated positions give uniform global receiver recovery | 4 | 7 | proved | |
| three-dimensional-gap-one-function In three dimensions the mass gap is the positivity of one function at infinity | 4 | 7 | conditional | |
| uv-halving-ir-confinement Halving goes to the ultraviolet; confinement lives in the infrared | 4 | 7 | none | |
| abelian-misses-the-box Why the abelian theory has no gap, in the language of the target box: its coupling does not run | 4 | 6 | mixed | |
| flow-before-decimation # Flowing before decimating leaves every norm-based criterion unchanged: what is needed is a statement about the state | 4 | 6 | mixed | |
| what-would-unblock What would unblock the confinement-scale region, and what was checked and fails | 4 | 6 | none | |
| gapped-set-critical-coupling # T2$'$ is the absence of a zero-temperature phase transition, and the missing input is closedness of the gapped set | 4 | 5 | mixed | |
| ground-state-measure-transfer # The ground-state measure is the time-slice marginal of the Euclidean measure, and that imports the local large-field estimate | 4 | 5 | mixed | |
| large-field-entropy-count # The large-field region costs more action than it has unstable directions, by the factor $2\pi^2/g^2$ | 4 | 5 | conjectural | |
| mass-gap-position The mass gap: current position of this programme | 4 | 5 | mixed | |
| typical-field-strength-window On typical configurations the flow truncation is controlled at any coupling; the whole obstruction is the large-field tail | 4 | 5 | superseded | |
| mass-gap-conditional-theorem The map as one conditional theorem: two hypotheses, both finite in kind, and an explicit lower bound $m\ge\hbar c\,\gamma'/a_*$ | 4 | 4 | conditional | |
| bound-orbit-action-observable Bound motion: transport variance and a canonical action estimator | 3 | 9 | proved | |
| bounded-acceleration-return A sharp mechanical cost for a finite-duration reversal | 3 | 9 | proved | |
| causal-force-information New information behind a delayed record | 3 | 9 | proved | |
| classical-readout-refinement Classical readout under cut refinement | 3 | 9 | proved | |
| clock-position-local-recovery A known clock position permits stable local recovery | 3 | 9 | proved | |
| comparison-and-bridges Navier–Stokes and Yang–Mills: comparison and bridges | 3 | 9 | none | |
| energy-constrained-apparatus-ambiguity Exact apparatus energy leaves a receiver-sign ambiguity | 3 | 9 | proved | |
| final-clock-momentum-recovery Final clock momentum restores global receiver recovery | 3 | 9 | proved | |
| finite-precision-cut Finite position precision and the reachable action area | 3 | 9 | proved | |
| interacting-ising-gap # A uniform relaxation gap with nearest-neighbour interactions | 3 | 9 | proved | |
| ising-hermitian-transfer # The Ising gap gives a conditional local parent Hamiltonian | 3 | 9 | proved | |
| passive-threshold-events A passive threshold creates events, but its scale belongs to the receiver | 3 | 9 | proved | |
| physical-cut-speed A physical cut: elastic reversal, finite speed and memory | 3 | 9 | proved | |
| principia-constant-force-action Newton's vanishing areas and the proposed action scale | 3 | 9 | proved | |
| reachable-cut-composition Reachable information across a classical cut | 3 | 9 | proved | |
| receding-centre-area-audit The surviving area is the matched-endpoint arc–chord defect | 3 | 9 | proved | |
| reversible-generator-constraints Product probabilities restrict reversible generators | 3 | 9 | proved | |
| spin-action-patching Global spin phases quantize a ratio, not an absolute action scale | 3 | 9 | proved | |
| stabilized-topology-action-scale Stabilizing a topological radius exposes an action coefficient | 3 | 9 | proved | |
| susceptibility-gap When an action plateau controls a spectral gap | 3 | 9 | proved | |
| two-position-recovery Two position records recover the phase state | 3 | 9 | proved | |
| block-apparatus-composition Independent apparatus blocks restore extensive composition | 3 | 8 | proved | |
| calibrated-canonical-ambiguity Calibrated two-energy records still hide both canonical coordinates | 3 | 8 | proved | |
| correlated-calibration-response Correlated calibration errors suppress the canonical response | 3 | 8 | conditional | |
| newton-record-parallel-move Newton's record as a parallel move: what forgetting a record leaves | 3 | 8 | proved | |
| quantum-exclusion-premises Two ways to exclude a classical operational model | 3 | 8 | none | |
| reversible-interaction-premise Reversible interaction excludes the minimal orientation composite | 3 | 8 | conditional | |
| shared-record-budget A shared record budget changes the composition exponent | 3 | 8 | proved | |
| single-calibration-fibres One uncertain calibration leaves an exact receiver curve | 3 | 8 | proved | |
| two-regulator-audit Two regulators: what survives when the paths shrink? | 3 | 8 | proved | |
| blocking-step-obstruction One blocking step: the obstruction is the variation, not the size, of the inter-block coupling | 3 | 7 | superseded | |
| composition-crossover-gap-checks Composition, crossover and gap product: verified calculations for A08, A09 and G01 | 3 | 7 | mixed | |
| discrete-substrate-actors From the continuum to discrete substrates: 't Hooft and other turns | 3 | 7 | none | |
| holography-lowest-dimensions # Holography in the lowest dimensions: at $d=0$ it is the wave-function identity, at $d=1$ it is the Schwarzian | 3 | 7 | none | |
| i003-double-limit-rigidity # I003: finite propagation, internal state and resolution | 3 | 7 | conjectural | |
| newton-NATP00385-audit Newton on discovery, demonstration and limiting ratios | 3 | 7 | none | |
| position-preparation-ambiguity Unknown probe positions can hide the receiver after momentum calibration | 3 | 7 | proved | |
| static-composition-classics Before the arrow: can the parts make a whole? | 3 | 7 | none | |
| agmon-ground-state-suppression An Agmon bound for the Kogut--Susskind ground state: large fields are suppressed at rate $1/g^2$ per plaquette | 3 | 6 | mixed | |
| su3-constants SU(3) in four dimensions: every constant of this programme, evaluated | 3 | 6 | mixed | |
| large-field-action-lower-bound # The large-field action lower bound is immediate in the natural variable, and the constant field saturates it | 3 | 4 | mixed | |
| finite-depth-spin-gap Local entangling gates preserve an energy gap uniformly in chain length | 2 | 9 | proved | |
| reciprocal-coupling-normalization Reciprocal exchange fixes relative mechanical scales | 2 | 9 | proved | |
| shared-readiness-chsh Independent settings test shared readiness, while leaving action units free | 2 | 9 | proved | |
| shared-resource-events A shared release produces exclusive fringe-weighted events | 2 | 9 | proved | |
| ancient-cuts-provenance Ancient cuts and modern readjustment: provenance | 2 | 8 | none | |
| cone-time-refinement From cone sections to time refinement | 2 | 8 | none | |
| ising-foundational-value # Foundational value of the established Ising gap | 2 | 8 | none | |
| millennium-problem-definitions The two Millennium problems | 2 | 8 | none | |
| bridge-crossover Midpoint crossover: consolidated manuscript | 1 | 8 | none | |
| jacobi-kernels-distinguishability # Variations, kernels and distinguishability | 1 | 8 | none | |
| ordered-beam-preparation A13: ordered-beam preparation | 1 | 7 | none |