Equal-mass sunset Taylor series

See Equal-mass sunset: vacuum and Euclidean continuation for the derivation, domain and precision hazard. This backend is separate from the generated RMT Gamma series.

Equal-mass D=2 sunset by a convergent transformed Taylor series.

This is a differential-equation series with a Clausen boundary value, not a Ramanujan/Gamma-family evaluator. It complements the strictly separate RMT API. The parameter-integral majorant proves convergence for finite Euclidean p^2. See docs/user_guide/sunset_taylor.md for normalization, recurrence and bounds.

class ramanujan_qft.sunset_taylor.SunsetTaylorSeries(graph: object, mass_squared: object, p_e_squared: object, ratio: object)

Bases: object

Graph-validated equal-mass series in y = p_E^2/(9*m^2+p_E^2).

Every finite nonnegative Euclidean invariant gives 0 <= y < 1. Close to one, the work budget may be insufficient. The recurrence has a growing parasitic solution: guard precision scales with the coefficient count.

evaluate(*, dps=30, max_terms=512, max_dps=2000)

Evaluate with a positive-integrand tail bound and two precision passes.

max_terms bounds each pass. max_dps bounds working decimal precision. Unmet targets raise SunsetTaylorConvergenceError; no quadrature or RMT fallback is invoked. The returned value is rounded to dps digits.

class ramanujan_qft.sunset_taylor.SunsetTaylorResult(value: object, error_estimate: object, truncation_bound: object, terms: int, working_dps: int, convergence_ratio: object, converged: bool = True, method: str = 'equal-mass sunset / transformed Taylor series')

Bases: object

Series value with mathematical tail and estimated arithmetic errors.

The bound is evaluated at working precision, not with interval arithmetic. terms counts coefficients in the final pass, not both precision passes.

exception ramanujan_qft.sunset_taylor.SunsetTaylorConvergenceError(message, result=None)

Bases: ArithmeticError

A Taylor evaluation exceeded its work or precision budget.

ramanujan_qft.sunset_taylor.compile_sunset_taylor(graph, D=2)

Compile the equal-mass, unit-power D=2 Euclidean sunset Taylor chart.

This API deliberately identifies a different method from compile_sunset_rmt. Unequal masses and other topologies/dimensions are not implemented.

ramanujan_qft.sunset_taylor.integrate_sunset_taylor(graph, D=2, *, dps=30, max_terms=512, max_dps=2000)

Compile and evaluate the separate equal-mass Taylor series backend.