IndisputableMonolith.Constants.GapWeightNumericsScaffold
This module certifies that the gap weight w₈ from the eight-tick structure matches its closed-form expression within tolerance. Researchers validating the parameter-free alpha pipeline in Recognition Science would cite it for numeric closure. The module achieves the check by importing the GapWeight definition and the explicit W8Bounds formula.
claimThe gap weight satisfies $w_8 = \frac{348 + 210\sqrt{2} - (204 + 130\sqrt{2})\phi}{7}$ and matches the DFT-8 projection value within tolerance.
background
In the alpha pipeline the gap term is written f_gap = w₈ ln(φ). The GapWeight module treats w₈ as the 8-tick projection weight that must remain parameter-free. The W8Bounds module supplies the closed-form expression w8_from_eight_tick = (348 + 210√2 - (204 + 130√2)φ)/7 together with its approximate numerical value 2.490569.
proof idea
This is a definition module, no proofs. It assembles the numeric match by importing GapWeight and W8Bounds and exposing the certified equality via its sibling declarations w8_matches_certified and w8_value.
why it matters in Recognition Science
The module feeds AlphaNumericsScaffold, which performs the numeric evaluation and CODATA match checks for the symbolic alpha derivation. It supplies the required numeric certificate for w₈ that GapWeight demands before the no-free-parameters claim can be asserted.
scope and limits
- Does not derive the closed form of w8 from first principles.
- Does not prove the match holds to arbitrary precision.
- Does not embed w8 into the full alpha formula.
- Does not replace the symbolic treatment in Alpha.