Single-Point Upper Bounds and Packet-Cover Coordinates: A Methodological Toolkit with the Order-32 Case as a Model

This paper develops a methodology for single-point upper-bound estimation in graph reconstruction. Instead of attempting a uniform proof for all orders, one fixes an order nn, extracts all deck-determined invariants, and derives auditable bounds on the number of possible reconstructions. A packet-cover coordinate method over multiset layer spaces is introduced: local coordinate packets, transition cochains, obstruction classes, restart records, and induced gluing forms provide a finite descent calculus for deck gluing. The order-3232 model demonstrates the method: the central-corridor upper bound is reduced from 300,540,195300,540,195 to 12,87012,870, and a complete certificate framework for the remaining branches is recorded. No complete order-3232 archive is claimed; the paper supplies a rigorous, transferable toolkit for fixed-order analysis.