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Manuscript VIII-A@3 · VIII-A-v3.tex · section · 2398a747

Principal results

Introduction and scope › Principal results · lines 159–192

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The four principal statements are:

  1. Fixed-presentation completeness. Once the developed realization, adapted charts, overlap components, reference framing, and seam maps are fixed, two different proposed values of a required transition cannot both pass the contract.

  2. Constraint-blindness. Equal complete accessible inputs give equal applicability, geometric outputs, evaluated packets, and deterministically selected certificates.

  3. Holonomy reduction. After realization and prescribed-transition checks, the holonomy obligations on a marked punctured disk reduce to regular identity relators, one primitive positive peripheral word, and its collar agreement.

  4. Independent rejection tests. A stale deficit rotation fails deficit/seam matching. A time-shifted rotation fails the spinless pointwise-axis condition. Neither failure can replace the other.

The worked fixed-cone certificate is the substantive geometric instance of the contract. A1 and A2 are deliberately short: they are uniqueness in a prescribed presentation and factorization through declared inputs, respectively. Neither is advertised as a classification or an existence theorem for sourced dynamics.