λEnter Calculus CompanionRegistered manuscripts, kept distinct

Manuscript Hawk02-C@2 · Hawk02-C.tex · section · bb332d66

Three different bridge claims

Question, contribution, and evidence › Three different bridge claims · lines 179–211

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We distinguish:

  1. Structural equivalence: an endpoint isometry is represented by a finite emission interface after declared output identifications;

  2. Finite access: a predetermined finite packet algebra captures the logical radiation mode with proved missed-weight and complete-output allowances;

  3. Predictive approximation: a finite Hamiltonian chosen independently of the calculated endpoint approximates the full evolution with a proved finite-time remainder.

The first does not imply the second or third.

Hawk02-A records the physical-acceptance and spectrum separations CheungHawk02A ({ass:physical, cor:spectrum}). Hawk02-B provides an externally scheduled finite exchange model, not the autonomous Hamiltonian constructed here CheungHawk02B. Theorem thm:C7 supplies an endpoint comparison with that model and, separately, a predictive finite-chain approximation.

Repeated-interaction and weak-coupling theories provide other approximation frameworks AttalPautrat,DerezinskiDeRoeck. No limit theorem is substituted for the finite-time estimate proved below.