The Principia Machina/TPS/2.3 The Translation Manifold

Instruction artifact: TPS 0.1.0, page 2.3 The Translation Manifold. Part of TPS 0.1.0 and the TPM hub. Human-only edit (TPS 5.13). Version 0.1.0, proposed; declaration pending. Governing section: this page, TPS 2.3. The text below is this page's unit of the TPS 0.1.0 artifact, verbatim; the whole artifact and its file digest are on The Principia Machina/TPS 0.1.0.

TPS 2.3  THE TRANSLATION MANIFOLD
purpose: every entry an isomorphism (TOTAL, SURJECTIVE, INJECTIVE,
         STRUCTURE-PRESERVING); the identification fields; DOMAIN and
         ENVIRONMENT; restrictions priced in the TPK; the four
         isomorphism checks by name, bodies owed
governs: 2.3 | version: 0.1.0 (proposed) | class: instruction artifact
audience: operator, agent

2.3.1  The TrM is the second zone of the TFK. Its identification fields
       (DOF, DOMAIN, the identification, FALSIFIER, BEARS) are immutable;
       every other field of an entry is carried by register records that
       name the entry (see 2.1.3). [I-021] [B-05]
2.3.2  Isomorphism only. Every TrM entry satisfies TOTAL, SURJECTIVE,
       INJECTIVE, STRUCTURE-PRESERVING unchanged. [B-02]
2.3.3  DOMAIN is the regime of validity, required on every TrM entry and
       every promoting record. ENVIRONMENT is what the TrM maps a TPK
       into. [I-030] [I-031]
2.3.4  A restriction (tabletop, uniform field, no rotation) is declared
       as CONSTRAINT entries in the TPK, so the TPK yields the restricted
       DOF inventory and the TrM is an isomorphism onto it. Restrictions
       are therefore covered by the kernel test suite T1-T6. No promotion
       ceiling; the restriction is priced in the TPK, not the entry.
       [B-02]
2.3.5  Each restricted configuration is its own TPK and its own
       container. A RESTRICTION object relating two containers is not
       offered, being excluded by 1.3.2. [B-02]
2.3.6  SURJECTIVE is the completeness test. Completeness is relative to
       the DOF inventory the TPK yields; an untied DOF is a named gap,
       never silently omitted. [B-02] [I-124]
2.3.7  The four isomorphism checks test TOTAL, SURJECTIVE, INJECTIVE and
       STRUCTURE-PRESERVING. TPX runs them as the TrM zone is entered
       and returns a rejected component to the author (see 5.5). [I-057]
       [B-02]
       NOTE: the correspondence of the four checks to the four
       properties is read from D2 and the guide's layer map; the guide
       confirms it when it lands (C-01).
       OWED: the executable body of the TOTAL check; kind: absence;
       C-01. [DI-4.1]
       OWED: the executable body of the SURJECTIVE check; kind: absence;
       C-01. [DI-4.1]
       OWED: the executable body of the INJECTIVE check; kind: absence;
       C-01. [DI-4.1]
       OWED: the executable body of the STRUCTURE-PRESERVING check;
       kind: absence; C-01. [DI-4.1]
2.3.8  While the body of an isomorphism check is owed, that check is
       INSPECTION, performed by H-DECL before the declaration that
       instantiates the container, and recorded as ratchet debt. TPX
       executes the check when its body lands. [DI-4.1]