Manuscript XXII-B@1 · XXII-B.tex · definition · 9d5c569c

Definition: Faithful generated representation obligation

Cone interface and hypothesis-ledger syntax · lines 563–585

XXII-B@1#def:representation, XXII-B@1#eq:faithfulness, XXII-B@1#eq:spanning, XXII-B@1#eq:generation

For datum $D$ , a proposed extraction must construct an event carrier $E_{D}$ , a declared partial order $⪯_{D}$ , and $(V_{D}, ι_{D}, K_{D})$ , with $ι_{D}$ injective and $K_{D}$ proper, such that

p ⪯_{D} q V_{D} K_{D} ⟺ ι_{D} (q) - ι_{D} (p) \in K_{D}, = span {ι_{D} (q) - ι_{D} (p) : p, q \in E_{D}}, = cone {ι_{D} (q) - ι_{D} (p) : p ⪯_{D} q, p \neq = q} .

Any quotient, completion, or enlargement defining $E_{D}$ is part of the extraction and must be justified.

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XXII-B@1#eq:faithfulness · line 569
$p ⪯_{D} q V_{D} K_{D} ⟺ ι_{D} (q) - ι_{D} (p) \in K_{D}, = span {ι_{D} (q) - ι_{D} (p) : p, q \in E_{D}}, = cone {ι_{D} (q) - ι_{D} (p) : p ⪯_{D} q, p \neq = q} .$
XXII-B@1#eq:spanning · line 569
$p ⪯_{D} q V_{D} K_{D} ⟺ ι_{D} (q) - ι_{D} (p) \in K_{D}, = span {ι_{D} (q) - ι_{D} (p) : p, q \in E_{D}}, = cone {ι_{D} (q) - ι_{D} (p) : p ⪯_{D} q, p \neq = q} .$
XXII-B@1#eq:generation · line 569
$p ⪯_{D} q V_{D} K_{D} ⟺ ι_{D} (q) - ι_{D} (p) \in K_{D}, = span {ι_{D} (q) - ι_{D} (p) : p, q \in E_{D}}, = cone {ι_{D} (q) - ι_{D} (p) : p ⪯_{D} q, p \neq = q} .$

Definition: Faithful generated representation obligation

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