Core Terms and Mathematical Expressions

Undefined

The terminal boundary role of zero positive ontological determination. It is not an object, a cause, an empty state, or a potential world.

Ordinary Nothing

A conceptual state that can still be assigned stable determinations such as “empty” or “there is no such thing.” It differs from Absolute Undefinedness, to which even these determinations do not apply.

Platonic Crystal

The total domain of statically describable forms, including formulae, complete histories, and possible structures. A form can be available for use without actually occurring.

Actual Occurrence

The ontological object selected by the system, expressed through ActualStep or an analogous relation. A relational formula in static language does not automatically instantiate a predicate of actual occurrence.

The First Beat

The minimal structure of actual occurrence when there is no pre-given matter, physical time, or external actual executor. It is not physical time $$t=1$$ .

PR

Paradoxical Re-entry (formerly Paradox–Reference). In its current strict meaning, it is the minimal normal form that is self-contained, actually occurring, non-fixed, and permits result re-entry. It is not the simultaneous assertion of $$p$$ and $\neg p$ within the same fixed evaluation.

\sigma(Y)=N,\qquad \sigma(N)=Y.

\operatorname{Fix}(\sigma)=\varnothing, \qquad \sigma^2=\operatorname{id}_D.

ER

Entity–Relation. It denotes relational situations, adjacency networks, effective entity identity, local structure, and structural memory.

LE

Lazy Evaluation. It denotes local, delayed, finite, on-demand, or truncated updating / evaluation. It is the implementation mechanism through which propagation scales and physical constants emerge.

RULE

The specific update law operating on the ER state space. PR–ER–LE is the architecture; RULE determines whether chaos, attractors, and higher-level organization form.

Jia Baolong Absolute Truth

U:\quad \forall M\in\mathfrak D\, \forall P\in\mathrm{Pos},\, \neg P(b_M).

In the specified model class, $$U$$ is the unique fundamental generative proposition for all absolute truths of root ontology in the root language; uniqueness is calculated by logical equivalence class.

The Static–Actuality Separation

\operatorname{Encodes}(S,H) \not\models \operatorname{Occurs}(H).

Undefined Does Not Entail an Event

T_U\not\models \exists a,b\, \operatorname{ActualStep}(a,b).

Classification of Binary Maps

D^D= \{\operatorname{id}_D,\sigma,c_Y,c_N\}.

After label equivariance:

\mathcal E(D^D)= \{\operatorname{id}_D,\sigma\}.

After adding the non-fixed condition:

\mathfrak R(D^D)=\{\sigma\}.

Atemporal Co-Arising

\operatorname{ActualFace}_{\mathcal M}(U_*) \cong \mathrm{PR},

U_*\mid\mathrm{PR}.

The vertical bar separates two aspects of the same root determination.

The Ascending Chain

\mathrm{PR} \to \mathrm{ER+LE} \xRightarrow{\mathrm{RULE}} \mathrm{Chaos} \to \mathrm{ProtoMatter} \to \mathrm{ProtoChemistry} \to \mathrm{Heredity} \to \mathrm{Selection} \to \mathrm{Protocell}.

This chain connects the PR root, medium-free dynamics, proto-matter, proto-chemistry, heredity, selection, and the first cell.

Historical Terminology in the English Archive

Editorial note for source-faithful reading: the terminology developed across papers written at different stages. English translations preserve the wording used by each source rather than silently rewriting earlier papers into the latest vocabulary.

PR: the current canonical expansion is Paradoxical Re-entry, formerly Paradox–Reference. Still earlier papers also use Primitive Reflexivity and Paradoxical Recursion. These expressions mark stages in the development and exposition of the same PR line; they should not be read as independent present-day axioms.
LE: the current canonical expansion is Lazy Evaluation. Lazy Expansion is retained where it appears in an earlier source and should be read in that source's historical context.
Trinity Theory / Trinity Topological Theory: these are official historical proper names used in the relevant papers. They are not to be silently replaced by “Triadic Theory.”
JBLAT / JBAT: the repository’s current canonical guides and commentary documents use JBLAT. JBAT in the original paper papers/21563153.md is its fixed release fingerprint, formal result name, and formula notation and must remain unchanged. Both abbreviations denote the same Jia Baolong Absolute Truth object, not two theories.
Undefined / undefined / $$U$$ : Undefined names the zero-positive ontological boundary; lowercase undefined may denote an ordinary programming-language value; $$U$$ is the formal root proposition in the current specification. Context must not be discarded when these forms are indexed or compared.