DD b12 — Legacy Naming for PET/JUB Axioms and Theorems#

The Design Decision #

Date: 2026m04d03

Problem: The earliest development sessions (2026m03d11 onward) used uppercase labels A1 through A25 for axioms and T1 through T11 for theorems. These labels appear extensively throughout dozens of llogs in HELL. However, the uppercase A# and T# namespace must be reserved for the final axiom and theorem names — names that cannot be assigned yet, because the optimal numbering sequence depends on research insights that do not yet exist.

If A1 is used for both the current transient name and the future permanent name, then the historical llogs will become ambiguous: does A1 in a 2026 llog refer to the same formal object as A1 in a 2030 document? It might — or it might not, if the numbering has been reorganized.

Decision: All transient axiom names use lowercase ax# (e.g., ax1 through ax25). All transient theorem names use lowercase th# (e.g., th1 through th11). In the historical llogs, every occurrence of the old A# / T# form was mechanically rewritten to compound form ax#_A# / th#_T#, where the underscore links the current transient name to the original legacy name for traceability.

This compound form makes three things unambiguous in every llog:

What the current name is (the ax# prefix).
What the original name was (the _A# suffix).
That these refer to the same formal object (joined by underscore).

Forward-facing pages (axioms, theorems, quest) use only the brief ax# / th# form. The compound form is reserved for historical records.

Implementation: The TELES compiler executed this as a one-time mechanical migration on 2026m04d03. See TELES Axiom/Theorem Compound Naming — Execution Prompt for the complete mapping and execution log.

Why the Final Names Cannot Be Assigned Yet #

The PET and JUB axiom systems were developed in the order that research insights arose, not in the order that would be most natural for a reader encountering them for the first time. Once sufficient research has been done to understand the logical dependencies and pedagogical flow, the axioms and theorems can be reordered and given final names (A1, A2, … in the new sequence) that make the system as clear and elegant as possible.

This final renaming requires deep understanding of:

Which axioms are foundational and which are derived.
Which ordering minimizes forward references.
Which groupings make the system easiest to learn.
Whether the current model boundaries (PET vs. JUB) are optimal.

None of these questions can be answered from the current state of knowledge. Premature assignment of final names would either require a second disruptive rename later or saddle future readers with a suboptimal naming sequence permanently.

Why This Is a Jubilee System Problem #

Naming conventions are a coordination problem: they only work when everyone agrees to use them simultaneously. Like driving on the left or right side of the road, naming conventions cannot be changed gradually. A partial transition — where some documents use old names and others use new names — is worse than either the old system or the new system alone.

This makes naming transitions a natural example for Jubilee System coordination (ax25 — Jubilee Recalibration). A Jubilee cycle provides:

A clear transition point. Everyone switches at the same time.
A bounded commitment. The new names are authoritative for one Jubilee cycle (50 years). If a ground-breaking discovery during that period reveals a better system, the next Jubilee can adopt it.
Clean separation for learners. Future generations learn the streamlined system without needing to know the historical idiosyncrasies. The legacy forms (ax#_A#) remain in the historical record for scholars who need provenance.

Without Jubilee-style coordination, a naming system accumulates layers of partial transitions, abbreviations, and exceptions that force every new participant to learn the history before they can learn the content. This is a concrete instance of BABL: agents talking past each other because the same symbols mean different things in different contexts.

Authoritative Name Sources #

This DD table is a legacy reference — it documents the relationship between naming forms as of the TELES migration on 2026m04d03. For current names and formal definitions, always use the authoritative source pages:

PET Axioms (ax1–ax14) — the current canonical definitions.
PET Theorems (th1–th4) — the current canonical proofs and statements.
PET Symbols — notation reference.
JUB Axioms (ax15–ax25) — the current canonical definitions.
JUB Theorems (th5–th11) — the current canonical proofs and statements.
JUB Symbols — notation reference.
Cross-Model Axioms Index — combined view.
Cross-Model Theorems Index — combined view.
Symbols Registry — cross-model notation.

If this DD table and a source page disagree, the source page is authoritative.

Legacy Naming Lookup Tables #

The tables below map every axiom and theorem identifier across all naming forms used in the balospe-com codebase and historical records.

PET Axioms (ax1 – ax14)#

Brief	Explicit Name	Summarizing Name	5D-link label	Compound label	First draft label
ax1	Containment	God contains the world	pet-ax1	ax1_A1	A1
ax2	Sustenance	God sustains the world	pet-ax2	ax2_A2	A2
ax3	Freedom	genuine freedom exists	pet-ax3	ax3_A3	A3
ax4	Responsiveness	God responds to world	pet-ax4	ax4_A4	A4
ax5	Temporality	God experiences time	pet-ax5	ax5_A5	A5
ax6	Love	God acts from love	pet-ax6	ax6_A6	A6
ax7	Purpose	God has purpose for creation	pet-ax7	ax7_A7	A7
ax8	Suffering	God suffers with creation	pet-ax8	ax8_A8	A8
ax9	Persuasion	God persuades, not coerces	pet-ax9	ax9_A9	A9
ax10	Creativity	God enables genuine novelty	pet-ax10	ax10_A10	A10
ax11	Dipolarity	God has two poles	pet-ax11	ax11_A11	A11
ax11b	Divine Simplicity	alternative to ax11_A11	pet-ax11b	ax11b_A11b	A11’
ax12	Universality	relation to all entities	pet-ax12	ax12_A12	A12
ax13	Knowability	God can be partially known	pet-ax13	ax13_A13	A13
ax14	Consistency	logical self-consistency	pet-ax14	ax14_A14	A14

JUB Axioms (ax15 – ax25)#

Brief	Explicit Name	Summarizing Name	5D-link label	Compound label	First draft label
ax15	Influence ordering	partial order on agents	jub-ax15	ax15_A15	A15
ax16	Delegation	God delegates responsibility	jub-ax16	ax16_A16	A16
ax17	Accountability	agents are accountable	jub-ax17	ax17_A17	A17
ax18	Inequality dynamics	wealth concentrates	jub-ax18	ax18_A18	A18
ax19	Maximal influence	uniquely maximal agent	jub-ax19	ax19_A19	A19
ax20	Reset mechanism	periodic rebalancing	jub-ax20	ax20_A20	A20
ax21	Voluntary participation		jub-ax21	ax21_A21	A21
ax22	Graduated implementation		jub-ax22	ax22_A22	A22
ax23	Institutional safeguards		jub-ax23	ax23_A23	A23
ax24	Knowledge distribution		jub-ax24	ax24_A24	A24
ax25	Succession design		jub-ax25	ax25_A25	A25

PET Theorems (th1 – th4)#

Brief	Explicit Name	5D-link label	Compound label	First draft label
th1	PET theorem 1	pet-th1	th1_T1	T1
th2	PET theorem 2	pet-th2	th2_T2	T2
th3	PET theorem 3	pet-th3	th3_T3	T3
th4	PET theorem 4	pet-th4	th4_T4	T4

JUB Theorems (th5 – th11)#

Brief	Explicit Name	5D-link label	Compound label	First draft label
th5	Bistability	jub-th5	th5_T5	T5
th6	JUB theorem 6	jub-th6	th6_T6	T6
th7	JUB theorem 7	jub-th7	th7_T7	T7
th8	Self-destruction dynamics	jub-th8	th8_T8	T8
th9	Ergodicity	jub-th9	th9_T9	T9
th10	JUB theorem 10	jub-th10	th10_T10	T10
th11	JUB theorem 11	jub-th11	th11_T11	T11

Notes #

Summarizing Name column left blank where no parenthetical description existed in the original source; to be populated in future sessions.
5D-link labels are RST cross-reference anchors and are NOT changed by the TELES migration. They remain stable across all naming changes.
First draft labels preserve the original temporary identifiers for backward compatibility with the earliest records.
This table is a legacy reference. Future synonym additions (from world literature engagement) are appended here.