Primary Directions Parallel Family Matrix

Purpose

This document turns the parallel-family question into explicit Moira policy.

It does not assume that all "parallels" are one computational object. It classifies each recoverable branch by:

• geometry family
• directional object
• governing law
• source quality
• Moira policy status
• next action

The rule is strict:

• no branch is admitted by label alone
• no branch is admitted globally if its law is method-bound
• no branch is widened beyond the recoverable mathematics

Governing Policy

Constitutional Rule

In primary directions, a parallel is admitted first as a relation class, not as a generic target class.

Only a method with an explicit governing law may realize that relation as a derived projected point or other computational endpoint.

Source Rule

For a parallel branch to be admitted, Moira requires:

1. an explicit mathematical law
2. a clear doctrinal meaning
3. a runtime realization specific enough to encode
4. validation material strong enough to test

If one of these is missing, the branch is deferred.

Branch Matrix

Branch	Geometry Family	Directional Object	Governing Law in Hand	Source Quality	Moira Status	Next Action
Ptolemaic zodiacal parallel	Ptolemy / semi-arc, in_zodiaco	declination-equivalent derived zodiacal point	Yes. Solve the declination-equivalent ecliptic point from sin(delta) = sin(eps) * sin(lambda), then measure by the active Ptolemaic sub-law (RA, OA/OD, or proportional semi-arc)	strong enough for narrow admission	implemented	keep as verified narrow branch
Ptolemaic zodiacal contra-parallel	Ptolemy / semi-arc, in_zodiaco	declination-equivalent derived zodiacal point with reflected declination	Yes. Same as above, with declination reflected to the opposite sign of the relation before solving the ecliptic equivalent	strong enough for narrow admission	implemented	keep as verified narrow branch
Placidian mundane parallel	Placidian classic / semi-arc, in_mundo	meridian-distance / semi-arc relational perfection	Partially. The historical material supports proportion by semi-arc and meridian distance, but the precise normalized law still needs one clean formula packet before runtime admission	moderate	research_candidate	extract a formula-grade law from one primary technical source before implementation
Placidian mundane rapt parallel	Placidian classic / semi-arc, in_mundo	joint motion of both bodies under primary motion	Yes, narrowly. The recoverable calculation is proportion-based: combine the relevant semi-arcs, compare them to the right-ascension difference, derive a secondary distance, then take the difference from the primary meridian distance	moderate-to-strong for narrow reconstruction	implemented_validated_branch	keep closed unless a stronger external worked example appears
Placidian converse rapt parallel	Placidian classic / semi-arc, in_mundo, converse	joint converse motion of both bodies	Yes, narrowly. The converse branch uses the promissor's converse semi-arc, the significator's active semi-arc, the forward converse right-ascension relation, and the promissor's converse meridian distance	moderate for narrow reconstruction	implemented_validated_branch	keep closed unless a stronger external worked example appears
Regiomontanian parallels	Regiomontanus	unclear: may be under-the-pole, mundane, or mixed by sub-branch	No single source-safe law in hand	weak	deferred	do not implement until one explicit branch law is recovered
Campanian parallels	Campanus	unclear: likely tied to wider mundane branch, not generic target doctrine	No single source-safe law in hand	weak	deferred	do not implement until one explicit branch law is recovered
Topocentric parallels	Topocentric	unclear: likely method-specific and pole-law dependent	No single source-safe law in hand	weak	deferred	do not implement until one explicit branch law is recovered
Morinian parallels	Morinus	unresolved relative to Morinian aspect-plane doctrine	No explicit primary-direction law in hand	weak	deferred	leave out of runtime until formula-grade evidence appears
Generic global parallel target family	cross-family	universal target point	No. This is doctrinally false on current evidence	strong enough to reject globally	rejected	keep rejected as a global consumer target class

Concrete Moira Policy

Declared Implementable Now

These branches are concrete enough to stand as policy:

• Ptolemaic zodiacal parallel
• Ptolemaic zodiacal contra-parallel

They are admitted as:

• relation-first branches
• method-specific derived-point realizations
• not as generic global target classes

Declared Implementable Next

The Placidian rapt-parallel family is now closed at the current evidence level.

Why:

• both recoverable branches are admitted
• both are now backed by published worked-example fixtures
• further widening would require new source-safe evidence, not more internal extrapolation

Declared Deferred

These remain deferred:

• Regiomontanian parallels
• Campanian parallels
• Topocentric parallels
• Morinian parallels

Reason:

• the label survives
• software may expose the label
• but Moira does not yet have one branch law explicit enough to encode

Declared Rejected

This remains rejected:

• global consumer-facing Parallel as a target class

Reason:

• it collapses a relation doctrine into a false generic target ontology

Implementation Order

The parallel family should proceed in this order:

1. keep the current Ptolemaic zodiacal parallel / contra-parallel branch stable
2. reassess whether any non-Placidian families have gained a source-safe branch law

The stop rule is explicit:

• if no explicit governing law is recovered for a branch, the branch stays deferred

Mathematical Notes

Ptolemaic Zodiacal Parallel Family

The current narrow law is:

1. take the source declination
2. preserve it for parallel, reflect it for contra-parallel
3. solve the equivalent ecliptic longitude from the declination relation
4. measure the resulting directional arc through the active Ptolemaic sub-law:
   • MC/IC by RA
   • ASC/DSC by OA/OD
   • non-angular points by proportional semi-arcs

This is already encoded and tested in Moira.

Placidian Mundane Rapt Parallel Family

The recoverable direct-family pattern is:

1. identify the relevant semi-arcs of the two bodies
2. form the required semi-arc sum
3. form the relevant right-ascension difference
4. use proportionality to derive a secondary distance
5. compare primary and secondary meridian distances to obtain the arc

The converse family follows the same proportion logic, but with converse semi-arcs and converse right-ascension handling.

This is precise enough to declare a next implementation target, but not yet admitted in runtime until the law is reduced to one explicit code-grade formula packet.

Sources Used

Strongest Current Sources

• Alan Leo, Primary Directions: direct and converse rapt-parallel worked examples and zodiacal parallel / declination-equivalent examples https://maestrosdelsaber.com/wp-content/uploads/ftp-files/Astrologia/Astro%20a%20Leo%2C%20Alan/Astro%20Leo%2C%20Alan%20-%20Primary%20Directions.pdf
• AstroAmerica, Primary Directions: Ptolemaic proportional-semi-arc basis and declination-equivalent zodiacal practice https://astroamerica.com/primary.pdf
• Heaven Astrolabe, "Calculating rapt parallels, Placido method": modern technical reconstruction of Placidian rapt-parallel arithmetic from Placido tables https://heavenastrolabe.wordpress.com/2010/08/20/calculating-rapt-parallels-placido-method/

Supporting Ecosystem Sources

• Halloran / Kolev software material: confirms that mundo parallels and mundo rapt parallels are treated as real Placidian branches in the wider software ecosystem https://www.halloran.com/placidus.htm
• AstroApp help: confirms current software exposure of mundane parallels and ASC-axis parallels in In Mundo https://astroapp.com/help/1/returnsW_53.html
• PyMorinus site: confirms that rapt parallels are treated as a recognizable research branch, though not thereby source-verified https://sites.google.com/site/pymorinus/

Present Declaration

Moira now has a concrete parallel-family policy:

• the Ptolemaic zodiacal branch is admitted
• the next implementation target inside parallels, if any, must be a new source-safe family rather than more internal widening of Placidian rapt work
• wider method families remain deferred until their governing law is explicit
• the global-target abstraction remains rejected