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Craft · lessons, benches & plates
Lesson 09 · The receipt

9 The receipt

Read G1's complete account, then reduce B3 alone and name the cause of every residual without silently correcting the paper.

Bench B3Stage 1 of 2 · Independent practice
Independent practice

B3 · Buenos Aires

Nothing is filled. Reduce the bench on the permanent form.

0 of 36 lines checked0%
Shared paper instrument · A1

Keep the difference.
Account for the cause.

Paper, frozen Moira & the difference

Reduce B3 one line at a time. A comparison enters this instrument only when its paper working is checked or revealed.

Paper → frozen Moira → Δ → cause

Begin with the civil date.

No computed comparison is admitted yet. Keep each checked value on your paper; at Part F, account for every difference, including zero and exact records.

The ten cause choices · vocabulary

This is the fixed vocabulary, without a line-to-cause answer key. Classifying a zero or exact record still names its method or input convention.

Zone or DST
Civil clock, standard zone and seasonal-time conventions.
Date change
A calendar day carried when the clock crosses midnight.
Sidereal-time rounding
Rounded sidereal clock entries and paper time arithmetic.
Table grid
Printed grid spacing or results derived from those table entries.
Latitude grid
Interpolation between latitude rows of the house plate.
Linear Moon
A linear midnight-to-midnight estimate of lunar motion.
Station
A station interval marked on the retained paper row; not a newly diagnosed event.
Mean vs true node
The distinction between mean and true nodal positions.
UT vs TT
The distinction between Universal Time and Terrestrial Time.
Ephemeris kernel
The ephemeris kernel used to calculate the source positions.
Frozen source & provenance

Frozen apparent geocentric tropical positions and Placidus houses for this teaching bench. The comparison uses the retained historical source, without a fresh engine request.

moira-astro 6.4.1 · de441.bsp · 0h UT · ΔT 69.02324259281158s · Placidus · not a reprint of ACS · generated Sep 4, 2026, 11:16:40.902385 PM UTC

ΔT policy
engine_default_hybrid

The printed form retains whole-minute longitudes. Original frozen source values, where used for a selected numeric residual, remain inspectable above.

Inspection is temporary. It changes no paper values, classifications, lesson checks or saved progress.

All source cells for A1
Permanent reduction formParts A–F

  1. Birth date, civil

    active line
    Shared paper instrument · A1

    Keep the difference.
    Account for the cause.

    Paper, frozen Moira & the difference

    Reduce B3 one line at a time. A comparison enters this instrument only when its paper working is checked or revealed.

    Paper → frozen Moira → Δ → cause

    Begin with the civil date.

    No computed comparison is admitted yet. Keep each checked value on your paper; at Part F, account for every difference, including zero and exact records.

    The ten cause choices · vocabulary

    This is the fixed vocabulary, without a line-to-cause answer key. Classifying a zero or exact record still names its method or input convention.

    Zone or DST
    Civil clock, standard zone and seasonal-time conventions.
    Date change
    A calendar day carried when the clock crosses midnight.
    Sidereal-time rounding
    Rounded sidereal clock entries and paper time arithmetic.
    Table grid
    Printed grid spacing or results derived from those table entries.
    Latitude grid
    Interpolation between latitude rows of the house plate.
    Linear Moon
    A linear midnight-to-midnight estimate of lunar motion.
    Station
    A station interval marked on the retained paper row; not a newly diagnosed event.
    Mean vs true node
    The distinction between mean and true nodal positions.
    UT vs TT
    The distinction between Universal Time and Terrestrial Time.
    Ephemeris kernel
    The ephemeris kernel used to calculate the source positions.
    Frozen source & provenance

    Frozen apparent geocentric tropical positions and Placidus houses for this teaching bench. The comparison uses the retained historical source, without a fresh engine request.

    moira-astro 6.4.1 · de441.bsp · 0h UT · ΔT 69.02324259281158s · Placidus · not a reprint of ACS · generated Sep 4, 2026, 11:16:40.902385 PM UTC

    ΔT policy
    engine_default_hybrid

    The printed form retains whole-minute longitudes. Original frozen source values, where used for a selected numeric residual, remain inspectable above.

    Inspection is temporary. It changes no paper values, classifications, lesson checks or saved progress.

    All source cells for A1

    Why Retaining A1 makes its contribution traceable in the final receipt.

    Tolerance · exact

  2. Clock time, 24-hour

    waiting

  3. Summer time in force?

    waiting

    Rule if Y subtract 1h · older war time may be 2h · stated on the bench

  4. Standard time = A2 − A3

    waiting

  5. Zone offset from Greenwich

    waiting

    Rule West add · East subtract

  6. Universal Time = A4 + A5

    waiting

    Rule if 24h or more subtract 24h and move A7 forward a day · if below 0 add 24h and move A7 back

  7. UT date

    waiting

    Rule may differ from A1 · every plate row is read on this date

  8. Plate GST at midnight (0h UT) on the A7 date

    waiting

    Rule read from the ephemeris row for A7

  9. Interval since 0h = A6

    waiting

  10. Acceleration = B2 × 9.86 s per hour

    waiting

    Magnitude check · always under 4 minutes

  11. Greenwich sidereal time at birth = B1 + B2 + B3

    waiting

    Rule carry at 60

  12. Longitude in time = longitude × 4 min per degree

    waiting

    Rule East add · West subtract

  13. Local sidereal time = B4 + B5

    waiting

    Rule if 24h or more subtract 24h

  14. Southern hemisphere?

    waiting

    Rule if Y add 12h to B6 and normalise · this is the table entry

  15. Table rows bracketing B7: lower ST, upper ST

    waiting

    Rule rows are 4 minutes apart

  16. Fraction f = (B7 − lower) in seconds ÷ 240

    waiting

    Magnitude check · always between 0 and 1

  17. MC: lower, upper, difference, × f, + lower

    waiting

    Rule the same for every latitude

  18. Latitude rows bracketing the birth: lower, upper; fraction g

    waiting

    Rule table rows are 1° apart

  19. 11 12 ASC 2 3 as columns: at the lower latitude, at the upper latitude, then by g

    waiting

    Rule a column that looks unlike its neighbours is the column with the mistake

  20. Southern? Reverse every sign on C3 and C5

    waiting

    Rule degrees and minutes unchanged

  21. Opposites: IC = MC + 180, DSC = ASC + 180, 5 6 8 9 = 11 12 2 3 + 180

    waiting

    Rule same degree and minute, opposite sign

  22. Sun: this midnight, next midnight, motion, × A6 ÷ 24, position

    waiting

    Rule negative motion is retrograde, write R · a negative travel subtracts

  23. Moon: this midnight, next midnight, motion, × A6 ÷ 24, position

    waiting

    Rule negative motion is retrograde, write R · a negative travel subtracts

  24. Mercury: this midnight, next midnight, motion, × A6 ÷ 24, position

    waiting

    Rule negative motion is retrograde, write R · a negative travel subtracts

  25. Venus: this midnight, next midnight, motion, × A6 ÷ 24, position

    waiting

    Rule negative motion is retrograde, write R · a negative travel subtracts

  26. Mars: this midnight, next midnight, motion, × A6 ÷ 24, position

    waiting

    Rule negative motion is retrograde, write R · a negative travel subtracts

  27. Jupiter: this midnight, next midnight, motion, × A6 ÷ 24, position

    waiting

    Rule negative motion is retrograde, write R · a negative travel subtracts

  28. Saturn: this midnight, next midnight, motion, × A6 ÷ 24, position

    waiting

    Rule negative motion is retrograde, write R · a negative travel subtracts

  29. Uranus: this midnight, next midnight, motion, × A6 ÷ 24, position

    waiting

    Rule negative motion is retrograde, write R · a negative travel subtracts

  30. Neptune: this midnight, next midnight, motion, × A6 ÷ 24, position

    waiting

    Rule negative motion is retrograde, write R · a negative travel subtracts

  31. Pluto: this midnight, next midnight, motion, × A6 ÷ 24, position

    waiting

    Rule negative motion is retrograde, write R · a negative travel subtracts

  32. True Node: this midnight, next midnight, motion, × A6 ÷ 24, position

    waiting

    Rule negative motion is retrograde, write R · a negative travel subtracts

  33. Cusps on the wheel. ASC at the left, houses counterclockwise, C11 filled

    waiting

  34. Bodies into houses by comparing D5 with the cusps

    waiting

    Rule note any body within 1° of a cusp

  35. Aspectarian: the five Ptolemaic aspects, applying or separating from motion

    waiting

    Rule orbs as on the free transits surface

  36. Receipt: paper, Moira, Δ, cause for every computed line

    waiting
Moira Craft School

Blank permanent A–F reduction form

Part ATime

LineOperation and ruleWorkingResult
A1Birth date, civil
A2Clock time, 24-hour
A3Summer time in force?if Y subtract 1h · older war time may be 2h · stated on the bench
A4Standard time = A2 − A3
A5Zone offset from GreenwichWest add · East subtract
A6Universal Time = A4 + A5if 24h or more subtract 24h and move A7 forward a day · if below 0 add 24h and move A7 back
A7UT datemay differ from A1 · every plate row is read on this date

Part BSidereal time

LineOperation and ruleWorkingResult
B1Plate GST at midnight (0h UT) on the A7 dateread from the ephemeris row for A7
B2Interval since 0h = A6
B3Acceleration = B2 × 9.86 s per hourCheck: always under 4 minutes
B4Greenwich sidereal time at birth = B1 + B2 + B3carry at 60
B5Longitude in time = longitude × 4 min per degreeEast add · West subtract
B6Local sidereal time = B4 + B5if 24h or more subtract 24h
B7Southern hemisphere?if Y add 12h to B6 and normalise · this is the table entry

Part CAngles and cusps

LineOperation and ruleWorkingResult
C1Table rows bracketing B7: lower ST, upper STrows are 4 minutes apart
C2Fraction f = (B7 − lower) in seconds ÷ 240Check: always between 0 and 1
C3MC: lower, upper, difference, × f, + lowerthe same for every latitude
C4Latitude rows bracketing the birth: lower, upper; fraction gtable rows are 1° apart
C511 12 ASC 2 3 as columns: at the lower latitude, at the upper latitude, then by ga column that looks unlike its neighbours is the column with the mistake
C10Southern? Reverse every sign on C3 and C5degrees and minutes unchanged
C11Opposites: IC = MC + 180, DSC = ASC + 180, 5 6 8 9 = 11 12 2 3 + 180same degree and minute, opposite sign

Part DBodies

LineOperation and ruleWorkingResult
D:sunSun: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts
D:moonMoon: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts
D:mercuryMercury: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts
D:venusVenus: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts
D:marsMars: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts
D:jupiterJupiter: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts
D:saturnSaturn: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts
D:uranusUranus: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts
D:neptuneNeptune: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts
D:plutoPluto: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts
D:trueNodeTrue Node: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts

Part EFigure and aspects

LineOperation and ruleWorkingResult
E1Cusps on the wheel. ASC at the left, houses counterclockwise, C11 filled
E2Bodies into houses by comparing D5 with the cuspsnote any body within 1° of a cusp
E3Aspectarian: the five Ptolemaic aspects, applying or separating from motionorbs as on the free transits surface

Part FReceipt

LineOperation and ruleWorkingResult
FReceipt: paper, Moira, Δ, cause for every computed line

Part F · continuationPaper-to-Moira discrepancy account

Retain the paper value; record Moira, the signed delta, and one cause from the fixed vocabulary.
LinePaperMoiraΔCause / notes
A4
A5
A6
A7
B1
B2
B3
B4
B5
B6
B7
C1
C2
C3
C4
C5
C10
C11
D:sun
D:moon
D:mercury
D:venus
D:mars
D:jupiter
D:saturn
D:uranus
D:neptune
D:pluto
D:trueNode
E2
E3

Blank permanent A–F reduction form · tropical zodiac · Placidus houses