The logigram is a program, not an argument. It takes the list of constraints as a row of predicates, lays them over a table of candidate cells and records, per cell, which predicate kills it. Run A is the freestanding output: no anchor on AD 27, no Luke 3:23, no baptism year in the input. What survives, survives on the sources around Herod's death and on Matthew 2 alone. That makes run A the measure against which the coupled run (chapter 9) is measured: everything the baptism/crucifixion axis adds must distinguish itself from what already stands here.
8.1 Variable space and conventions
A cell is a combination of chain, year of death and year of birth. The four chains fix the death-year side — C, CA and HV at 4 BC, SY at 1 BC — and the logigram outputs the birth side. Two conventions carry all the arithmetic: for years before Christ, greater is earlier (8 BC lies before 4 BC), and there is no year 0, so that an age equals baptism year + birth year − 1. That age formula is dormant in run A, because there is no baptism year; it is in the model nonetheless and is validated below. Run A counts 252 cells: 124 living, 128 dead.
8.2 The constraints as predicates
V-1, the eclipse. An umbral lunar eclipse visible from Jerusalem must precede the death, in the year of death or in the December before a death early in the next year; the predicate stands on the date of the eclipse, not on the calendar year of the death. The scan leaves five eclipses in the window: 23 March and 15 September 5 BC, 13 March 4 BC, 10 January and 29 December 1 BC. The predicate excludes 7, 6, 3 and 2 BC as year of death. Both years of death the chains offer pass: 4 BC (C, CA, HV) and 1 BC (SY). A death in January AD 1 would pass it as well; it dies on Antipas's year 43, the Paneas era and Gaius (§6.2), not on the eclipse. The eclipse fixes the year, not the season; whether Herod died in the spring of 4 or in the winter of 4/3 remains open in run A, and the day count (§6.1) leans it to the spring. HV holds: spring 4 BC; the winter of 4/3 remains possible but is less likely.
G-1, Matthew 2. This is the only predicate that kills cells in run A, and it cuts on two sides. The late edge is a hard floor: the birth lies before the death. But that floor is not a full year. Herod reckons generously, and the floor admits a birth shortly before the death, with the months the story itself requires. A birth in the year of death is therefore a living cell. The early edge is stepped. A birth two years or less before the death falls within "two years and under" and counts as ok. Three years before the death leaves one year's margin on Herod's limit: soft. Four years before the death leaves two years' margin and counts as a postulate (P). Five years or more before the death is dead.
G-2, the season of birth. Undetermined. Every season survives; whoever picks one pays a postulate for the choice, because the feast is not a date.
The axes at zero. Census, priestly courses, stars, letter clock and patristics stand in the model as predicates, but as empty ones: they do not restrict the space and kill nothing. An empty axis is not removed from the model; it stays in place, so that whoever wants to fill it sees exactly where it would cut.
Switched off in run A. B-1a (Tiberius's 15th year, the baptism floor) and G-3 (Luke 3:23, the age band) belong to the coupled run and are off here.
8.3 Validation
Three checks precede the output. The age sum reproduces the count-back table exactly: with baptism in AD 27, 7 BC gives 33, 6 BC 32, 5 BC 31, 4 BC 30, 3 BC 29 and 2 BC 28. The chain profiles are those of the cost accounting in its standing form (below). And Matthew 2 hard excludes a birth after the death — checked on the output. A model that reproduces the tables from which it was built says nothing about the case thereby; it says only that it calculates what is written.
8.4 The output
chain
year of death
year of birth (BC)
early edge
C
4 BC
8, 7, 6, 5, 4
8: P · 7: soft · 6, 5, 4: ok
SY
1 BC
5, 4, 3, 2, 1
5: P · 4: soft · 3, 2, 1: ok
CA
4 BC
8, 7, 6, 5, 4
8: P · 7: soft · 6, 5, 4: ok
HV
4 BC
8, 7, 6, 5, 4
8: P · 7: soft · 6, 5, 4: ok
Three things stand out.
First: the three 4/3 chains give one and the same window, 8-4 BC. C, CA and HV differ on the death-year side in their price (below), not in their year of death, and on the birth side the logigram knows no distinction other than the year of death. The window is a function of the year 4 BC and of Matthew 2, of nothing else.
Second: SY's window, 5-1 BC, is the same window shifted three years. That too is Matthew 2 at work: the same five steps (P, soft, ok, ok, ok), hung on a different year of death. The minority chronology gets no extra hurdle and no exemption; it gets its own band.
Third: the two bands overlap in exactly two cells, 5 and 4 BC. Only those years live under both years of death — for the 4/3 chains as ok, for SY as P (5) and soft (4). Whoever leaves the year of death open is thus left, freestanding, with 5 and 4 BC, at SY's price; whoever sets the year of death at 4 gets 8-4 with a postulate at the early edge and a soft cell at 7.
8.5 The kill matrix
Of the 128 dead cells, 88 die of "after the death" and 40 of "≥5 years before". Both cuts are Matthew 2. In run A the logigram records not a single death on the eclipse, on the season or on any of the zero axes: the eclipse has done its work before the output, on the death-year side, by removing four years from the input. That deserves emphasis. The eclipse determines which years of death enter the table; after that the window is Matthew 2 alone. Whoever flips the eclipse exclusion therefore changes not the shape of the bands but the place where they hang.
8.6 The cost accounting per cell
Every cell carries two prices: that of its chain on the death-year side and that of its step on the birth side. The death-year side is fixed from the chain profiles across 20 data:
chain
year of death
rejections (V)
emendations (E)
postulates (P)
hard cost (V+E)
C
4/3 BC
0
0
2
0
CA
4/3 BC
1
0
0
1
SY
1 BC
3
0
8
3
HV shares C's four input values and thus pays C's price on the death-year side. The cheapest chain in rejections is C (0 V), then CA (1 V), then SY (3 V + 8 P). The year of death 4/3 BC is the cheapest reading, with as its season spring 4 BC; the winter of 4/3 remains possible but is less likely (§6.2). 1 BC costs the most.
The birth side adds the step: ok costs nothing, soft costs one year's margin on Herod's limit, P costs a postulate, dead is dead. The cheapest cells of run A are thereby C (and HV) with 6, 5 or 4 BC: zero rejections on the death-year side, ok on the birth side. Behind them C with 7 BC (soft) and C with 8 BC (a postulate added). Every SY cell starts with three rejections and eight postulates before the birth side counts; SY's ok cells (3, 2, 1 BC) are as cheap on the birth side as C's ok cells and on the death-year side the most expensive in the field.
Two falsifiers from the symmetric list are decided here. "A cell at 1 BC or at 3/2 BC costs less than every cell at 4 BC" — false: SY carries 3 V + 8 P against C's 0 V. And, with the same firmness in the other direction: "every cell at 1 BC costs more than the cheapest cell at 4 BC" — true, for the same reason. Both statements concern the death-year side; on the birth side the logigram makes no difference between the chains.
8.7 What run A says and does not say
The first falsifier against HV read: run A does not narrow below 5 BC. It is true. Freestanding, the logigram gives 8-4 BC for C, CA and HV, with 8 as a postulate and 7 as a soft cell; 6, 5 and 4 BC are ok. A window of 5 BC alone, or of 5-4, does not come out of the machine without the baptism axis. What the coupling changes in that is measured in chapter 9; here it stands only that the freestanding band is five years wide and that the three ok cells lie on the late side.
On the season, run A says nothing that makes a choice cheaper. The falsifier "Tabernacles is not the cheapest season" stands: no season is cheaper, because no predicate cuts on season. That is an outcome, not a gap — the model has the axis, and the axis is empty.
Every cell is traceable to a constraint, every constraint to an entry. Whoever flips one constraint — the eclipse exclusion, the Matthew edge, the step at two years' margin — sees in `logigram.py` what happens to the output. The logigram delivers no certainty; it delivers a cheapest reading with the prices of the rivals beside it, and the account is public.
The logigram is a program, not an argument. It takes the list of constraints as a row of predicates, lays them over a table of candidate cells and records, per cell, which predicate kills it. Run A is the freestanding output: no anchor on AD 27, no Luke 3:23, no baptism year in the input. What survives, survives on the sources around Herod's death and on Matthew 2 alone. That makes run A the measure against which the coupled run (chapter 9) is measured: everything the baptism/crucifixion axis adds must distinguish itself from what already stands here.
8.1 Variable space and conventions
A cell is a combination of chain, year of death and year of birth. The four chains fix the death-year side — C, CA and HV at 4 BC, SY at 1 BC — and the logigram outputs the birth side. Two conventions carry all the arithmetic: for years before Christ, greater is earlier (8 BC lies before 4 BC), and there is no year 0, so that an age equals baptism year + birth year − 1. That age formula is dormant in run A, because there is no baptism year; it is in the model nonetheless and is validated below. Run A counts 252 cells: 124 living, 128 dead.
8.2 The constraints as predicates
V-1, the eclipse. An umbral lunar eclipse visible from Jerusalem must precede the death, in the year of death or in the December before a death early in the next year; the predicate stands on the date of the eclipse, not on the calendar year of the death. The scan leaves five eclipses in the window: 23 March and 15 September 5 BC, 13 March 4 BC, 10 January and 29 December 1 BC. The predicate excludes 7, 6, 3 and 2 BC as year of death. Both years of death the chains offer pass: 4 BC (C, CA, HV) and 1 BC (SY). A death in January AD 1 would pass it as well; it dies on Antipas's year 43, the Paneas era and Gaius (§6.2), not on the eclipse. The eclipse fixes the year, not the season; whether Herod died in the spring of 4 or in the winter of 4/3 remains open in run A, and the day count (§6.1) leans it to the spring. HV holds: spring 4 BC; the winter of 4/3 remains possible but is less likely.
G-1, Matthew 2. This is the only predicate that kills cells in run A, and it cuts on two sides. The late edge is a hard floor: the birth lies before the death. But that floor is not a full year. Herod reckons generously, and the floor admits a birth shortly before the death, with the months the story itself requires. A birth in the year of death is therefore a living cell. The early edge is stepped. A birth two years or less before the death falls within "two years and under" and counts as ok. Three years before the death leaves one year's margin on Herod's limit: soft. Four years before the death leaves two years' margin and counts as a postulate (P). Five years or more before the death is dead.
G-2, the season of birth. Undetermined. Every season survives; whoever picks one pays a postulate for the choice, because the feast is not a date.
The axes at zero. Census, priestly courses, stars, letter clock and patristics stand in the model as predicates, but as empty ones: they do not restrict the space and kill nothing. An empty axis is not removed from the model; it stays in place, so that whoever wants to fill it sees exactly where it would cut.
Switched off in run A. B-1a (Tiberius's 15th year, the baptism floor) and G-3 (Luke 3:23, the age band) belong to the coupled run and are off here.
8.3 Validation
Three checks precede the output. The age sum reproduces the count-back table exactly: with baptism in AD 27, 7 BC gives 33, 6 BC 32, 5 BC 31, 4 BC 30, 3 BC 29 and 2 BC 28. The chain profiles are those of the cost accounting in its standing form (below). And Matthew 2 hard excludes a birth after the death — checked on the output. A model that reproduces the tables from which it was built says nothing about the case thereby; it says only that it calculates what is written.
8.4 The output
Three things stand out.
First: the three 4/3 chains give one and the same window, 8-4 BC. C, CA and HV differ on the death-year side in their price (below), not in their year of death, and on the birth side the logigram knows no distinction other than the year of death. The window is a function of the year 4 BC and of Matthew 2, of nothing else.
Second: SY's window, 5-1 BC, is the same window shifted three years. That too is Matthew 2 at work: the same five steps (P, soft, ok, ok, ok), hung on a different year of death. The minority chronology gets no extra hurdle and no exemption; it gets its own band.
Third: the two bands overlap in exactly two cells, 5 and 4 BC. Only those years live under both years of death — for the 4/3 chains as ok, for SY as P (5) and soft (4). Whoever leaves the year of death open is thus left, freestanding, with 5 and 4 BC, at SY's price; whoever sets the year of death at 4 gets 8-4 with a postulate at the early edge and a soft cell at 7.
8.5 The kill matrix
Of the 128 dead cells, 88 die of "after the death" and 40 of "≥5 years before". Both cuts are Matthew 2. In run A the logigram records not a single death on the eclipse, on the season or on any of the zero axes: the eclipse has done its work before the output, on the death-year side, by removing four years from the input. That deserves emphasis. The eclipse determines which years of death enter the table; after that the window is Matthew 2 alone. Whoever flips the eclipse exclusion therefore changes not the shape of the bands but the place where they hang.
8.6 The cost accounting per cell
Every cell carries two prices: that of its chain on the death-year side and that of its step on the birth side. The death-year side is fixed from the chain profiles across 20 data:
HV shares C's four input values and thus pays C's price on the death-year side. The cheapest chain in rejections is C (0 V), then CA (1 V), then SY (3 V + 8 P). The year of death 4/3 BC is the cheapest reading, with as its season spring 4 BC; the winter of 4/3 remains possible but is less likely (§6.2). 1 BC costs the most.
The birth side adds the step: ok costs nothing, soft costs one year's margin on Herod's limit, P costs a postulate, dead is dead. The cheapest cells of run A are thereby C (and HV) with 6, 5 or 4 BC: zero rejections on the death-year side, ok on the birth side. Behind them C with 7 BC (soft) and C with 8 BC (a postulate added). Every SY cell starts with three rejections and eight postulates before the birth side counts; SY's ok cells (3, 2, 1 BC) are as cheap on the birth side as C's ok cells and on the death-year side the most expensive in the field.
Two falsifiers from the symmetric list are decided here. "A cell at 1 BC or at 3/2 BC costs less than every cell at 4 BC" — false: SY carries 3 V + 8 P against C's 0 V. And, with the same firmness in the other direction: "every cell at 1 BC costs more than the cheapest cell at 4 BC" — true, for the same reason. Both statements concern the death-year side; on the birth side the logigram makes no difference between the chains.
8.7 What run A says and does not say
The first falsifier against HV read: run A does not narrow below 5 BC. It is true. Freestanding, the logigram gives 8-4 BC for C, CA and HV, with 8 as a postulate and 7 as a soft cell; 6, 5 and 4 BC are ok. A window of 5 BC alone, or of 5-4, does not come out of the machine without the baptism axis. What the coupling changes in that is measured in chapter 9; here it stands only that the freestanding band is five years wide and that the three ok cells lie on the late side.
On the season, run A says nothing that makes a choice cheaper. The falsifier "Tabernacles is not the cheapest season" stands: no season is cheaper, because no predicate cuts on season. That is an outcome, not a gap — the model has the axis, and the axis is empty.
Every cell is traceable to a constraint, every constraint to an entry. Whoever flips one constraint — the eclipse exclusion, the Matthew edge, the step at two years' margin — sees in `logigram.py` what happens to the output. The logigram delivers no certainty; it delivers a cheapest reading with the prices of the rivals beside it, and the account is public.