Conclusion: the narrowest defensible window, and the cost of the alternatives
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In-depth:
Herod dies in the spring of 4 BC; the winter of 4/3 remains possible but is less likely. The year of death 4/3 BC is the cheapest reading: across the 20 primary data, chain C rejects nothing and emends nothing; the one datum outside them that it sets aside, the 184th olympiad of AJ 14.389, every chain sets aside. The regnal figures 34 and 37 yield the year plainly, on every chain; only a choice of counting rule moves it off, and that choice is an entry on the account, not a datum.
The birth window that follows from this is 6-4 BC — a band of years, without a season, since the sweep reckons on the birth year and not on the month —, coinciding in run B-consistent for C, CA and HV. Within that window the cells are not equal. 5 BC is the most robust: it survives both seasons of death (spring 4 and winter 4/3), run A and run B, and baptism years 27 and 28. 6 BC stands at the early edge: it leans on one baptism year (only baptism in 27; at 28 the child is 33, outside the age band). That is reckoned in year cells. With the boundary of Tiberius' 15th year on 20 October 27 the baptism falls late in the autumn of 27 or in the winter of 27/28; in completed years 6 BC stands even with a winter baptism (§9.3). 4 BC is tight: it hangs on the winter scenario and on a birth shortly before the death — admitted, because the late Matthew edge is not hard. Most probable, therefore, is 5 BC, on robustness; within it Sukkot is HV's working expectation and not an outcome of the derivation. Not because 6 BC carries a demonstrable cost: it is not a dead cell, it is a cell that survives fewer constraints.
10.1 The cost of the alternatives
SY (death 1 BC, birth 3/2 BC) is the most expensive chain: three rejections and eight postulates, on the year-of-death side alone. Its patristic trump card — "virtually all early Christian authors" — dissolves on inspection into a reckoning tradition of at most two families; its census in 3/2 BC is attested nowhere. Whoever chooses SY buys an eclipse-valid year of death at the highest bill on the table.
CA (death 3/2 BC) is cheaper, but carries one rejection. Here too the regnal figures give 4/3; the last step to 3/2 comes from the antedating rule, not from a figure. Philip is the loss entry.
C itself is not free, only cheapest. Its inclusive counting rule is rejected by the same edition for the Hasmoneans and retained for Herod, and what licenses that asymmetry is the eclipse. That is no rejection and no emendation; it is a counting choice that belongs on the account and is entered there.
10.2 What does not carry the window
The window does not derive its firm core from the baptism and crucifixion axis. Run A, freestanding — without the AD 27 anchor and without Luke 3:23 — already gives 8-4 BC for C, CA and HV, with 8 as a postulate and 7 as a soft edge. Run B-consistent gives 6-4. The coupling removes the two softest cells — 8 (already a postulate) and 7 (which falls outside Plummer's age band 28-32); the firm core 6-5-4 stays on Matthew. The baptism axis (the Tiberius reckoning, Luke 3:23, the 69 weeks) is a defensible minority reading and not a refuted constraint; it trims the early edge but does not touch the core. Nor is the window forced by baptism in 27 alone: over baptism in 27, 28 and 29 together, C/CA/HV stays at 6-4. The early edge does hang on the band width: on Hoehner's ±3 it would run to 7, on Plummer's ±2 to 6 — this work adopts ±2. The earlier, narrower outcome "5 or 4 BC" rested on an imported floor — Hoehner's "no earlier than 5 B.C.", which hangs on baptism in 29 and not on Luke 3:23 — and has therefore been withdrawn.
Census, patristics and shemitah do not carry the window either. They are axes at zero: they kill no cell. What they do is remove props from under the rival chronologies.
10.3 Two open axes — themselves a result
The season of death stands as above: spring leads, the winter of 4/3 is not excluded. The travel clock excludes only a death immediately before Passover. The illness clock is a topos and does not keep time. The Ptolemy sweep prices Kushnir-Stein's block calculation, but does not break it. What separates the two is the day count from the eclipse to the Passover of AJ 17.213: 30 days under the spring, 414 under the winter. This hinge decides whether 4 BC takes part as a birth year; it stands open only for whoever detaches the eclipse from the chronology.
The season of birth is underdetermined. Sukkot and spring finish level on canonical typology; winter stands one step behind, carried by reception alone. No ancient source places the birth in Tishri. The feast is not a date: the choice of Tabernacles is a postulate, and that is how it is booked.
That both axes remain open is not a shortcoming of the derivation. It is a measurement: the sources reach this far and no further, and a work that reaches further than its sources charges a price it does not name.
10.4 What this work is
A derivation with a cost accounting. Not a survey of the field, not a rehearsal of who found what. Every cell is traceable to a constraint, every constraint to an entry, and the account lies open beside those of the rivals. Year of death 4/3 BC is the cheapest reading, with the season of death as above. 5 BC is the most robust cell in a window that reaches to 6 BC; the season of birth is open.
It is no more than that. There is a cheapest chain with the rivals beside it, and a reproducible logigram. Whoever flips one constraint — the eclipse exclusion, the Luke 3:23 band, the Matthew edge — sees in `logigram.py` what happens to the outcome. That is the test this work leaves to its reader, and the only one it asks.
Herod dies in the spring of 4 BC; the winter of 4/3 remains possible but is less likely. The year of death 4/3 BC is the cheapest reading: across the 20 primary data, chain C rejects nothing and emends nothing; the one datum outside them that it sets aside, the 184th olympiad of AJ 14.389, every chain sets aside. The regnal figures 34 and 37 yield the year plainly, on every chain; only a choice of counting rule moves it off, and that choice is an entry on the account, not a datum.
The birth window that follows from this is 6-4 BC — a band of years, without a season, since the sweep reckons on the birth year and not on the month —, coinciding in run B-consistent for C, CA and HV. Within that window the cells are not equal. 5 BC is the most robust: it survives both seasons of death (spring 4 and winter 4/3), run A and run B, and baptism years 27 and 28. 6 BC stands at the early edge: it leans on one baptism year (only baptism in 27; at 28 the child is 33, outside the age band). That is reckoned in year cells. With the boundary of Tiberius' 15th year on 20 October 27 the baptism falls late in the autumn of 27 or in the winter of 27/28; in completed years 6 BC stands even with a winter baptism (§9.3). 4 BC is tight: it hangs on the winter scenario and on a birth shortly before the death — admitted, because the late Matthew edge is not hard. Most probable, therefore, is 5 BC, on robustness; within it Sukkot is HV's working expectation and not an outcome of the derivation. Not because 6 BC carries a demonstrable cost: it is not a dead cell, it is a cell that survives fewer constraints.
10.1 The cost of the alternatives
SY (death 1 BC, birth 3/2 BC) is the most expensive chain: three rejections and eight postulates, on the year-of-death side alone. Its patristic trump card — "virtually all early Christian authors" — dissolves on inspection into a reckoning tradition of at most two families; its census in 3/2 BC is attested nowhere. Whoever chooses SY buys an eclipse-valid year of death at the highest bill on the table.
CA (death 3/2 BC) is cheaper, but carries one rejection. Here too the regnal figures give 4/3; the last step to 3/2 comes from the antedating rule, not from a figure. Philip is the loss entry.
C itself is not free, only cheapest. Its inclusive counting rule is rejected by the same edition for the Hasmoneans and retained for Herod, and what licenses that asymmetry is the eclipse. That is no rejection and no emendation; it is a counting choice that belongs on the account and is entered there.
10.2 What does not carry the window
The window does not derive its firm core from the baptism and crucifixion axis. Run A, freestanding — without the AD 27 anchor and without Luke 3:23 — already gives 8-4 BC for C, CA and HV, with 8 as a postulate and 7 as a soft edge. Run B-consistent gives 6-4. The coupling removes the two softest cells — 8 (already a postulate) and 7 (which falls outside Plummer's age band 28-32); the firm core 6-5-4 stays on Matthew. The baptism axis (the Tiberius reckoning, Luke 3:23, the 69 weeks) is a defensible minority reading and not a refuted constraint; it trims the early edge but does not touch the core. Nor is the window forced by baptism in 27 alone: over baptism in 27, 28 and 29 together, C/CA/HV stays at 6-4. The early edge does hang on the band width: on Hoehner's ±3 it would run to 7, on Plummer's ±2 to 6 — this work adopts ±2. The earlier, narrower outcome "5 or 4 BC" rested on an imported floor — Hoehner's "no earlier than 5 B.C.", which hangs on baptism in 29 and not on Luke 3:23 — and has therefore been withdrawn.
Census, patristics and shemitah do not carry the window either. They are axes at zero: they kill no cell. What they do is remove props from under the rival chronologies.
10.3 Two open axes — themselves a result
The season of death stands as above: spring leads, the winter of 4/3 is not excluded. The travel clock excludes only a death immediately before Passover. The illness clock is a topos and does not keep time. The Ptolemy sweep prices Kushnir-Stein's block calculation, but does not break it. What separates the two is the day count from the eclipse to the Passover of AJ 17.213: 30 days under the spring, 414 under the winter. This hinge decides whether 4 BC takes part as a birth year; it stands open only for whoever detaches the eclipse from the chronology.
The season of birth is underdetermined. Sukkot and spring finish level on canonical typology; winter stands one step behind, carried by reception alone. No ancient source places the birth in Tishri. The feast is not a date: the choice of Tabernacles is a postulate, and that is how it is booked.
That both axes remain open is not a shortcoming of the derivation. It is a measurement: the sources reach this far and no further, and a work that reaches further than its sources charges a price it does not name.
10.4 What this work is
A derivation with a cost accounting. Not a survey of the field, not a rehearsal of who found what. Every cell is traceable to a constraint, every constraint to an entry, and the account lies open beside those of the rivals. Year of death 4/3 BC is the cheapest reading, with the season of death as above. 5 BC is the most robust cell in a window that reaches to 6 BC; the season of birth is open.
It is no more than that. There is a cheapest chain with the rivals beside it, and a reproducible logigram. Whoever flips one constraint — the eclipse exclusion, the Luke 3:23 band, the Matthew edge — sees in `logigram.py` what happens to the outcome. That is the test this work leaves to its reader, and the only one it asks.