Herod's year of death is overdetermined, his season of death underdetermined — and Jesus's season of birth even more so. Behind the fixed year 4/3 BC lie two orthogonal sub-axes. The season of death (spring 4 BC or winter 4/3 BC) determines the late edge of the birth window. The season of birth (Sukkot, spring or winter) chooses the month within the birth year and does not touch the edge. Both are weighed separately, with the same measure.
A cell — one season reading — survives if no primary datum in the dossier excludes it. Its price is the set of constraints it must drop, reject, emend or postulate; cheapest is the cell with the fewest postulated steps that, moreover, does not lean on a convention the chain does not independently defend elsewhere. Every cell gets four questions: does it survive, what does it cost, does it read the source correctly (with "presumably", "possibly" and square brackets weighed in), and which falsifier would break it. The symmetry is strict. The consensus gets no exemption, HV no extra hurdle, and testing more strictly because a finding serves HV is itself an asymmetry. The dossier held to that where it hurt: a price on winter 4/3 was withdrawn "not in favor of the tidy outcome", and the strictest test fell where the outcome helped HV.
6.1 The season of death: the constraints
Regnal years. The double figure 34/37, in BJ and AJ alike, allows nothing before 1 Nisan 4 BC. It excludes a death in the winter of 5/4; a death in the spring of 4 it leaves standing.
Antipas's year 43. RPC I 4934 places year 1 of the sons in 4/3 BC; the death falls before the summer of 4. January 1 BC drops out with this.
The eclipse. The only umbral lunar eclipse before Passover 4 BC is that of 13 March. Josephus gives four words, no magnitude and no duration; every evening or amplitude criterion is an addition to the source. Between Passover 4 BC and Passover 3 BC none is visible from Judaea at all: 5 September 4 BC falls in daylight, 31 January 3 BC below the horizon, and 2 March 3 BC is penumbral at 0.12, invisible to the naked eye. Josephus places the eclipse not at the death but on the night Matthias was burned; the death follows after the illness, Callirrhoe, the summons of the notables from all Judaea, the letter from Rome and the execution of Antipater.
The day count. From the eclipse to the Passover of AJ 17.213 the text counts only two things itself: four or five days from Antipater's execution to the death, and seven days of mourning. The other eleven events it names but does not count. On one measure fixed in advance — the physical minimum at stated travel rates, and ordinary travel with a day's stay where the text names a stay — the chain needs 22 to 57 days. Against that window: 13 March 4 BC to Passover 4 BC is 30 days (counted inclusively; 29 full, as casus-31 counts), inside; 13 March 4 BC to Passover 3 BC is 414 days, of which 357 Josephus does not narrate; 15 September 5 BC to Passover 4 BC is 208 (151 unnarrated); 10 January 1 BC to Passover 1 BC is 90 (33 unnarrated); 29 December 1 BC to Passover AD 1 is 91 (34 unnarrated), in the same slot. Every eclipse whose umbra could be seen counts, including one seen only at moonrise: the text sets no amplitude and no horizon criterion. The day count excludes nothing, since no interval falls below the floor, but it orders, and on its order the spring eclipse of 4 BC stands at the top. The upper edge is a judgement and not a measurement: whoever gives the unrest of 17.206-212 twenty days instead of ten brings 1 BC inside. The ten-week minimum argued for the 1 BC chronology, and Smallwood's verdict that 13 March "allows inadequate time", do not hold on this measure.
eclipse
to
days
unnarrated (above the 57)
13 March 4 BC
Passover 4 BC
30
— (inside the window)
13 March 4 BC
Passover 3 BC
414
357
15 September 5 BC
Passover 4 BC
208
151
10 January 1 BC
Passover 1 BC
90
33
29 December 1 BC
Passover AD 1
91
34
The travel clock. Kushnir-Stein excludes only a death immediately before Passover — on 1 Nisan her sequence is "plainly impossible". A death shortly after the eclipse, with about four weeks to Passover, survives; winter 4/3 survives just as well.
The illness clock — withdrawn. The syndrome Josephus ascribes to Herod is a retribution topos: Thucydidean in Ladouceur, borrowed in Africa, a literary type in Zeichmann. A topos does not clock. The step from "a clinical picture of weeks" to "so not 258 days" was a construal; once the topos reading was read primary, it was withdrawn. The 258-day price on winter 4/3 lapses; the clock is neutral.
The Ptolemy sweep. Block 2 of Kushnir-Stein — the strong, branch-excluding form of her travel constraint — identifies the Ptolemy whom Varus summons with the keeper of the seal. Josephus does not make that identification: he distinguishes at least two Ptolemies and does not mark this one. Kushnir-Stein herself calls the schedule "a calculation exempli gratia" — "a precise schedule cannot be worked out" — which weighs against the strong form of her own constraint, not against the weak. The automated sweep across both Greek texts puts a price on block 2 but does not break it.
The two-letters argument. One reply from Augustus settles both missions — a soft cost on winter 4/3.
Death era or investiture era. Winter 4/3 requires that the sons counted from the death; otherwise Antipas's year 43 falls after his deposition. The Nabataean counting rule supports the investiture era, not the death era. The premise stands in the dossier twice marked as "if his first year started on Nisan 1, 4 BC" — untested.
7 Kislev. Megillat Ta'anit points to the winter but does not choose the year: 7 December 5 BC or 26 November 4 BC. The scroll is silent on the reason; the scholion is post-Talmudic and swaps with 2 Shevat.
No second Adar in 4 BC. There is no calendar escape, for either season.
6.2 Four candidates, four accounts
Spring 4 BC — the consensus cell (C; CA shares it). It survives and places the death between the eclipse and Passover. Its price: it reads block 2 of the travel clock at zero or as a boat leg — the travel sequence requires 14 to 17 days after the eclipse, feasible by boat over the actual distance — and it hangs on a Nisan-inclusive reckoning. The block-2 reading is a construal, but the counter-premise (block 2 strong) itself rests on an unmarked identification; the price on spring 4 is lighter than it seemed and does not hang on a convention C does not carry elsewhere. There is no cheaper surviving cell. On the season of death HV goes with Schürer, but keeps the winter of 4/3 open as a less likely possibility; the consensus commits to the spring. Cameron shares the death in 4/3 BC; his antedating touches the year epoch, not the choice within the year. His positive case for a late birth year (3/2 BC) stands in the package only as a title and carries nothing here. On the day count it carries the eclipse without a further assumption: 30 days to Passover, inside the window, with the death about 1–3 April 4 BC.
Winter 4/3 BC — Kushnir-Stein, the survivor that carries HV's reservation. It survives, at a higher price than before. After the withdrawal of the illness clock it carries three costs. Two are soft and independent: the two-letters argument and the death era, a convention the chain nowhere else independently defends, while the Nabataean counting rule supports the investiture era. The third is heavy: with the only eclipse available, 13 March 4 BC, the chain of AJ 17.167-213 must run 414 days to the Passover of 3 BC, of which 357 are not narrated, while Josephus opens that Passover with κατὰ τόνδε τὸν καιρόν, "about this time". Winter 4/3 escapes that cost only if the eclipse note is detached from the chronology, as a literary element and not as a clock — a postulate the spring cell does not need. Spring 4 carries none of the three.
Winter 5/4 BC — Barnes (7 December 5 BC). It does not survive. The date lies before 1 Nisan 4 BC and collides with the regnal years; 7 Kislev is not "precise" and does not choose the year; the amplitude eclipse that would carry it is an addition to Josephus. In the field Barnes stands unanswered; in this dossier the cell is closed.
January 1 BC — SY. It does not survive, and that on four legs: Antipas's year 43, Barnes's unrefuted external checks, the Paneas era that cannot lie later than 2/1 BC, and the impossibility on Zuckermann's 36 BC while Wacholder himself holds 37. Steinmann and Young's non-inclusive Tishri convention does not carry the cell over these legs. A death in January AD 1, after the partial eclipse of 29 December 1 BC, falls a fortiori on three of these legs, and with it Mahieu's death on 9 March AD 1 (Mahieu 2012): Antipas's year 43 would fall in AD 43, four years after his deposition; the Paneas era cannot lie later than 2/1 BC; and Gaius, consul at Antioch on 1 January AD 1, cannot sit on Augustus's consilium after a death in AD 1. The eclipse does not kill that cell; these legs do.
The account. Two survivors, two excluded. Spring 4 BC is clearly the cheaper; winter 4/3 BC survives only with a detached eclipse. The travel clock excludes only the extreme, the illness clock is a topos, and the Ptolemy sweep prices block 2 without breaking it; what separates the two is the day count. It is not decided on the sources, for winter 4/3 falls only if the eclipse is read as a clock, and that is a reading, not a datum. But the hinge no longer leans by a hair, and HV therefore holds: spring 4 BC; the winter of 4/3 remains possible but is less likely. Under spring 4 the death falls about 1–3 April 4 BC.
death cell
bearer
outcome
the price
spring 4 BC
the consensus cell (C; CA shares it)
survives; the cheaper
block 2 of the travel clock at zero or as a boat leg; a Nisan-inclusive reckoning
winter 4/3 BC
Kushnir-Stein
survives, at a higher price
the two-letters argument and the death era (soft); 414 days to the Passover of 3 BC, of which 357 are not narrated (heavy), unless the eclipse is detached from the chronology
winter 5/4 BC
Barnes (7 December 5 BC)
does not survive
lies before 1 Nisan 4 BC and collides with the regnal years
January 1 BC
SY
does not survive
four legs: Antipas's year 43, Barnes's external checks, the Paneas era, Zuckermann's 36 BC
What the hinge does do is divide the late edge of the window. Under spring 4 that edge runs to 5 BC: every birth in 4 BC lies after the death. The table reckons with a baptism on 15 Tishri AD 27 (5 October). With the boundary of Tiberius' 15th year on 20 October 27 the baptism falls later, late in the autumn of 27 or in the winter of 27/28, and every age comes out at most 0.4 years higher. The ages are exact, in years and tenths. Reckoned exactly, 15 Tishri 6 BC (31.9) can then slide over the edge of the band; in completed years the later baptism changes no cell of the window, and in the year cells of run B only 6 BC, which drops out if a baptism in the winter counts as baptism 28 (§9.3). At a baptism on 15 Tishri AD 27 the ages are:
birth
before the death (about 3 April 4 BC)
age at baptism, Tishri AD 27
under a death in spring 4 BC
15 Nisan 6 BC
23.0 months
32.4
outside Plummer's band
15 Tishri 6 BC
17.1 months
31.9
at the edge of the band
15 Nisan 5 BC
11.4 months
31.5
ample
15 Tishri 5 BC
5.5 months
31.0
tight for magi, flight and massacre
15 Nisan 4 BC
after the death
30.5
falls
15 Tishri 4 BC
after the death
30.0
only under winter 4/3
The full 31 hangs on no season of death; the bare 30 hangs exclusively on the more expensive branch. Luke's ὡσεί carries 31 and 31½ without cost on the band this work adopts (28–32); only a reading "exactly thirty" puts a price of one year on it, and that reading is not in the text.
6.3 The season of birth: framing rule and constraints
Two rules come first and apply equally on all three sides. A typological convergence does not date, and a test that every hypothesis passes does not distinguish. And in Josephus's material the named feast is a crowd operator, not a dating operator: the feast is not a date. Whoever places a birth on a feast must therefore have something in hand other than the feast.
b. Rosh Hashanah 10b-11a. One baraita, three outcomes: Tishri with R. Eliezer, Nisan with R. Joshua, 25 December via Augustine's shift to the conception. A fork, not a verdict — and both Tannaim place Isaac at Passover.
The priestly courses. They do not choose: Sukkot 5 BC stands at +8.9 weeks, Passover 5 BC at +10.3, both within the chain's tolerance; the continuous model yields no Tishri outside 3 BC.
The comet. Ho no. 63 was in the sky on 22 April 5 BC on every reading of the Chinese month. It indicates a season under two unmeasured premises: that it is the star of Matthew, and that it marks the birth itself.
ἐν τῇ ἀνατολῇ. If the expression means the heliacal rising, the comet does not satisfy it. One of the two must yield.
The eighth day. Birth on 15 Tishri gives circumcision on 22 Tishri, Shemini Atzeret, the day that Lev 23:36 and 39 themselves sanctify as "the eighth"; 15 Nisan and 1 Tishri do not give that. It is a sum on the hypothesis, not an external datum, and the 40th day yields nothing from Sukkot (24/25 Cheshvan).
Ancient attestation. No source before the third century names a season of birth. Spring has the oldest calculated days (Clement's "others": 19/20 April, 20 May; De Pascha Computus of 243: 28 March), winter the oldest liturgical ones (Chronograph of 354; Epiphanius c. 375). Tishri has none at all.
Census and travel season. Beckwith names "August to October" — an autumn argument from the author the dossier took to be partial to December. It points away from the winter.
Deut 16:16. Lanser's pilgrimage bar: at all three pilgrimage feasts Joseph belongs in Jerusalem, not in Bethlehem (Lanser, "Pinpointing the Date of Christ's Birth", ABR 2019). It hits Sukkot and Passover alike; it is the only argument that places the winter above both feasts. Lanser's own road passes it to 1 Nisan, by the mishkan of Exod 40:2, 34, not by John 1:14 and Sukkot.
Exod 40:2 and 17. The prototype of the σκηνή of John 1:14 stands on 1 Nisan — against Sukkot.
Hippolytus, In Dan. IV.23. The winter date is absent in J and Georg, erased in A, and A carries an April date in square brackets; Bonwetsch: "doch dürften J und Georg die ursprüngliche Lesart darbieten".
6.4 Three seasons, three accounts
Sukkot — HV's working expectation. It survives; nothing excludes it. The courses do not choose, the comet costs it at most a year, the window admits it, and the travel season of the census points its way. Its price is of one kind: typology, plus one sum (the eighth day). Against that stands the heaviest item of the whole triptych: zero ancient attestation. Clement, the Chronograph and Epiphanius independently confirm the same silence about an autumn day, and there is no academic defender. The chief witness from the Talmud cuts both ways, with Isaac at Passover on the other side. Its own seven-feasts grid places Sukkot at the consummation, not at the beginning — a tension the cell's advocate himself names as "the outcome steers the premise". The prototype of the tent stands on 1 Nisan. Luke nowhere names Sukkot. Deut 16:16 has not been removed. On the third question: the convergence Tishri 457, baptism Tishri AD 27, Sukkot birth (the baptism itself, under the boundary of Tiberius' 15th year, 20 October 27, falls later: late in the autumn of 27 or in the winter of 27/28) is "one autumn preference applied three times, not three witnesses", and the eighth day is a sum that recovers its own premise.
At the early edge Sukkot 7 BC is under pressure: Smallwood's own paragraph excludes it on all four death scenarios. In Maier, Tabernacles does not appear as a birth candidate; in Smallwood, the season of birth does not appear at all.
Spring. It survives. It holds the strongest non-typological leg of the triptych, the comet, and it carries canon typology. Its price: no heliacal rising, a head-on collision with the public technical reading of the expression. Humphreys's ministry chronology (baptism AD 29, crucifixion AD 33) stands against that of the companion volume (Visser, 2026a: baptism after 20 October AD 27, crucifixion 25 April AD 31). The census leg is gone; the courses stand at 10.3 weeks; the 40-day chain closes only if the comet was first seen late in the Chinese month; Clement's own year is 3/2 BC, outside the window. The silent assumption is that the comet is the star and marks the birth itself — not measured. And under the two-year clause of Matthew 2:16 the comet is compatible with every season of 6 BC: it chooses nothing and leaves Sukkot 6 BC standing.
Winter — in its strongest form 6 January, not 25 December. It survives as an admitted candidate. Its price: no witness before the third century, everything reception and calculation. Hippolytus is text-critically eroded. Clement does not name the date, and the vague-years reading that makes him say 6 January goes against the official Alexandrian calendar — without that assumption, 18 November remains. The Koreion, "the Virgin has borne the Aiōn" on 6 January, comes from the mouth of its own chief witness, Epiphanius. The census points to August–October; 25 December and 6 January exclude each other; the oldest calculated birthday, that of 243, is a spring day. On the third question: the vague-years assumption is the convention on which the whole 6 January card stands, and it is not independently defended; its only independent check, the April Passover hit, lands in AD 29 — a crucifixion year that volume rejects. Beckwith links 25 December to the solstice only "possibly"; in the chief witness himself that explanation stands conditional. Sukkot and spring draw their figure from the canon, winter only from reception — the weakest typological density.
birth season
outcome
what carries it
its price
Sukkot
survives; HV's working expectation
typology; nothing excludes it, and the travel season of the census points its way
zero ancient attestation; the eighth day is a sum on the hypothesis
spring
survives
the comet, the strongest non-typological leg, and canon typology
no heliacal rising; a head-on collision with the public technical reading
winter (6 January)
survives as an admitted candidate
reception and calculation only
no witness before the third century
6.5 The account — and the chains
On the fixed measure no season has been measured. All three are admitted, unmeasured candidates. If a ranking by typological density is forced — and that is no finding — then Sukkot and spring end level at the top, both with canon typology, spring with one conditional non-typological piece added and Sukkot with the census construal; winter stays one step behind, with reception only. By postulates, none of the three dates. Sukkot survives only as a working expectation on figure. Its heaviest outstanding price is thereby fixed: no ancient source whatever places the birth in Tishri, and its chief witness cuts both ways.
The chains yield no independent season of birth. C, SY and CA differ on the birth year and the counting rule, not on the month; the season is orthogonal and underdetermined for all three. The late year of SY and CA (3/2 BC) leans, via Matthew 2, on the death in January 1 BC, and that sub-axis is closed. Their implicit winter 3/2 cell falls with its year, not with its season.
6.6 What would break the cells
Sukkot falls if 9/10 Av AD 70 is fixed and the rotational continuity of the priestly courses over 78 years is demonstrated: then the course month becomes determinately Kislev or Cheshvan, not Tishri. That falsifier has half sprung. The anchor closed on Sabbath 4 August AD 70, with zero weeks of tolerance; the rotation over 78 years remains unclosable. In principle open, in practice inert — and were it to spring, then against Sukkot and Passover alike.
Spring falls if a 干支 day-date places the first observation of the comet between 10 and 23 March 5 BC: then the Passover form falls. Open.
Winter falls if Clement's two intervals (194 y 1 m 13 d and 163 y 9 m 24 d) cannot be held under one year-length. Open; the Greek of Strom. 1.21 has been seen by none of the three advocates — the most important shared item.
The season of death now has a falsifier, and it lies on the upper edge of the day count (§6.1). That edge is a judgement: a source that gives the unrest of AJ 17.206-212, or any other uncounted link of the chain, a duration of weeks would bring the longer intervals inside the window and return the hinge to a hair. In the other direction, winter 4/3 falls outright if the eclipse note of 17.167 is shown to come from the chronological source Josephus follows rather than to be his literary addition. The Rome letter as a second clock has never been investigated.
6.7 What the season yields
The account of the two sub-axes together: the season of death is spring 4 BC; the winter of 4/3 remains possible but is less likely, for it survives only with a detached eclipse. The season of birth is underdetermined, with Sukkot and spring level on canon typology and winter a step behind — none of the three writable as a finding. That is the outcome, not the absence of one. The sources say less about the month than about the year, and a method that counts the price can only report that difference, not remove it.
What the seasons do do is color the edge of the window. Sukkot 5 BC hangs on no season of death and is robust across both survivors; Sukkot 4 BC hangs exclusively on winter 4/3, the more expensive branch; Sukkot 7 BC falls outside run B on Plummer's age band (§9.2) and moreover stands under Smallwood's pressure. The window itself — 6–4 BC, a band of years without a season — is not fixed on this axis but on the Matthew axis and the baptism axis (chapters 4, 8 and 9); the season of death colors only the late edge. On that edge 5 BC is the most probable — on robustness, not on a lower price. Whoever wants to keep the late edge at 4 BC buys the more expensive season of death for it; whoever takes 5 BC buys nothing.
Herod's year of death is overdetermined, his season of death underdetermined — and Jesus's season of birth even more so. Behind the fixed year 4/3 BC lie two orthogonal sub-axes. The season of death (spring 4 BC or winter 4/3 BC) determines the late edge of the birth window. The season of birth (Sukkot, spring or winter) chooses the month within the birth year and does not touch the edge. Both are weighed separately, with the same measure.
A cell — one season reading — survives if no primary datum in the dossier excludes it. Its price is the set of constraints it must drop, reject, emend or postulate; cheapest is the cell with the fewest postulated steps that, moreover, does not lean on a convention the chain does not independently defend elsewhere. Every cell gets four questions: does it survive, what does it cost, does it read the source correctly (with "presumably", "possibly" and square brackets weighed in), and which falsifier would break it. The symmetry is strict. The consensus gets no exemption, HV no extra hurdle, and testing more strictly because a finding serves HV is itself an asymmetry. The dossier held to that where it hurt: a price on winter 4/3 was withdrawn "not in favor of the tidy outcome", and the strictest test fell where the outcome helped HV.
6.1 The season of death: the constraints
Regnal years. The double figure 34/37, in BJ and AJ alike, allows nothing before 1 Nisan 4 BC. It excludes a death in the winter of 5/4; a death in the spring of 4 it leaves standing.
Antipas's year 43. RPC I 4934 places year 1 of the sons in 4/3 BC; the death falls before the summer of 4. January 1 BC drops out with this.
The eclipse. The only umbral lunar eclipse before Passover 4 BC is that of 13 March. Josephus gives four words, no magnitude and no duration; every evening or amplitude criterion is an addition to the source. Between Passover 4 BC and Passover 3 BC none is visible from Judaea at all: 5 September 4 BC falls in daylight, 31 January 3 BC below the horizon, and 2 March 3 BC is penumbral at 0.12, invisible to the naked eye. Josephus places the eclipse not at the death but on the night Matthias was burned; the death follows after the illness, Callirrhoe, the summons of the notables from all Judaea, the letter from Rome and the execution of Antipater.
The day count. From the eclipse to the Passover of AJ 17.213 the text counts only two things itself: four or five days from Antipater's execution to the death, and seven days of mourning. The other eleven events it names but does not count. On one measure fixed in advance — the physical minimum at stated travel rates, and ordinary travel with a day's stay where the text names a stay — the chain needs 22 to 57 days. Against that window: 13 March 4 BC to Passover 4 BC is 30 days (counted inclusively; 29 full, as casus-31 counts), inside; 13 March 4 BC to Passover 3 BC is 414 days, of which 357 Josephus does not narrate; 15 September 5 BC to Passover 4 BC is 208 (151 unnarrated); 10 January 1 BC to Passover 1 BC is 90 (33 unnarrated); 29 December 1 BC to Passover AD 1 is 91 (34 unnarrated), in the same slot. Every eclipse whose umbra could be seen counts, including one seen only at moonrise: the text sets no amplitude and no horizon criterion. The day count excludes nothing, since no interval falls below the floor, but it orders, and on its order the spring eclipse of 4 BC stands at the top. The upper edge is a judgement and not a measurement: whoever gives the unrest of 17.206-212 twenty days instead of ten brings 1 BC inside. The ten-week minimum argued for the 1 BC chronology, and Smallwood's verdict that 13 March "allows inadequate time", do not hold on this measure.
The travel clock. Kushnir-Stein excludes only a death immediately before Passover — on 1 Nisan her sequence is "plainly impossible". A death shortly after the eclipse, with about four weeks to Passover, survives; winter 4/3 survives just as well.
The illness clock — withdrawn. The syndrome Josephus ascribes to Herod is a retribution topos: Thucydidean in Ladouceur, borrowed in Africa, a literary type in Zeichmann. A topos does not clock. The step from "a clinical picture of weeks" to "so not 258 days" was a construal; once the topos reading was read primary, it was withdrawn. The 258-day price on winter 4/3 lapses; the clock is neutral.
The Ptolemy sweep. Block 2 of Kushnir-Stein — the strong, branch-excluding form of her travel constraint — identifies the Ptolemy whom Varus summons with the keeper of the seal. Josephus does not make that identification: he distinguishes at least two Ptolemies and does not mark this one. Kushnir-Stein herself calls the schedule "a calculation exempli gratia" — "a precise schedule cannot be worked out" — which weighs against the strong form of her own constraint, not against the weak. The automated sweep across both Greek texts puts a price on block 2 but does not break it.
The two-letters argument. One reply from Augustus settles both missions — a soft cost on winter 4/3.
Death era or investiture era. Winter 4/3 requires that the sons counted from the death; otherwise Antipas's year 43 falls after his deposition. The Nabataean counting rule supports the investiture era, not the death era. The premise stands in the dossier twice marked as "if his first year started on Nisan 1, 4 BC" — untested.
7 Kislev. Megillat Ta'anit points to the winter but does not choose the year: 7 December 5 BC or 26 November 4 BC. The scroll is silent on the reason; the scholion is post-Talmudic and swaps with 2 Shevat.
No second Adar in 4 BC. There is no calendar escape, for either season.
6.2 Four candidates, four accounts
Spring 4 BC — the consensus cell (C; CA shares it). It survives and places the death between the eclipse and Passover. Its price: it reads block 2 of the travel clock at zero or as a boat leg — the travel sequence requires 14 to 17 days after the eclipse, feasible by boat over the actual distance — and it hangs on a Nisan-inclusive reckoning. The block-2 reading is a construal, but the counter-premise (block 2 strong) itself rests on an unmarked identification; the price on spring 4 is lighter than it seemed and does not hang on a convention C does not carry elsewhere. There is no cheaper surviving cell. On the season of death HV goes with Schürer, but keeps the winter of 4/3 open as a less likely possibility; the consensus commits to the spring. Cameron shares the death in 4/3 BC; his antedating touches the year epoch, not the choice within the year. His positive case for a late birth year (3/2 BC) stands in the package only as a title and carries nothing here. On the day count it carries the eclipse without a further assumption: 30 days to Passover, inside the window, with the death about 1–3 April 4 BC.
Winter 4/3 BC — Kushnir-Stein, the survivor that carries HV's reservation. It survives, at a higher price than before. After the withdrawal of the illness clock it carries three costs. Two are soft and independent: the two-letters argument and the death era, a convention the chain nowhere else independently defends, while the Nabataean counting rule supports the investiture era. The third is heavy: with the only eclipse available, 13 March 4 BC, the chain of AJ 17.167-213 must run 414 days to the Passover of 3 BC, of which 357 are not narrated, while Josephus opens that Passover with κατὰ τόνδε τὸν καιρόν, "about this time". Winter 4/3 escapes that cost only if the eclipse note is detached from the chronology, as a literary element and not as a clock — a postulate the spring cell does not need. Spring 4 carries none of the three.
Winter 5/4 BC — Barnes (7 December 5 BC). It does not survive. The date lies before 1 Nisan 4 BC and collides with the regnal years; 7 Kislev is not "precise" and does not choose the year; the amplitude eclipse that would carry it is an addition to Josephus. In the field Barnes stands unanswered; in this dossier the cell is closed.
January 1 BC — SY. It does not survive, and that on four legs: Antipas's year 43, Barnes's unrefuted external checks, the Paneas era that cannot lie later than 2/1 BC, and the impossibility on Zuckermann's 36 BC while Wacholder himself holds 37. Steinmann and Young's non-inclusive Tishri convention does not carry the cell over these legs. A death in January AD 1, after the partial eclipse of 29 December 1 BC, falls a fortiori on three of these legs, and with it Mahieu's death on 9 March AD 1 (Mahieu 2012): Antipas's year 43 would fall in AD 43, four years after his deposition; the Paneas era cannot lie later than 2/1 BC; and Gaius, consul at Antioch on 1 January AD 1, cannot sit on Augustus's consilium after a death in AD 1. The eclipse does not kill that cell; these legs do.
The account. Two survivors, two excluded. Spring 4 BC is clearly the cheaper; winter 4/3 BC survives only with a detached eclipse. The travel clock excludes only the extreme, the illness clock is a topos, and the Ptolemy sweep prices block 2 without breaking it; what separates the two is the day count. It is not decided on the sources, for winter 4/3 falls only if the eclipse is read as a clock, and that is a reading, not a datum. But the hinge no longer leans by a hair, and HV therefore holds: spring 4 BC; the winter of 4/3 remains possible but is less likely. Under spring 4 the death falls about 1–3 April 4 BC.
What the hinge does do is divide the late edge of the window. Under spring 4 that edge runs to 5 BC: every birth in 4 BC lies after the death. The table reckons with a baptism on 15 Tishri AD 27 (5 October). With the boundary of Tiberius' 15th year on 20 October 27 the baptism falls later, late in the autumn of 27 or in the winter of 27/28, and every age comes out at most 0.4 years higher. The ages are exact, in years and tenths. Reckoned exactly, 15 Tishri 6 BC (31.9) can then slide over the edge of the band; in completed years the later baptism changes no cell of the window, and in the year cells of run B only 6 BC, which drops out if a baptism in the winter counts as baptism 28 (§9.3). At a baptism on 15 Tishri AD 27 the ages are:
The full 31 hangs on no season of death; the bare 30 hangs exclusively on the more expensive branch. Luke's ὡσεί carries 31 and 31½ without cost on the band this work adopts (28–32); only a reading "exactly thirty" puts a price of one year on it, and that reading is not in the text.
6.3 The season of birth: framing rule and constraints
Two rules come first and apply equally on all three sides. A typological convergence does not date, and a test that every hypothesis passes does not distinguish. And in Josephus's material the named feast is a crowd operator, not a dating operator: the feast is not a date. Whoever places a birth on a feast must therefore have something in hand other than the feast.
b. Rosh Hashanah 10b-11a. One baraita, three outcomes: Tishri with R. Eliezer, Nisan with R. Joshua, 25 December via Augustine's shift to the conception. A fork, not a verdict — and both Tannaim place Isaac at Passover.
The priestly courses. They do not choose: Sukkot 5 BC stands at +8.9 weeks, Passover 5 BC at +10.3, both within the chain's tolerance; the continuous model yields no Tishri outside 3 BC.
The comet. Ho no. 63 was in the sky on 22 April 5 BC on every reading of the Chinese month. It indicates a season under two unmeasured premises: that it is the star of Matthew, and that it marks the birth itself.
ἐν τῇ ἀνατολῇ. If the expression means the heliacal rising, the comet does not satisfy it. One of the two must yield.
The eighth day. Birth on 15 Tishri gives circumcision on 22 Tishri, Shemini Atzeret, the day that Lev 23:36 and 39 themselves sanctify as "the eighth"; 15 Nisan and 1 Tishri do not give that. It is a sum on the hypothesis, not an external datum, and the 40th day yields nothing from Sukkot (24/25 Cheshvan).
Ancient attestation. No source before the third century names a season of birth. Spring has the oldest calculated days (Clement's "others": 19/20 April, 20 May; De Pascha Computus of 243: 28 March), winter the oldest liturgical ones (Chronograph of 354; Epiphanius c. 375). Tishri has none at all.
Census and travel season. Beckwith names "August to October" — an autumn argument from the author the dossier took to be partial to December. It points away from the winter.
Deut 16:16. Lanser's pilgrimage bar: at all three pilgrimage feasts Joseph belongs in Jerusalem, not in Bethlehem (Lanser, "Pinpointing the Date of Christ's Birth", ABR 2019). It hits Sukkot and Passover alike; it is the only argument that places the winter above both feasts. Lanser's own road passes it to 1 Nisan, by the mishkan of Exod 40:2, 34, not by John 1:14 and Sukkot.
Exod 40:2 and 17. The prototype of the σκηνή of John 1:14 stands on 1 Nisan — against Sukkot.
Hippolytus, In Dan. IV.23. The winter date is absent in J and Georg, erased in A, and A carries an April date in square brackets; Bonwetsch: "doch dürften J und Georg die ursprüngliche Lesart darbieten".
6.4 Three seasons, three accounts
Sukkot — HV's working expectation. It survives; nothing excludes it. The courses do not choose, the comet costs it at most a year, the window admits it, and the travel season of the census points its way. Its price is of one kind: typology, plus one sum (the eighth day). Against that stands the heaviest item of the whole triptych: zero ancient attestation. Clement, the Chronograph and Epiphanius independently confirm the same silence about an autumn day, and there is no academic defender. The chief witness from the Talmud cuts both ways, with Isaac at Passover on the other side. Its own seven-feasts grid places Sukkot at the consummation, not at the beginning — a tension the cell's advocate himself names as "the outcome steers the premise". The prototype of the tent stands on 1 Nisan. Luke nowhere names Sukkot. Deut 16:16 has not been removed. On the third question: the convergence Tishri 457, baptism Tishri AD 27, Sukkot birth (the baptism itself, under the boundary of Tiberius' 15th year, 20 October 27, falls later: late in the autumn of 27 or in the winter of 27/28) is "one autumn preference applied three times, not three witnesses", and the eighth day is a sum that recovers its own premise.
At the early edge Sukkot 7 BC is under pressure: Smallwood's own paragraph excludes it on all four death scenarios. In Maier, Tabernacles does not appear as a birth candidate; in Smallwood, the season of birth does not appear at all.
Spring. It survives. It holds the strongest non-typological leg of the triptych, the comet, and it carries canon typology. Its price: no heliacal rising, a head-on collision with the public technical reading of the expression. Humphreys's ministry chronology (baptism AD 29, crucifixion AD 33) stands against that of the companion volume (Visser, 2026a: baptism after 20 October AD 27, crucifixion 25 April AD 31). The census leg is gone; the courses stand at 10.3 weeks; the 40-day chain closes only if the comet was first seen late in the Chinese month; Clement's own year is 3/2 BC, outside the window. The silent assumption is that the comet is the star and marks the birth itself — not measured. And under the two-year clause of Matthew 2:16 the comet is compatible with every season of 6 BC: it chooses nothing and leaves Sukkot 6 BC standing.
Winter — in its strongest form 6 January, not 25 December. It survives as an admitted candidate. Its price: no witness before the third century, everything reception and calculation. Hippolytus is text-critically eroded. Clement does not name the date, and the vague-years reading that makes him say 6 January goes against the official Alexandrian calendar — without that assumption, 18 November remains. The Koreion, "the Virgin has borne the Aiōn" on 6 January, comes from the mouth of its own chief witness, Epiphanius. The census points to August–October; 25 December and 6 January exclude each other; the oldest calculated birthday, that of 243, is a spring day. On the third question: the vague-years assumption is the convention on which the whole 6 January card stands, and it is not independently defended; its only independent check, the April Passover hit, lands in AD 29 — a crucifixion year that volume rejects. Beckwith links 25 December to the solstice only "possibly"; in the chief witness himself that explanation stands conditional. Sukkot and spring draw their figure from the canon, winter only from reception — the weakest typological density.
6.5 The account — and the chains
On the fixed measure no season has been measured. All three are admitted, unmeasured candidates. If a ranking by typological density is forced — and that is no finding — then Sukkot and spring end level at the top, both with canon typology, spring with one conditional non-typological piece added and Sukkot with the census construal; winter stays one step behind, with reception only. By postulates, none of the three dates. Sukkot survives only as a working expectation on figure. Its heaviest outstanding price is thereby fixed: no ancient source whatever places the birth in Tishri, and its chief witness cuts both ways.
The chains yield no independent season of birth. C, SY and CA differ on the birth year and the counting rule, not on the month; the season is orthogonal and underdetermined for all three. The late year of SY and CA (3/2 BC) leans, via Matthew 2, on the death in January 1 BC, and that sub-axis is closed. Their implicit winter 3/2 cell falls with its year, not with its season.
6.6 What would break the cells
Sukkot falls if 9/10 Av AD 70 is fixed and the rotational continuity of the priestly courses over 78 years is demonstrated: then the course month becomes determinately Kislev or Cheshvan, not Tishri. That falsifier has half sprung. The anchor closed on Sabbath 4 August AD 70, with zero weeks of tolerance; the rotation over 78 years remains unclosable. In principle open, in practice inert — and were it to spring, then against Sukkot and Passover alike.
Spring falls if a 干支 day-date places the first observation of the comet between 10 and 23 March 5 BC: then the Passover form falls. Open.
Winter falls if Clement's two intervals (194 y 1 m 13 d and 163 y 9 m 24 d) cannot be held under one year-length. Open; the Greek of Strom. 1.21 has been seen by none of the three advocates — the most important shared item.
The season of death now has a falsifier, and it lies on the upper edge of the day count (§6.1). That edge is a judgement: a source that gives the unrest of AJ 17.206-212, or any other uncounted link of the chain, a duration of weeks would bring the longer intervals inside the window and return the hinge to a hair. In the other direction, winter 4/3 falls outright if the eclipse note of 17.167 is shown to come from the chronological source Josephus follows rather than to be his literary addition. The Rome letter as a second clock has never been investigated.
6.7 What the season yields
The account of the two sub-axes together: the season of death is spring 4 BC; the winter of 4/3 remains possible but is less likely, for it survives only with a detached eclipse. The season of birth is underdetermined, with Sukkot and spring level on canon typology and winter a step behind — none of the three writable as a finding. That is the outcome, not the absence of one. The sources say less about the month than about the year, and a method that counts the price can only report that difference, not remove it.
What the seasons do do is color the edge of the window. Sukkot 5 BC hangs on no season of death and is robust across both survivors; Sukkot 4 BC hangs exclusively on winter 4/3, the more expensive branch; Sukkot 7 BC falls outside run B on Plummer's age band (§9.2) and moreover stands under Smallwood's pressure. The window itself — 6–4 BC, a band of years without a season — is not fixed on this axis but on the Matthew axis and the baptism axis (chapters 4, 8 and 9); the season of death colors only the late edge. On that edge 5 BC is the most probable — on robustness, not on a lower price. Whoever wants to keep the late edge at 4 BC buys the more expensive season of death for it; whoever takes 5 BC buys nothing.