The constraints on Herod's life, and the cost accounting of the three chains
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In-depth:
Herod's year of death hangs on a small number of primary constraints, each of which cuts off part of the variable space, and on two regnal figures that point to the year within it. The three chains read the same constraints; they differ in which ones they leave standing plainly and which ones they neutralize by a counting convention, a postulate or a rejection. That difference is the cost accounting, and its outcome is not a chain but a figure.
3.1 The constraints
The eclipse.AJ 17.167 places a lunar eclipse shortly before the death. It cuts hard: only 5, 4 and 1 BC have an umbral eclipse visible from Jerusalem — 1 BC twice, total on 10 January and partial (0.57) on 29 December, the latter visible for about an hour at moonrise; 7, 6, 3 and 2 BC have none. It leaves 4 BC (C) and 1 BC (SY) alive and kills 3/2 BC: the cell of Cameron's antedating, and the cell on which six of the eight knob combinations land (3.2).
The regnal figures. Josephus gives Herod 37 regnal years from the Roman investiture and 34 from the capture of Jerusalem. This is the calculator of every chain. Counted plainly from the consensus anchors 40 and 37 BC, both figures yield 4/3 BC; Cameron too reckons this way, up to his last step. That 37 from 40/39 and 34 from 37/36 come out at the same year is presented as "double confirmation". It is empty: the two anchors lie exactly three Nisan years apart and the two figures differ by exactly three, so that every pair (n from Y; n−3 from Y+3) coincides, whatever n one fills in — with Schürer just as neatly, one year earlier.
The anchors: AJ 14.389 and 14.487. The investiture is set on the consuls of 40 BC. The capture is set on the consuls of 37 BC, on the 185th Olympiad and on "27 years after Pompey, on the same day". That last specification is the sharpest constraint on the counting rule. With two identical calendar dates there is no part-year that can count as a full year; the Mishnaic form of the inclusive convention — "portions of a year as full years" — does not take hold here, and what remains is endpoint counting, which does not let the 27 years close on the consuls of 37. The consensus edition names the way out itself: "Josephus made a mistake in calculation [...] twenty-seven instead of twenty-six".
The shemitah: AJ 14.475. A sabbatical year fell during the siege. Which year, hangs on the calendar: on Zuckermann the sabbatical year encloses the siege of 37; on Wacholder it runs from Tishri 37 to Tishri 36, so that a siege in Sivan 36 falls within it and a siege in Sivan 37 does not. SVM sides with Wacholder — "the year 37 B.C. (Oct.)–36 B.C. [...] was sabbatical" — and calls the passage "a considerable difficulty".
The coin gaps and the sons. No coins of Antipas and Philip from regnal years 1, 2 and 3 are known. AJ 18.106 gives Philip 37 regnal years and has him die in Tiberius's 20th year. The civic era of Caesarea Paneas — Cameron reads "year 220" as an era beginning in 3/2 or 2/1 BC — has not been independently measured. These data carry the two antedating theses: SY has the sons count from the Tishri year 6 BC; Cameron assigns the transition year to the successor.
3.2 Four knobs, eight combinations
Every chain sets four knobs: investiture year, capture year, counting rule and year-beginning.
investiture
capture
counting rule
year-beginning
year of death
C (Schürer/SVM; HV on these four)
40 BC
37 BC
inclusive
Nisan
4/3 BC
SY (Steinmann & Young)
39
36
non-inclusive, "except when an ordinal number is used"
Tishri
January 1 BC
CA (Cameron 2018)
40/39 implicit
37, Tishri
antedating
Nisan, varying
4/3 → winter 3/2
The eight combinations of investiture year, counting rule and year-beginning have been computed mechanically. Exactly two reach January 1 BC, both with investiture 39 and non-inclusive reckoning; the year-beginning is indifferent for that endpoint. Exactly one reaches the spring of 4 BC: 40, inclusive, Nisan. One more, 40, inclusive, Tishri, is the winter branch 4/3, Tishri 4 to Tishri 3 BC (§6). The remaining four land in 3 or 2 BC, where the eclipse kills them. The consensus cell thus stands on one of eight combinations, the SY cell on two. On robustness that argues for SY and against C, and it belongs up front because it runs against the outcome of this chapter.
From this it follows directly: the year-beginning bears the year of death on no chain. Nisan or Tishri decides only where the seasonal boundary falls within the year. Whoever presents the year-beginning as a load-bearing knob presents it wrongly.
3.3 Chain C
Revised profile: 11 L · 5 T · 3 P · 0 V · 0 E · 3 U. Zero rejections, zero emendations: C nowhere declares a datum erroneous and nowhere alters the text. The cheapest profile, but not without a price.
Three anomalies. The shemitah of AJ 14.475, which its own edition concedes on Wacholder and leaves unexplained; on Zuckermann C would read it plainly, but then it stands against its own edition. The coin gap of years 1–3 of Antipas and Philip, for which C has no explanation. And the 13 days between eclipse and Passover on a Nisan count, which Kushnir-Stein calls "plainly impossible"; the constraint can be made more expensive, not lifted.
One expensive counting entry.AJ 14.487 is booked as T, but the edition itself sets the rejection beside it ("twenty-seven instead of twenty-six"). Booked T, V defensible.
Three postulates. The siege month (τῷ τρίτῳ μηνί), which requires two unnamed starting points; the "15th year" of BJ 1.401 for the temple building, "either incorrect or refers to the start of building preparations"; and the inclusive count of Tiberius's years, against which positive measurements stand (3.6).
The heaviest constraint. The inclusive counting rule is the only knob the consensus does not defend independently. SVM 2014 rejects inclusive reckoning in Josephus for the Hasmoneans and retains it for Herod, on one ground. Cameron identifies the passages: the edition has "rightly rejected the notion of inclusive reckoning by Josephus for the Hasmonean era (vol. 1, p. 200-201, n. 1), but maintains the original argument concerning the reign of Herod (p. 326-327, n. 165)", and it "acknowledges that the stated lengths for Herod's reign suggest that he died in 3 BCE, but he then falls back on [...] inclusive reckoning necessitated by the 4 BCE eclipse". The counting rule is thus not derived from Josephus's practice but licensed by the eclipse, and the same move licenses the spring of 4 BC. An internal inconsistency, identifiable in the source.
What lowers the constraint. That the counting rule is not derived from Josephus's practice is itself a claim, and Josephus's practice is measurable. Three places count the begun year as a full year. AJ 15.121 and BJ 1.370 put the battle of Actium (September 31 BC) and the earthquake of the spring before it "in the seventh year" of Herod's reign: from the capture of 37 BC, 31/30 is the seventh year only if 37/36 is the first, for counted by anniversaries the spring of 31 falls in the sixth. AJ 18.26 places the registration of AD 6 "in the thirty-seventh year after Actium", and those are 36 elapsed years. And AJ 20.250 counts 107 years from Herod to the fall of the temple, where 70 from 37 BC gives 106; non-inclusively the starting point would be 38 BC, too early for the deposition of Antigonus. The first two have been seen at primary level, the last two via Bernegger; at gate 5 those two carry for now as citation, not as measurement. What it does, on the same measure as the constraint itself. Internal logic: the step from three places to AJ 17.191 is an inference, and Bernegger himself says that Josephus does not count the same way everywhere; the constraint thus does not vanish, it drops: the inclusive counting rule has a practice behind it and not only the eclipse, and the edition's inconsistency remains an inconsistency of the edition, not of the source. External coherence: Actium in the seventh year fits Cameron's calendar years with 37/36 as year 1 just as well as C, and collides with SY, for whom 36 is the first year and Actium falls in the fifth or sixth; SY catches the two ordinals with its exception, but the 107 of AJ 20.250 is a cardinal number, and that its rule reckons non-inclusively. For CA it cuts the other way: whoever reads 107 as 106 plus one must say why the 34 of AJ 17.191 is not also 33 plus one, with the death in the 34th year, 4/3, and not after it. Correct reading: "in the seventh year" and "in the thirty-seventh year" are there; the "first year" from which they count is read into them, on every side. Falsifier: the Greek text of 18.26 and 20.250 itself; if the figure differs there, only Actium remains of the three. The finding falls in HV's favor and therefore receives no stricter and no milder test than the constraint it lowers.
The cell "4/3 BC", finally, conceals two positions: Schürer's death on 1–14 Nisan and Kushnir-Stein's death in the winter of 4/3. On the season of death HV, after the weighing of §6, comes out with SVM, with a reservation SVM does not make: spring 4 BC; the winter of 4/3 remains possible but is less likely.
3.4 Chain SY
Revised profile: 10 L · 2 T · 7 P · 3 V · 0 E · 0 U. Zero anomalies — SY leaves nothing standing unexplained — but three rejections and seven postulates against zero rejections with C.
Three rejections. The consuls of 40 BC ("the consensus date for this event must be in error"), the consuls of 37 and the 185th Olympiad ("Josephus gives a consular year and an Olympiad that correspond to 37 BC, but this is contradicted [...]").
Seven postulates, six on one knob. The antedating of the sons bears six data from the chronology of the sons, the coin gap among them; SY pays for that once, not six times, but that one knob must bear six data is itself the objection. The siege month and BJ 1.401 are added to that on postulates of their own.
The counting rule carries an exception. Non-inclusive, "except when an ordinal number is used"; without that exception their own argument from Herod's "third year" collapses.
The antedating has no event. The knob was born on a single page to accommodate Julias and Paneas — "we may surmise that Philip, like his brothers, post-dated his reign from 4 BCE" — and was then shifted in four published steps from 4 to 6 BC (Tishri years). The epoch year itself is not a free parameter: it follows from three lines (Archelaus AD 5, Antipas AD 38, Philip AD 14, all as Tishri years). But the event is entirely free; the only condition S&Y impose is the one-sided inequality t(event) < t(death). Their own counting choice moreover enlarges the backdating (four years instead of three). Neither of the two passages they name as the event survives the Greek text: BJ 1.461 concerns Antipater, Alexander and Aristobulus, around 12 BC, and S&Y themselves date the passage "before the trials", which excludes their own epoch year; BJ 1.573 / AJ 17.53 names not Philip but "Ἡρώδης ὁ ἐκ Μαριάμμης", so that the only motive for Philip's backdating rests on a mistaken identity. The epoch hangs in the air. The Herodian precedent helps halfway: counting from before actual power is standard (Herod's own era of 40 BC), but every attested era begins with a Roman act; an era at a private event is nowhere attested, and precisely that is what the thesis needs.
A cheaper cell it must reject. Their strongest argument rests on AJ 14.487, but that constraint has a way out that makes their rejection of consuls and Olympiad superfluous: Cameron keeps consuls, Olympiad and the 27 years exact and pays on one different consular year for Pompey. Non-inclusive reckoning therefore does not force 36 BC.
What only SY explains. The shemitah on Wacholder encloses their siege of 36; three months between eclipse and Passover replace the 13 days; the coin gap becomes a consequence of the antedating. C and CA leave all three open. On explanatory power SY is not the poorest; on fidelity to the sources it is the most expensive. Both stand.
3.5 Chain CA
Revised profile: 9 L · 3 T · 2 P · 2 V · 0 E · 6 U. The six anomalies are largely silence: the article is about Pompey, not about Herod's last years.
The regnal years yield 4/3, not 3/2. Cameron works it out himself: year 34 from 37/36 (Nisan) is 4/3, and also year 37 from 40/39. "However, if Josephus was true to form, the year of Herod's death would not have been 4/3 BCE (Nisan), but rather the following year, 3/2". The step from 4/3 to 3/2 comes not from a figure but from the antedating rule — and that picks one branch of Schürer's rule, the transition year to the successor, and calls it a "clarification". It is a choice, and it is the whole dispute.
The counting rule is not ad hoc. Cameron demonstrates his rule on Josephus's own arithmetic before he uses it: AJ 15.260 gives 12 years from 37/36, AJ 15.299 calls that same year Herod's 13th, and recalculated that comes out at 25/24. But within his own antedating stand three anomalies (Simon, Aristobulus I, Hyrcanus I), and with Simon the rule demonstrably works the other way — the counter-hypothesis in operation in Josephus.
Cheapness forfeited. For 3/2 he rejects two data — AJ 14.66 and the eclipse — and postulates two: Gaius's presence and Philip's 37 years. Exhaustively counted, his construction carries 19 corrections to the tradition (two emendations, nine declarations of error, four rereadings, four coin data absorbed); five of them are specific to 3/2, and four of those five touch the two sons for whom the Antiquitates give a figure.
Philip is the loss entry.AJ 18.106 fits 4/3 untouched: Tiberius's 20th year is AD 33/34, and that is year 37 from 4/3 — Cameron's own note 53. For 3/2 the same verse requires two interventions: 20 → 22 on Latin editions without a Greek witness, which he himself says "cannot be said to be compelling", and "37 years" read as "in the 38th".
A cheaper cell he must reject. It is his own: 4/3 BC. His 3/2 is an admissible reading alongside 4/3, distinguished by one counting rule and one city era; that city era — "year 220" of Caesarea Paneas — is his only compelling datum, and he himself makes it depend on his rejection of the eclipse constraint.
3.6 HV's distinctive positions
HV shares the calculator with the consensus, not the outcomes: the four knobs are shared and independently supported, the capture of 37 is fixed independently of any chain. Beyond that, HV carries two counting rules of its own on this axis, and both receive the same measure as the rivals' knobs.
The Tiberius count: Tishri AD 27. HV counts Luke's 15th year of Tiberius autumn-inclusively: baptism after 20 October AD 27, late in the autumn of 27 or in the winter of 27/28. Steinmann works out the window himself — "For the inclusive method, the fifteenth year would have been one year earlier, AD 28 or autumn AD 27 to summer AD 28" — and Smallwood, a consensus authority, calls Luke's count "presumably by Jewish reckoning" and reckons "Tiberius' 15th year ran from October 27", with reference to Mishnah RH i,1. A defensible minority reading with mainstream cover.
The price is real but bounded. Against inclusive reckoning of Tiberius's years there are positive measurements, not silence: RPC I 4270 (Antioch, year Α equated with Actian year 45, a double dating that excludes inclusive reckoning on an autumn calendar), RPC I 4330 (Seleucia, year Γ = Actian 47), the Alexandrian final-year test (year 23 present, year 24 absent in the year in which Tiberius died), the Egyptian inscriptional corpus and Philo's twice-repeated 23. But this material measures the pagan provincial systems — Roman, Syrian, Egyptian, Actian — and shows that those counted Tiberius non-inclusively. It does not measure the Jewish Tishri framework that Luke would be using; there is nothing to measure there, because no Judean or Tishri-dated corpus exists, and the Judean prefect coins cannot separate the two counts. The bounded costs are two. First: the attested default is non-inclusive, so HV must postulate that Luke reckons Jewishly — the postulate entry that C and HV bear together (3.3). Second: even within the Jewish framework a Nisan count, with the 15th year from about April AD 28, is a live alternative alongside Tishri 27. The symmetry with S&Y is thereby incomplete but not empty: the non-inclusive default is on their side; the Jewish Tishri framework is unmeasured for both. HV's knob is not refuted; nor is it exempted.
Steinmann's own outcome is more fragile than his sentence: on his own Table 1, with his own season ("summer or early autumn"), an autumn baptism falls in AD 28 on three of the four rows, not AD 29; only the Tertullian row — called unreliable by himself, without coin or inscriptional support — gives autumn AD 29. The Steinmann–HV difference is two years: one year of counting rule, one year of seasonal placement and zero years of epoch, since both reckon from August/September AD 14. Undecided, without a counter-witness.
The shemitah chain. HV adduces the sabbatical calendar under the capture of 37 and, via the same calendar, under the baptism anchor. At the siege year that leg bears zero. Zuckermann's calendar is derived from the siege year 37 — "Gehen wir zunächst vom Gewissesten aus" — and his epoch 422/421 BC he himself calls "historisch nicht beurkundet [...] mit der Bescheidenheit einer Hypothese". Whoever adduces Zuckermann as ground under 37 adduces the output as ground for the input. On Wacholder AJ 14.475 argues for 36, not against. Circular on the one calendar, negative on the other: the siege year does not shift, but neither does the shemitah hold it up. The baptism anchor does shift: Tishri 27 on Zuckermann, Tishri 28 on Wacholder, and via Luke 3:23 the crucifixion axis and the birth window shift with it. The coupling is asymmetric — the siege reaches 37 on both calendars; the baptism anchor reaches AD 27 on Wacholder only by also switching the opening rule. Wacholder's deviation rests on one document, Mur 18, and that reading is contested: according to Yaron line 7 is a prosbul clause, not a date. Undecided between the calendars.
In HV's own book the birth window on this axis is not a load but a mirror — "not a pillar [...] a mirror anchor", "the most favorable admissible reading, not a measurement of the birth year itself" — hence no circle. Only, the sentence "the smoothest edge falls on thirty-one" hangs on Zuckermann; on Wacholder that edge shifts to 4 BC.
3.7 The cost accounting
Over the 20 data of the ledger:
chain
year of death
profile
hard cost (V+E)
C (HV shares this)
4/3 BC
10 L · 5 T · 2 P · 0 V · 0 E · 3 U
0
CA
4/3 → 3/2 BC
9 L · 4 T · 0 P · 1 V · 0 E · 6 U
1
SY
1 BC
7 L · 2 T · 8 P · 3 V · 0 E · 0 U
3
The revised count (with the Tiberius entry added) does not change the ranking — C 0 V · 0 E · 3 U, CA 2 V · 2 P · 6 U, SY 3 V · 7 P · 0 U — but narrows the distances.
The cheapest surviving reading on this axis, however, is not a chain but a figure: 4/3 BC, and within that year spring 4 BC; the winter of 4/3 remains possible but is less likely (§6). The regnal figures 34 and 37, counted plainly, yield that year on every chain — with C, and with Cameron's own antedating before his last step. Only a counting-rule choice moves away from it, and every choice has a price that belongs next to the figure:
- C buys the spring of 4 BC with an inclusive counting rule that the same edition rejects for the Hasmoneans, licensed by the eclipse, but with Josephus's own counting practice behind it (3.3). - CA buys winter 3/2 with the transition-year choice, Philip as loss entry and 19 corrections to the tradition. - SY buys January 1 BC with three rejections (consuls and Olympiad erroneous) and an antedating without an attested event. - HV buys, on top of C's account, a Jewish Tishri framework for Luke's Tiberius count against a pagan non-inclusive default, and carries a shemitah leg that yields zero at the siege year.
Within 4/3 BC the season remains open on this axis: no datum in the dossier decides between Schürer's spring and Kushnir-Stein's winter. The only candidate — Gaius Caesar on the consilium versus his consulate at Antioch on 1 January AD 1 — lies outside all counting conventions and has been measured on neither side.
3.8 Falsifiers
Three tests are feasible.
1. Year 1 of the civic era of Caesarea Paneas. If it falls in 3/2 or 2/1 BC, SY's scheme — Philip without territory before 1 BC — is falsified; if it falls in 1 BC/AD 1, Barnes's argument drops away. 2. One dated piece from year 1, 2 or 3 of Antipas or Philip would break the antedating thesis. That requires a new find. The probability argument by which the coin gap is borne, moreover, reckons in the wrong unit — specimens instead of issues; in the right unit one in 10 million becomes roughly one in three. 3. One Josephus passage with a demonstrably inclusively counted regnal year would falsify Cameron's antedating. Cameron parries Schürer's three candidates, but Simon stands as a counterexample in his own appendix.
One measure, with the same weight in every direction. The inclusive counting rule is the hinge: against C because its own edition rejects it elsewhere, against HV because for Tiberius it requires a framework that has not been measured, and for both because the figure they pull away from, 4/3 BC, costs a rejection on no chain. SY pays the most and explains the most; CA pays in the middle and loses Philip; and the year-beginning does not decide the year at all.
Herod's year of death hangs on a small number of primary constraints, each of which cuts off part of the variable space, and on two regnal figures that point to the year within it. The three chains read the same constraints; they differ in which ones they leave standing plainly and which ones they neutralize by a counting convention, a postulate or a rejection. That difference is the cost accounting, and its outcome is not a chain but a figure.
3.1 The constraints
The eclipse. AJ 17.167 places a lunar eclipse shortly before the death. It cuts hard: only 5, 4 and 1 BC have an umbral eclipse visible from Jerusalem — 1 BC twice, total on 10 January and partial (0.57) on 29 December, the latter visible for about an hour at moonrise; 7, 6, 3 and 2 BC have none. It leaves 4 BC (C) and 1 BC (SY) alive and kills 3/2 BC: the cell of Cameron's antedating, and the cell on which six of the eight knob combinations land (3.2).
The regnal figures. Josephus gives Herod 37 regnal years from the Roman investiture and 34 from the capture of Jerusalem. This is the calculator of every chain. Counted plainly from the consensus anchors 40 and 37 BC, both figures yield 4/3 BC; Cameron too reckons this way, up to his last step. That 37 from 40/39 and 34 from 37/36 come out at the same year is presented as "double confirmation". It is empty: the two anchors lie exactly three Nisan years apart and the two figures differ by exactly three, so that every pair (n from Y; n−3 from Y+3) coincides, whatever n one fills in — with Schürer just as neatly, one year earlier.
The anchors: AJ 14.389 and 14.487. The investiture is set on the consuls of 40 BC. The capture is set on the consuls of 37 BC, on the 185th Olympiad and on "27 years after Pompey, on the same day". That last specification is the sharpest constraint on the counting rule. With two identical calendar dates there is no part-year that can count as a full year; the Mishnaic form of the inclusive convention — "portions of a year as full years" — does not take hold here, and what remains is endpoint counting, which does not let the 27 years close on the consuls of 37. The consensus edition names the way out itself: "Josephus made a mistake in calculation [...] twenty-seven instead of twenty-six".
The shemitah: AJ 14.475. A sabbatical year fell during the siege. Which year, hangs on the calendar: on Zuckermann the sabbatical year encloses the siege of 37; on Wacholder it runs from Tishri 37 to Tishri 36, so that a siege in Sivan 36 falls within it and a siege in Sivan 37 does not. SVM sides with Wacholder — "the year 37 B.C. (Oct.)–36 B.C. [...] was sabbatical" — and calls the passage "a considerable difficulty".
The coin gaps and the sons. No coins of Antipas and Philip from regnal years 1, 2 and 3 are known. AJ 18.106 gives Philip 37 regnal years and has him die in Tiberius's 20th year. The civic era of Caesarea Paneas — Cameron reads "year 220" as an era beginning in 3/2 or 2/1 BC — has not been independently measured. These data carry the two antedating theses: SY has the sons count from the Tishri year 6 BC; Cameron assigns the transition year to the successor.
3.2 Four knobs, eight combinations
Every chain sets four knobs: investiture year, capture year, counting rule and year-beginning.
The eight combinations of investiture year, counting rule and year-beginning have been computed mechanically. Exactly two reach January 1 BC, both with investiture 39 and non-inclusive reckoning; the year-beginning is indifferent for that endpoint. Exactly one reaches the spring of 4 BC: 40, inclusive, Nisan. One more, 40, inclusive, Tishri, is the winter branch 4/3, Tishri 4 to Tishri 3 BC (§6). The remaining four land in 3 or 2 BC, where the eclipse kills them. The consensus cell thus stands on one of eight combinations, the SY cell on two. On robustness that argues for SY and against C, and it belongs up front because it runs against the outcome of this chapter.
From this it follows directly: the year-beginning bears the year of death on no chain. Nisan or Tishri decides only where the seasonal boundary falls within the year. Whoever presents the year-beginning as a load-bearing knob presents it wrongly.
3.3 Chain C
Revised profile: 11 L · 5 T · 3 P · 0 V · 0 E · 3 U. Zero rejections, zero emendations: C nowhere declares a datum erroneous and nowhere alters the text. The cheapest profile, but not without a price.
Three anomalies. The shemitah of AJ 14.475, which its own edition concedes on Wacholder and leaves unexplained; on Zuckermann C would read it plainly, but then it stands against its own edition. The coin gap of years 1–3 of Antipas and Philip, for which C has no explanation. And the 13 days between eclipse and Passover on a Nisan count, which Kushnir-Stein calls "plainly impossible"; the constraint can be made more expensive, not lifted.
One expensive counting entry. AJ 14.487 is booked as T, but the edition itself sets the rejection beside it ("twenty-seven instead of twenty-six"). Booked T, V defensible.
Three postulates. The siege month (τῷ τρίτῳ μηνί), which requires two unnamed starting points; the "15th year" of BJ 1.401 for the temple building, "either incorrect or refers to the start of building preparations"; and the inclusive count of Tiberius's years, against which positive measurements stand (3.6).
The heaviest constraint. The inclusive counting rule is the only knob the consensus does not defend independently. SVM 2014 rejects inclusive reckoning in Josephus for the Hasmoneans and retains it for Herod, on one ground. Cameron identifies the passages: the edition has "rightly rejected the notion of inclusive reckoning by Josephus for the Hasmonean era (vol. 1, p. 200-201, n. 1), but maintains the original argument concerning the reign of Herod (p. 326-327, n. 165)", and it "acknowledges that the stated lengths for Herod's reign suggest that he died in 3 BCE, but he then falls back on [...] inclusive reckoning necessitated by the 4 BCE eclipse". The counting rule is thus not derived from Josephus's practice but licensed by the eclipse, and the same move licenses the spring of 4 BC. An internal inconsistency, identifiable in the source.
What lowers the constraint. That the counting rule is not derived from Josephus's practice is itself a claim, and Josephus's practice is measurable. Three places count the begun year as a full year. AJ 15.121 and BJ 1.370 put the battle of Actium (September 31 BC) and the earthquake of the spring before it "in the seventh year" of Herod's reign: from the capture of 37 BC, 31/30 is the seventh year only if 37/36 is the first, for counted by anniversaries the spring of 31 falls in the sixth. AJ 18.26 places the registration of AD 6 "in the thirty-seventh year after Actium", and those are 36 elapsed years. And AJ 20.250 counts 107 years from Herod to the fall of the temple, where 70 from 37 BC gives 106; non-inclusively the starting point would be 38 BC, too early for the deposition of Antigonus. The first two have been seen at primary level, the last two via Bernegger; at gate 5 those two carry for now as citation, not as measurement. What it does, on the same measure as the constraint itself. Internal logic: the step from three places to AJ 17.191 is an inference, and Bernegger himself says that Josephus does not count the same way everywhere; the constraint thus does not vanish, it drops: the inclusive counting rule has a practice behind it and not only the eclipse, and the edition's inconsistency remains an inconsistency of the edition, not of the source. External coherence: Actium in the seventh year fits Cameron's calendar years with 37/36 as year 1 just as well as C, and collides with SY, for whom 36 is the first year and Actium falls in the fifth or sixth; SY catches the two ordinals with its exception, but the 107 of AJ 20.250 is a cardinal number, and that its rule reckons non-inclusively. For CA it cuts the other way: whoever reads 107 as 106 plus one must say why the 34 of AJ 17.191 is not also 33 plus one, with the death in the 34th year, 4/3, and not after it. Correct reading: "in the seventh year" and "in the thirty-seventh year" are there; the "first year" from which they count is read into them, on every side. Falsifier: the Greek text of 18.26 and 20.250 itself; if the figure differs there, only Actium remains of the three. The finding falls in HV's favor and therefore receives no stricter and no milder test than the constraint it lowers.
The cell "4/3 BC", finally, conceals two positions: Schürer's death on 1–14 Nisan and Kushnir-Stein's death in the winter of 4/3. On the season of death HV, after the weighing of §6, comes out with SVM, with a reservation SVM does not make: spring 4 BC; the winter of 4/3 remains possible but is less likely.
3.4 Chain SY
Revised profile: 10 L · 2 T · 7 P · 3 V · 0 E · 0 U. Zero anomalies — SY leaves nothing standing unexplained — but three rejections and seven postulates against zero rejections with C.
Three rejections. The consuls of 40 BC ("the consensus date for this event must be in error"), the consuls of 37 and the 185th Olympiad ("Josephus gives a consular year and an Olympiad that correspond to 37 BC, but this is contradicted [...]").
Seven postulates, six on one knob. The antedating of the sons bears six data from the chronology of the sons, the coin gap among them; SY pays for that once, not six times, but that one knob must bear six data is itself the objection. The siege month and BJ 1.401 are added to that on postulates of their own.
The counting rule carries an exception. Non-inclusive, "except when an ordinal number is used"; without that exception their own argument from Herod's "third year" collapses.
The antedating has no event. The knob was born on a single page to accommodate Julias and Paneas — "we may surmise that Philip, like his brothers, post-dated his reign from 4 BCE" — and was then shifted in four published steps from 4 to 6 BC (Tishri years). The epoch year itself is not a free parameter: it follows from three lines (Archelaus AD 5, Antipas AD 38, Philip AD 14, all as Tishri years). But the event is entirely free; the only condition S&Y impose is the one-sided inequality t(event) < t(death). Their own counting choice moreover enlarges the backdating (four years instead of three). Neither of the two passages they name as the event survives the Greek text: BJ 1.461 concerns Antipater, Alexander and Aristobulus, around 12 BC, and S&Y themselves date the passage "before the trials", which excludes their own epoch year; BJ 1.573 / AJ 17.53 names not Philip but "Ἡρώδης ὁ ἐκ Μαριάμμης", so that the only motive for Philip's backdating rests on a mistaken identity. The epoch hangs in the air. The Herodian precedent helps halfway: counting from before actual power is standard (Herod's own era of 40 BC), but every attested era begins with a Roman act; an era at a private event is nowhere attested, and precisely that is what the thesis needs.
A cheaper cell it must reject. Their strongest argument rests on AJ 14.487, but that constraint has a way out that makes their rejection of consuls and Olympiad superfluous: Cameron keeps consuls, Olympiad and the 27 years exact and pays on one different consular year for Pompey. Non-inclusive reckoning therefore does not force 36 BC.
What only SY explains. The shemitah on Wacholder encloses their siege of 36; three months between eclipse and Passover replace the 13 days; the coin gap becomes a consequence of the antedating. C and CA leave all three open. On explanatory power SY is not the poorest; on fidelity to the sources it is the most expensive. Both stand.
3.5 Chain CA
Revised profile: 9 L · 3 T · 2 P · 2 V · 0 E · 6 U. The six anomalies are largely silence: the article is about Pompey, not about Herod's last years.
The regnal years yield 4/3, not 3/2. Cameron works it out himself: year 34 from 37/36 (Nisan) is 4/3, and also year 37 from 40/39. "However, if Josephus was true to form, the year of Herod's death would not have been 4/3 BCE (Nisan), but rather the following year, 3/2". The step from 4/3 to 3/2 comes not from a figure but from the antedating rule — and that picks one branch of Schürer's rule, the transition year to the successor, and calls it a "clarification". It is a choice, and it is the whole dispute.
The counting rule is not ad hoc. Cameron demonstrates his rule on Josephus's own arithmetic before he uses it: AJ 15.260 gives 12 years from 37/36, AJ 15.299 calls that same year Herod's 13th, and recalculated that comes out at 25/24. But within his own antedating stand three anomalies (Simon, Aristobulus I, Hyrcanus I), and with Simon the rule demonstrably works the other way — the counter-hypothesis in operation in Josephus.
Cheapness forfeited. For 3/2 he rejects two data — AJ 14.66 and the eclipse — and postulates two: Gaius's presence and Philip's 37 years. Exhaustively counted, his construction carries 19 corrections to the tradition (two emendations, nine declarations of error, four rereadings, four coin data absorbed); five of them are specific to 3/2, and four of those five touch the two sons for whom the Antiquitates give a figure.
Philip is the loss entry. AJ 18.106 fits 4/3 untouched: Tiberius's 20th year is AD 33/34, and that is year 37 from 4/3 — Cameron's own note 53. For 3/2 the same verse requires two interventions: 20 → 22 on Latin editions without a Greek witness, which he himself says "cannot be said to be compelling", and "37 years" read as "in the 38th".
A cheaper cell he must reject. It is his own: 4/3 BC. His 3/2 is an admissible reading alongside 4/3, distinguished by one counting rule and one city era; that city era — "year 220" of Caesarea Paneas — is his only compelling datum, and he himself makes it depend on his rejection of the eclipse constraint.
3.6 HV's distinctive positions
HV shares the calculator with the consensus, not the outcomes: the four knobs are shared and independently supported, the capture of 37 is fixed independently of any chain. Beyond that, HV carries two counting rules of its own on this axis, and both receive the same measure as the rivals' knobs.
The Tiberius count: Tishri AD 27. HV counts Luke's 15th year of Tiberius autumn-inclusively: baptism after 20 October AD 27, late in the autumn of 27 or in the winter of 27/28. Steinmann works out the window himself — "For the inclusive method, the fifteenth year would have been one year earlier, AD 28 or autumn AD 27 to summer AD 28" — and Smallwood, a consensus authority, calls Luke's count "presumably by Jewish reckoning" and reckons "Tiberius' 15th year ran from October 27", with reference to Mishnah RH i,1. A defensible minority reading with mainstream cover.
The price is real but bounded. Against inclusive reckoning of Tiberius's years there are positive measurements, not silence: RPC I 4270 (Antioch, year Α equated with Actian year 45, a double dating that excludes inclusive reckoning on an autumn calendar), RPC I 4330 (Seleucia, year Γ = Actian 47), the Alexandrian final-year test (year 23 present, year 24 absent in the year in which Tiberius died), the Egyptian inscriptional corpus and Philo's twice-repeated 23. But this material measures the pagan provincial systems — Roman, Syrian, Egyptian, Actian — and shows that those counted Tiberius non-inclusively. It does not measure the Jewish Tishri framework that Luke would be using; there is nothing to measure there, because no Judean or Tishri-dated corpus exists, and the Judean prefect coins cannot separate the two counts. The bounded costs are two. First: the attested default is non-inclusive, so HV must postulate that Luke reckons Jewishly — the postulate entry that C and HV bear together (3.3). Second: even within the Jewish framework a Nisan count, with the 15th year from about April AD 28, is a live alternative alongside Tishri 27. The symmetry with S&Y is thereby incomplete but not empty: the non-inclusive default is on their side; the Jewish Tishri framework is unmeasured for both. HV's knob is not refuted; nor is it exempted.
Steinmann's own outcome is more fragile than his sentence: on his own Table 1, with his own season ("summer or early autumn"), an autumn baptism falls in AD 28 on three of the four rows, not AD 29; only the Tertullian row — called unreliable by himself, without coin or inscriptional support — gives autumn AD 29. The Steinmann–HV difference is two years: one year of counting rule, one year of seasonal placement and zero years of epoch, since both reckon from August/September AD 14. Undecided, without a counter-witness.
The shemitah chain. HV adduces the sabbatical calendar under the capture of 37 and, via the same calendar, under the baptism anchor. At the siege year that leg bears zero. Zuckermann's calendar is derived from the siege year 37 — "Gehen wir zunächst vom Gewissesten aus" — and his epoch 422/421 BC he himself calls "historisch nicht beurkundet [...] mit der Bescheidenheit einer Hypothese". Whoever adduces Zuckermann as ground under 37 adduces the output as ground for the input. On Wacholder AJ 14.475 argues for 36, not against. Circular on the one calendar, negative on the other: the siege year does not shift, but neither does the shemitah hold it up. The baptism anchor does shift: Tishri 27 on Zuckermann, Tishri 28 on Wacholder, and via Luke 3:23 the crucifixion axis and the birth window shift with it. The coupling is asymmetric — the siege reaches 37 on both calendars; the baptism anchor reaches AD 27 on Wacholder only by also switching the opening rule. Wacholder's deviation rests on one document, Mur 18, and that reading is contested: according to Yaron line 7 is a prosbul clause, not a date. Undecided between the calendars.
In HV's own book the birth window on this axis is not a load but a mirror — "not a pillar [...] a mirror anchor", "the most favorable admissible reading, not a measurement of the birth year itself" — hence no circle. Only, the sentence "the smoothest edge falls on thirty-one" hangs on Zuckermann; on Wacholder that edge shifts to 4 BC.
3.7 The cost accounting
Over the 20 data of the ledger:
The revised count (with the Tiberius entry added) does not change the ranking — C 0 V · 0 E · 3 U, CA 2 V · 2 P · 6 U, SY 3 V · 7 P · 0 U — but narrows the distances.
The cheapest surviving reading on this axis, however, is not a chain but a figure: 4/3 BC, and within that year spring 4 BC; the winter of 4/3 remains possible but is less likely (§6). The regnal figures 34 and 37, counted plainly, yield that year on every chain — with C, and with Cameron's own antedating before his last step. Only a counting-rule choice moves away from it, and every choice has a price that belongs next to the figure:
- C buys the spring of 4 BC with an inclusive counting rule that the same edition rejects for the Hasmoneans, licensed by the eclipse, but with Josephus's own counting practice behind it (3.3). - CA buys winter 3/2 with the transition-year choice, Philip as loss entry and 19 corrections to the tradition. - SY buys January 1 BC with three rejections (consuls and Olympiad erroneous) and an antedating without an attested event. - HV buys, on top of C's account, a Jewish Tishri framework for Luke's Tiberius count against a pagan non-inclusive default, and carries a shemitah leg that yields zero at the siege year.
Within 4/3 BC the season remains open on this axis: no datum in the dossier decides between Schürer's spring and Kushnir-Stein's winter. The only candidate — Gaius Caesar on the consilium versus his consulate at Antioch on 1 January AD 1 — lies outside all counting conventions and has been measured on neither side.
3.8 Falsifiers
Three tests are feasible.
1. Year 1 of the civic era of Caesarea Paneas. If it falls in 3/2 or 2/1 BC, SY's scheme — Philip without territory before 1 BC — is falsified; if it falls in 1 BC/AD 1, Barnes's argument drops away. 2. One dated piece from year 1, 2 or 3 of Antipas or Philip would break the antedating thesis. That requires a new find. The probability argument by which the coin gap is borne, moreover, reckons in the wrong unit — specimens instead of issues; in the right unit one in 10 million becomes roughly one in three. 3. One Josephus passage with a demonstrably inclusively counted regnal year would falsify Cameron's antedating. Cameron parries Schürer's three candidates, but Simon stands as a counterexample in his own appendix.
One measure, with the same weight in every direction. The inclusive counting rule is the hinge: against C because its own edition rejects it elsewhere, against HV because for Tiberius it requires a framework that has not been measured, and for both because the figure they pull away from, 4/3 BC, costs a rejection on no chain. SY pays the most and explains the most; CA pays in the middle and loses Philip; and the year-beginning does not decide the year at all.