{"id":"07bea735-027d-47f3-98d0-85b91542a780","arxiv_id":"2505.18161","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Most historic Fuerteventura churches face within the solar arc, with a cluster near declination -14 degrees and another slightly north of east, the latter possibly tied to Easter sunrise.","lead":"This paper measures the compass orientations of 48 historic churches and chapels on the Canary Island of Fuerteventura, finding that most face sunrise directions but that two clusters stand out. It offers several tentative explanations, including alignment with Easter sunrise and, more speculatively, with the star Sirius.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The two declination groups are not statistically established: the paper's own KS tests fail to reject a random origin, and the 3σ curvigram peaks depend on a flat-horizon, mean-latitude null and a fixed kernel bandwidth.","rationale":"The reader's weakest assumption identifies the same load-bearing concern: the statistical significance of the two orientation groups depends on model choices that are not independently validated, and the paper's own KS tests cannot reject a random origin. My stress-test sharpens this by pointing to the specific mismatch between the formal KS non-rejection and the later use of a 3σ threshold from a uniform-in-azimuth Monte Carlo null. The flat-horizon, mean-latitude assumption is especially problematic because some measured horizon heights are large (up to 12.9° and 38.5°), and the null should reflect actual site conditions if it is used to assess whether observed clusters are anomalous. The paper is honest about the weakness of its interpretive explanations: for the -14° peak it lists four possibilities and says none is conclusive, and for the +5° Easter explanation it admits that 'it is not difficult' to find a matching Easter date. That honesty does not rescue the statistical detection claim, because the two groups are the basis for the paper's headline result. The descriptive core, that 70% of the sample (91% of pre-20th-century buildings) falls within the solar range, is robust and well documented in Table 1. Therefore the appropriate verdict remains CONDITIONAL: the survey data and descriptive finding are valuable, but the two-group statistical claim needs to be redone with a more appropriate null and tested for robustness before it can be accepted.","tokens_in":20725,"tokens_out":5456,"duration_ms":62984,"concrete_test":"Recompute the normalized curvigram using each church's measured horizon height and actual latitude instead of a flat horizon and the mean latitude of 28.5°N, and repeat the analysis for kernel bandwidths of 1σ, 2σ, and 3σ (where σ is the reported mean error). If the +5° and -14° peaks do not remain above the corresponding 3σ threshold in all bandwidth variants, or if a Hartigan dip test on the declinations of the 34 solar-range churches fails to reject unimodality, the two-group claim should be downgraded to a tentative observation rather than a statistical result.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that the data reveal two distinct orientation groups rests on the normalized curvigram in Figure 8, but the paper's own formal test in 'Data sample and methods' states that the Kolmogorov-Smirnov tests 'indicated that we cannot discard the null hypothesis with confidence' for both uniform and solar null distributions. Despite this, the Results section treats the +5° and -14° maxima as notable, and the authors define a 3σ threshold as statistically significant. That threshold is computed by normalizing the observed curvigram against 100 random samples drawn from a uniform distribution in azimuth, assuming a flat horizon and a single mean latitude of 28.5°N, with kernel bandwidth fixed to twice the mean error. A uniform-in-azimuth null is not the appropriate null for detecting an excess of easterly orientations: because most historic churches are known to face east for cultural reasons, such a null will make any concentration inside the solar arc look significant. The -14° peak is additionally fragile because the authors themselves note that several contributing churches (29, 30, 31, 33) sit in valleys trending near 105° azimuth with low horizons, so local topography may account for their common orientation without any shared astronomical or calendrical intent. The descriptive finding that most pre-20th-century churches fall within the solar range is well supported by the data, but the two-group interpretation is not independently established by the statistical procedure as presented.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper presents field measurements of the orientations of 48 historic churches and chapels on Fuerteventura, listing for each building the azimuth, horizon height, and computed solar declination with uncertainties. The descriptive claim is that the great majority of pre-20th-century constructions (91%) fall within the solar range, and that wind avoidance is accommodated through south-facing lateral doors rather than through non-canonical orientations. The paper further claims that the declination distribution contains two notable groups: a peak near delta = +5 degrees, interpreted as orientation to the sunrise on Easter Sundays near the construction date, and a peak near delta = -14 degrees, concentrated in central-island churches and attributed speculatively to Los Finaos, valley topography, sunset orientations, or Sirius (the Gañanera). The stated statistical basis for the two-group claim is the normalized curvigram in Figure 8 with a 3-sigma threshold, despite the paper's own Kolmogorov-Smirnov tests failing to reject random null distributions.","tokens_in":20959,"tokens_out":5985,"duration_ms":61802,"significance":"If the two-group interpretation were established, the paper would make a useful contribution to Canarian archaeoastronomy, connecting colonial church orientations with Iberian Easter-orientation traditions and with local ethnographic stellar lore. The descriptive dataset itself is valuable: the measurements are carefully documented, with corrected magnetic azimuths, horizon-height estimates, error propagation, a full table, maps, and comparisons with previous studies on Lanzarote and La Gomera. The paper also offers a sensible practical explanation, the south-facing lateral door, for reconciling canonical orientation with prevailing winds. However, the identification of the two declination groups is the load-bearing claim of the abstract, and it is not currently supported by the statistical tests presented in the manuscript.","major_comments":[{"comment":"The paper's own formal tests contradict the claim that the two declination groups are statistically established. In the methods section the authors state that the Kolmogorov-Smirnov tests 'indicated that we cannot discard the null hypothesis with confidence' for both the uniform and the solar distributions, and they acknowledge that the maxima 'might have the same relative frequency when compared to an individual random distribution.' Despite this, the Results section and the abstract treat the +5 and -14 degree peaks as a statistically revealed two-group structure, with the 3-sigma threshold in Fig. 8 as the criterion. That threshold is not an independent test: it is obtained by normalizing the empirical curvigram against 100 random samples drawn from a uniform azimuth distribution with a flat horizon and a single mean latitude of 28.5 degrees N, and with the kernel bandwidth fixed to twice the mean error. A uniform-in-azimuth null is inappropriate for detecting an excess of easterly orientations, because any concentration inside the narrow solar arc will tend to look significant against it. The claim should either be re-derived with a null that respects the expected easterly distribution and the actual horizon and latitude of each church, or explicitly relabeled as a descriptive rather than statistically significant pattern.","section":"Data sample and methods; Results, Fig. 8"},{"comment":"The test for Easter orientation is circular in effect. Churches are selected for Table 2 precisely because their declination lies in the range +5 +/- 5 degrees, and then Easter Sundays are located in a range of years near the often poorly constrained construction date whose solar declination matches that value. Because Easter Sunday moves across a roughly month-long interval and construction dates carry large uncertainties, such a match is almost guaranteed; the authors themselves concede that 'given a church value of declination, it is not difficult to find a Sun's declination close to it but occurring during Easter Sunday in a small range of years around the date of construction.' This does not discriminate Easter sunrise from an equinoctial orientation or from any date within the same season. The interpretation would need a control, for example the same matching exercise with non-Easter dates or with a null distribution of movable feasts, together with a propagation of construction-date uncertainty.","section":"Table 2 and Discussion (Easter test)"},{"comment":"The -14 degree peak is not robust against the topographical explanation that the authors themselves offer. Churches 29, 30, 31, and 33 are described as located in valleys that descend toward the sea near 105 degrees in azimuth with very low or negative horizon heights; this geometry alone produces declinations near -14 degrees even without any shared calendrical or stellar intention. Because these same churches are the main contributors to the peak, the 'second group' may be an artifact of valley orientation rather than a separate cultural tradition. The Sirius hypothesis does not resolve this: the 17th-century declination of Sirius (-16.3 degrees) differs from -14 degrees by more than the stated uncertainties, and the one church discussed under that hypothesis (no. 8, Agua de Bueyes) has its altar direction at delta about +19 degrees, so its narthex direction is being used in the opposite sense; that church is not itself part of the -14 degree peak. A quantitative test comparing the valley-church orientations with the distribution of local valley axes would be needed before treating the -14 degree concentration as a distinct group.","section":"Discussion (-14 degree peak); churches 29-33"}],"minor_comments":[{"comment":"The test name is misspelled as 'Kolmogorov-Smirnoff'; it should be 'Kolmogorov-Smirnov'.","section":"Data sample and methods"},{"comment":"The text says San Isidro Labrador was built in 1714, while Table 1 lists 1713; please reconcile these dates.","section":"Historic churches of Fuerteventura"},{"comment":"The sentence describing the normalized curvigram as 'including geographical location and local topography' is misleading: the normalization uses a flat horizon and a single mean latitude, and only the measured horizon heights of individual churches enter the declination computation. Please rephrase to avoid implying that the null model includes local topography.","section":"Results, Fig. 8"}],"recommendation":"major_revision","confidential_remarks":"The descriptive dataset is a solid contribution, and the paper's candor about its own statistical limitations, the failed KS tests, the 'not conclusive' verdict on the -14 degree group, and the 'speculative' label for Sirius, is commendable. However, the abstract and Results still assert a two-group structure 'revealed' by statistical analysis, which the tests do not support. Acceptance should require either a reanalysis with an appropriate null model or a clear downgrading of the claim to a descriptive working hypothesis. The Easter test in Table 2 also needs a control or at least an explicit statement of its circularity."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nThe useful part of this paper is the survey data, not the interpretations. Muratore et al. give a clean table of azimuths, horizon heights, and declinations for 48 Fuerteventura churches, and the descriptive result—91% of pre-20th-century churches fall within the solar range—is solid. The comparison with Lanzarote and La Gomera is a real addition, and the lateral-south-door reading of wind avoidance is plausible and locally grounded. I would trust the measurements and want them in the regional database.\n\nThe interpretive superstructure is weaker. The two “groups” in the declination curvigram are not established by the paper’s own statistics. The KS tests against uniform and solar nulls fail to reject randomness, and the 3-sigma peaks in Figure 8 come from normalizing against a flat-horizon, mean-latitude uniform azimuth null—a null that will make any easterly concentration look significant. The authors acknowledge part of this, which I respect, but they then proceed to treat the +5° and -14° peaks as if they carried weight. The -14° group is especially fragile: they note themselves that four of the contributing churches sit in valleys trending near 105° azimuth with low horizons. Topography alone can explain that cluster. The Easter hypothesis for +5° is presented honestly—Table 2 shows that for any church in the window you can find a nearby Easter Sunday with matching solar declination—but that means the test has little probative value. It is a familiar, plausible tradition imported from Iberia, not a discovery made by this dataset. The Sirius/Gañanera material is explicitly speculative and stays that way.\n\nSo: the paper is a careful field report with an over-interpreted statistical layer. The data deserve publication; the two-group astronomical story needs either a stronger null model (per-site horizons, better treatment of the known east-facing baseline) or reframing as descriptive peaks worth future testing. The authors are transparent about limitations, and the measurement work is reproducible from the table, so I would send it to a serious archaeoastronomy referee. A good referee could push them to demote the interpretive claims and keep the survey as the contribution.","headline":"Solid survey data, over-interpreted peaks: the Fuerteventura orientation table is the contribution; the two declination groups and Easter test don't survive their own statistics.","tokens_in":21542,"tokens_out":1630,"would_cite":true,"duration_ms":16754,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The measured axes of 48 Fuerteventura churches concentrate in two groups: one aimed slightly north of east, tied to Easter sunrise, and one near declination −14° that the paper leaves open to four readings.","keywords":["archaeoastronomy","church orientation","ad orientem","Fuerteventura","Canary Islands","Easter sunrise","Sirius","declination curvigram"],"falsifier":"Recompute the curvigram using actual horizon profiles and local latitude for every church, then re-run the 3σ significance test; if the +5° and −14° peaks no longer exceed the threshold, the two-group structure is an artifact of the flat-horizon normalization.","tokens_in":20493,"feed_emoji":"⛪","tokens_out":8723,"duration_ms":82892,"temperature":0.7,"pith_summary":"The paper measures the altar orientations of 48 colonial-era churches on Fuerteventura and asks whether builders followed the Christian rule that the apse face the rising Sun. It finds that about 70% of the sample, and 91% of pre-20th-century buildings, lie within the solar arc, so the tradition was largely respected. The declination distribution shows two prominent concentrations: a peak near +5°, slightly north of due east, which the authors link to sunrise on Easter Sunday near the construction date, and a peak near −14° concentrated in central-island churches, for which they weigh four non-exclusive explanations: Easter sunset, the local All Souls' vigil \"Los Finaos\", the 105° azimuth of central valleys, and the star Sirius, known locally as the Gañanera. None of the four is conclusive, and the paper also notes that many canonical churches add a south-facing side door, reconciling tradition with the island's strong trade winds.","feed_headline":"Fuerteventura churches point to Easter sunrise and a −14° sky","feed_subtitle":"Survey of 48 colonial churches: most follow the solar arc, with two distinct orientation groups.","key_machinery":"The analysis is carried by the declination curvigram: each measured azimuth and horizon height is converted into a solar declination δ using standard positional-astronomy formulae, then smoothed with an Epanechnikov kernel whose bandwidth is twice the mean measurement error of 0.7°. The resulting density is normalized by the mean of 100 random subsamples drawn from a uniform azimuth distribution over a flat horizon at a mean island latitude of 28.5°N, and peaks rising above three standard deviations are treated as potentially significant. The same conversion from declination to calendar dates lets the authors match the +5° peak to Easter Sundays near construction years and the −14° peak to dates such as 2 November, while a Kolmogorov-Smirnov test against random distributions is used to frame what the normalized peaks can and cannot establish.","core_discovery":"On the paper's own terms, the discovery is that most measured churches, 34 of 48, keep their main axes within the solar range, and the sample's declination curvigram, normalized against a uniform azimuth distribution, shows two peaks above the 3σ threshold: a principal maximum at δ ≈ +5° and a secondary maximum at δ ≈ −14°. The +5° peak is interpreted as Easter sunrise orientation, because for a dozen churches with declinations in the +5±5° range there is an Easter Sunday in the years around construction whose solar declination matches. The −14° peak is treated as anomalous; the authors explicitly reject patron-saint dates, magnetic compass use, and wind avoidance as explanations, then present Los Finaos, local valley topography, Easter sunset, and Sirius as candidate causes, with the stellar reading called speculative and supported only by circumstantial ethnographic and iconographic evidence.","pith_inferences":["A sharper test of the −14° group than the paper performs would separate the four hypotheses by horizon: churches on flat, open ground cannot be explained by valley topography, so any of them that still fall near −14° would point to Los Finaos, Easter sunset, or Sirius rather than terrain.","If the Easter-peak interpretation is right, the orientation scatter should correlate with the year of construction: the +5° peak would be tighter where parish archives fix the building date and wider where dates are uncertain, which could be checked against the church account books the paper cites.","Applying the same measurement protocol on Gran Canaria would be a natural out-of-sample test: if the two-group pattern is a real island tradition it should appear there too, while if it is local topography it should track that island's different valley systems.","The star and rosette plaques on the Agua de Bueyes barbican could motivate a focused ethnographic survey of Gañanera observation practices in the central island before the Sirius alignment is taken beyond speculation."],"forward_implications":["If the Easter-sunrise reading of the +5° peak is correct, Fuerteventura's builders followed a movable feast rather than the fixed equinoctial east, matching a practice found in the Castilian regions that supplied the colonizers.","If the −14° group is real, it marks a local orientation custom with no parallel in the previously surveyed Canary Islands; the paper's four candidate explanations all remain open.","The finding that pre-20th-century churches are 91% within the solar range, while most exceptions are modern or private chapels, implies the liturgical tradition remained normative on the island until recent times.","The south-facing side-door pattern gives a concrete architectural mechanism for reconciling canonical eastward orientation with the prevailing trade winds, distinct from Lanzarote's whole-building rotation.","Completing the survey on Gran Canaria would test whether these patterns are specific to Fuerteventura or common to the archipelago's colonial churches."],"supporting_citations":[{"why":"Defines the Christian solar-orientation tradition against which the sample is judged.","marker":"McCluskey 2015"},{"why":"The canonical instruction that church altars face equinoctial east, the baseline from which measured deviations depart.","marker":"Borromeo 1985 [1577]"},{"why":"The earlier fieldwork paper that supplies the measured sample of 48 Fuerteventura churches analyzed here.","marker":"Muratore and Gangui 2020"},{"why":"Provides the normalized curvigram and kernel-density method used to identify the +5° and −14° peaks.","marker":"González-García and Sprajc 2016"},{"why":"Documents Easter-sunrise orientation in Castilian churches, the precedent invoked for the +5° peak.","marker":"Urrutia-Aparicio et al. 2021a"},{"why":"The Lanzarote study whose wind-driven orientations form the main island-to-island contrast.","marker":"Gangui et al. 2016a"},{"why":"The La Gomera study whose valley-topography explanation is a comparator for the −14° group.","marker":"Di Paolo et al. 2020"},{"why":"Records the Gañanera (Sirius) agricultural lore and observations that ground the stellar hypothesis.","marker":"Belmonte and Sanz de Lara 2020"},{"why":"Supplies the standard conversion from azimuth and horizon height to declination and the error propagation used to build Table 1.","marker":"Ruggles 2015a"}],"fun_headline_variants":["Fuerteventura churches reveal Easter sunrise and a −14° anomaly","Two groups of 48 churches: Easter sunrise and a −14° offset","Church orientations split: Easter sunrise and a −14° cluster","Fuerteventura's churches: Easter sunrise alignment and a −14° skew","Easter sunrise aligns some Fuerteventura churches; others turn −14°"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The reality of the two orientation groups depends on a null model that assumes a flat horizon, a single island-wide latitude, and a smoothing width of twice the mean error—and the paper's own Kolmogorov-Smirnov tests, a standard goodness-of-fit check, cannot reject that the whole sample is random.","fun_headline_variants_meta":{"raw":{"variants":["Fuerteventura churches reveal Easter sunrise and a −14° anomaly","Two groups of 48 churches: Easter sunrise and a −14° offset","Church orientations split: Easter sunrise and a −14° cluster","Fuerteventura's churches: Easter sunrise alignment and a −14° skew","Easter sunrise aligns some Fuerteventura churches; others turn −14°"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001301,"raw_usage":{"total_tokens":5341,"prompt_tokens":1014,"completion_tokens":4327,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":630,"completion_tokens_details":{"reasoning_tokens":4228}},"tokens_in":630,"tokens_out":4327,"duration_ms":28541,"temperature":1.0,"reasoning_tokens":4228,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T22:26:41.431910+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Recompute the curvigram using actual horizon profiles and local latitude for every church, then re-run the 3σ significance test; if the +5° and −14° peaks no longer exceed the threshold, the two-group structure is an artifact of the flat-horizon normalization.","supporting_citations":[{"cited_title":"Instrucciones de la fábrica y del ajuar eclesiásticos , translated and edited by B","cited_arxiv_id":null,"evidence_quote":"The canonical instruction that church altars face equinoctial east, the baseline from which measured deviations depart."}],"review_version":1}