Geometrical Analysis of the Coffers of the Pantheon’s Dome in Rome
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Written from the paper’s full text.
TL;DR
The paper uses digital photogrammetry and 3D laser scanning to compare the Pantheon dome’s surveyed soffit with an ideal spherical model, analyzing the 28 coffer sectors and five levels. It finds surprising overall regularity but also localized irregularities, especially along the North–South axis, and argues the coffers were adjusted empirically rather than by rigid geometric construction.
Key findings
- The average ideal sphere has a radius of 22.03 m, and its centre is calculated at −0.37 m behind the cornice line. Comparing survey points to the ideal surface, 72.5% fall within a 10 cm tolerance, 21% are under 15 cm, and 6.5% are over this measure; a depression is detected along the North–South axis.
- The 28-sector radial layout is highly accurate: angles between coffer-sector bisectors are close to 12°50′ (12.85°), with an average deviation of barely 0°36′. The sector opposite the entry portal is parallel to the North–South axis at 15 cm; quadrants I and III are perfectly aligned, while quadrants II and IV are not, with maximum divergence of 39 cm.
- Coffer dimensions decrease progressively upward: average vertical arcs follow the progression 0.93, 0.86, 0.75, 0.60 from level A to E; bottom widths fall from 3.88 m to 2.38 m, upper widths from 3.77 m to 2.02 m, and heights from 4.08 m to 2.39 m. The North–South sector’s first-level coffer A1 measures 4.00 m at its lower part, versus 3.83–3.94 m for others.
- Intermediate and deepest coffer surfaces tend to be flat rather than spherical, with raised points only 2–3 cm from a flat average surface. From the centre of the room at 1.70 m height, the coffers appear almost square, and the inner levels change from horizontal to vertical rectangles; the design seems not to depend on a single projection point.
Methods
- A contemporary double survey was developed using digital photogrammetry and a three-dimensional laser scan, producing a point cloud of the dome’s soffit.
- An ideal model was constructed from an average sphere based on survey-point coordinates, divided into 28 equal sectors and five coffer levels, then compared with the survey model using average calculations, vector-drawing graphical tools, orthogonal projections, and perspective projections.
- Detailed dimensional analysis focused on the North-East quadrant, using sectors 2–6 to calculate average coffer widths, heights, depths, horizontal bands, vertical separations, and transition-surface alignments.
Limitations
- The paper states that results are based on the current state of the coffers registered by the point cloud, which may have been slightly modified by the cladding restoration works of Terenzio (1933) and Belardi (2006), especially for the smallest surfaces.
- The paper states that exact definition of transition-surface directions is difficult because the connecting planes are much shorter than the entire dome, and that the complex coffer design has yet to be analysed and understood in all details.
- Evident from the text: detailed dimensional analysis is concentrated on one quadrant (North-East, sectors 2–6), so variation across all 28 sectors is not fully quantified; thermal expansion was excluded by choice, though the paper argues thermal inertia makes this reasonable.
Model-written summary. Check it against the paper before relying on it.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
1 of 19 cited sources checked · 1 supported · 0 flagged
- Findingown data
The sectors of quadrants II and IV are not aligned with their opposites.
“However, the sectors of quadrants II and IV are not aligned with their opposites.”
Quote in the paperNot a substantial claim - Findingown data
The slight divergence recorded between the first three internal surfaces measures a maximum of 4 cm.
“The slight divergence recorded between the first three internal surfaces measures a maximum of 4 cm.”
Quote in the paperSubstantial claim - Findingreasoning
From the third level to the fifth, the inner figure is a vertical rectangle.
“From the third level to the fifth, the inner figure is a vertical rectangle.”
Quote in the paperNot a substantial claim - Findingnone given
The six opposing coffer sectors of quadrants I and III are perfectly aligned.
“If we observe the alignment between the sectors of quadrants I and III, we can see that the six opposing coffer sectors are perfectly aligned.”
Quote in the paperNot a substantial claim - Findingown data
The greatest decrease in depth appears in the last surface.
“It is evident that the greatest decrease in depth appears in the last surface.”
Quote in the paperNot a substantial claim
- Findingown data
The perceptive differences of the coffer parts are not visible from the centre of the room.
“The perceptive differences of the coffer parts are not visible from the centre of the room.”
Quote in the paperNot a substantial claim - Findingown data
The coffer sector of the North-South axis opposite from the entrance portal has a major difference in width.
“The analysis shows that the coffer sector of the North-South axis opposite from the entrance portal has a major difference in width”
Quote in the paperSubstantial claim - Findingown data
The longitudinal and transversal axes are approximately orthogonal.
“In studying the division of the circumference into four quadrants, it is evident that the longitudinal and transversal axes are approximately orthogonal.”
Quote in the paperNot a substantial claim - Findingown data
The construction of an ideal sphere from the photogrammetric model results in an average radius of 22.03 m.
“The construction of an ideal sphere considers the points of a photogrammetric model and results in an average radius of 22.03 m.”
Quote in the paperSubstantial claim - Findingnone given
All maximum slope lines of the planes defined by the circumferences are oriented northwest/southeast.
“All maximum slope lines of the planes defined by the circumferences are oriented northwest/southeast.”
Quote in the paperNot a substantial claim - Findingreasoning
The vertexes that present the greatest distance from the centre are located in the North-South area.
“In fact, the vertexes that present the greatest distance from the centre are located in this area.”
Quote in the paperNot a substantial claim - Findingown data
The average circumferences following the points defined by horizontal edges generally present a slight slope relative to the horizontal plane, with an average value of approximately 0° 19 0.
“The average circumferences following the points defined by horizontal edges generally present a slight slope relative to the horizontal plane, with an average value of approximately 0° 19 0 (Fig. 6).”
Quote in the paperNot a substantial claim - Findingnone given
The width of the coffers progressively decreased as they progressed towards the upper levels.
“The width of the coffers also progressively decreased as they progressed towards the upper levels.”
Quote in the paperNot a substantial claim - Findingown data
An area of depression is detected along the North-South axis.
“A area of depression is detected along the North-South axis.”
Quote in the paperSubstantial claim - Findingown data
The average values from the first level (A) to the last level generated a numerical progression: 0.93, 0.86, 0.75, 0.60 (B:A, C:A, D:A, E:A).
“The average values from the first level (A) to the last level generated a numerical progression: 0.93 0.86 0.75 0.60 (B:A) (C:A) (D:A) (E:A)”
Quote in the paperSubstantial claim - Findingown data
There was a progressive variation in the inclination of the diagonals, which in the first levels clearly pointed towards the upper part of the coffers and gradually declined in the last levels.
“There was a progressive variation in the inclination of the diagonals, which in the first levels clearly pointed towards the upper part of the coffers and gradually declined in the last levels.”
Quote in the paperNot a substantial claim - Findingown data
The last level of coffers shows the greatest difference with the previous level.
“The last level of coffers shows the greatest difference with the previous level.”
Quote in the paperNot a substantial claim - Findingreasoning
These rectangles with different proportions are approximately centred in a perspective view from the centre of the room.
“In any case, it is highly relevant that these rectangles with different proportions are approximately centred in a perspective view from the centre of the room.”
Quote in the paperSubstantial claim - Findingown data
The depth of the intermediate surfaces changed at different coffer levels.
“The depth of the intermediate surfaces changed at different coffer levels.”
Quote in the paperNot a substantial claim - Findingown data
There is a small and gradual decrease in depth from the first level to the fifth level.
“As we can see in Table 3, there is a small and gradual decrease in depth from the first level to the fifth level.”
Quote in the paperNot a substantial claim - Findingown data
The maximum divergence is registered in the two sectors of quadrants II and IV, where the bisectors reach a distance of 39 cm from the centre of the ideal sphere.
“The maximum divergence is registered in the two sectors of quadrants II and IV, where the bisectors reach a distance of 39 cm from the centre of the ideal sphere.”
Quote in the paperNot a substantial claim - Findingown data
The results show a gradual decrease of the length of the vertical arcs of the coffers.
“The results show a gradual decrease of the length of the vertical arcs of the coffers.”
Quote in the paperSubstantial claim - Findingreasoning
The inferior transition surfaces present a greater inclination.
“The inferior transition surfaces present a greater inclination in order to open the visual field and leave every edge of the coffers visible.”
Quote in the paperSubstantial claim - Findingnone given
The upper width of the last coffer was approximately half of the lower length of the coffers at the first level.
“The upper width of the last coffer was approximately half of the lower length of the coffers at the first level.”
Quote in the paperNot a substantial claim - Findingnone given
The extension of the external lines of each sector generates a vertex at a certain distance from the centre of the sphere.
“The extension of these external lines of each sector generates a vertex at a certain distance from the centre of the sphere.”
Quote in the paperSubstantial claim - Findingown data
A viewer will have a reduced and changing vision of the interior of the coffers from the area next to the circular wall.
“We can confirm that a viewer can see a complete view of the coffers from the centre of the space: he can see all the lowest inner edges and many of the upper edges of the coffers from a circular zone at a certain distance from the centre, and he will have a reduced and changing vision of the interior of the coffers from the area next to the circular wall.”
Quote in the paperSubstantial claim- Rests on an assumption: The point cloud generated from the centre of the room accurately represents the visual field from that point.
- Findingown data
The meridian rib is reduced to almost half of its width from beginning to end.
“According to these data, the meridian rib is reduced to almost half of its width from beginning to end, a fact that is not perceived from the overall view of the dome, where these strips appear to have almost uniform dimensions.”
Quote in the paperSubstantial claim - Findingown data
The coffer arrangement allows complete visibility from the centre of the floor.
“The coffer arrangement allows complete visibility from the centre of the floor.”
Quote in the paperNot a substantial claim- Rests on an assumption: The point cloud generated from the centre of the room accurately represents the visual field from that point.
- Findingreasoning
The average thermal expansion value results in a length variation of 8.7 mm for an initial length of 44.06 m and a temperature difference of 20 °C.
“The average value considered above results in a length variation of 8.7 mm for an initial length of 44.06 m (the approximated value of the Pantheon's dome) and a temperature difference of 20 °C with regard to the average temperature.”
Quote in the paperSubstantial claim- Rests on an assumption: The average coefficient of thermal expansion of concrete is 10^-5 °C^-1 and can vary by about ±30% depending on concrete composition and conditions.
- Findingnone given
The axis of the coffer sector situated opposite the entry portal is parallel to the North-South axis at a distance of 15 cm.
“We noted that the axis of the coffer sector situated opposite the entry portal is parallel to the North-South axis at a distance of 15 cm.”
Quote in the paperNot a substantial claim - Findingreasoning
The difference between the upper and lower edges of each coffer increased in the higher levels.
“The difference between the upper and lower edges of each coffer increased in the higher levels, reflecting the necessity to adapt to the spherical curvature.”
Quote in the paperNot a substantial claim - Findingown data
The four lines that result slightly diverge from the centre of the ideal sphere.
“However, we can also observe that the four lines that result slightly diverge from the centre of the ideal sphere.”
Quote in the paperNot a substantial claim - Findingreasoning
The resulting shape is different from the usual theoretical image of coffers.
“The resulting shape is different from the usual theoretical image of coffers.”
Quote in the paperSubstantial claim - Findingown data
This regularity is also reflected in the separation between the vertical sectors of the coffers.
“This regularity is also reflected in the separation between the vertical sectors of the coffers.”
Quote in the paperNot a substantial claim - Findingown data
The position of the centre of the ideal sphere was calculated at -0.37 m behind the cornice line.
“The position of the centre of the ideal sphere was calculated at -0.37 m behind the cornice line.”
Quote in the paperSubstantial claim - Findingown data
The sectors tend to converge with high approximation towards the centre of the sphere.
“Based on our study of the bisectors of the coffers, the sectors tend to converge with high approximation towards the centre of the sphere.”
Quote in the paperSubstantial claim - Findingnone given
The locations of these vertex points do not approximate a circumference but rather show evident irregularities.
“The locations of these points do not approximate a circumference but rather show evident irregularities.”
Quote in the paperSubstantial claim - Findingown data
The general layout of the 28 sectors of coffers is approximately uniform.
“We can state that the general layout of the 28 sectors of coffers is approximately uniform, but we must stress the special evidence of the irregularity of the sector situated on the North-South axis and the consequent distribution of the sectors of the North-East quadrant.”
Quote in the paperSubstantial claim - Findingown data
The curves representing the alignments of the external points of the coffers do not converge towards the sphere's pole.
“By studying the shape of the vertical sectors, it can be seen that the curves representing the alignments of the external points of the coffers do not converge towards the sphere's pole, as might be assumed (Fig. 7).”
Quote in the paperSubstantial claim - Findingown data
The fourth surface disappears in the upper level of the coffers.
“This fourth surface disappears in the upper level of the coffers; therefore, the third surface follows a different design.”
Quote in the paperNot a substantial claim - Findingnone given
The upper connecting surfaces appear to be orthogonal to the spherical surface of the dome.
“Nevertheless, we can note that the upper connecting surfaces appear to be orthogonal to the spherical surface of the dome.”
Quote in the paperNot a substantial claim - Findingreasoning
There is a circular zone where a viewer can see all the inferior edges of the coffers and almost all the upper edges.
“Although the constructed object is not as exact as the ideal model, these convergences indicate that there is a circular zone where a viewer can see all the inferior edges of the coffers and almost all the upper edges.”
Quote in the paperSubstantial claim - Findingown data
The average recorded deviation between the bisectors of the coffer sectors and the axes that theoretically divide the circumference into 28 equal parts barely reaches 0° 36 0.
“When observing deviations in the plan between the bisectors of the coffer sectors and the axes that theoretically divide the circumference into 28 equal parts, the average recorded deviation barely reaches 0° 36 0 (Table 1).”
Quote in the paperSubstantial claim - Findingown data
The present work confirms the existence of a gap between the plane of the cornice and the centre of the sphere.
“The present work, like Fine Licht (1968), Pelletti (1989) and Graßhoff et al. (2006), confirms the existence of a gap between the plane of the cornice and the centre of the sphere.”
Quote in the paperSubstantial claim0 of 3 sources checked- cites Fine Licht (1968)
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- cites Pelletti (1989)
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- cites Graßhoff et al. (2006)
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Findingown data
The distances of the raised point from the flat average surface were minimal, 2-3 cm.
“The distances of the raised point from this flat average surface were minimal (2-3 cm).”
Quote in the paperSubstantial claim - Findingnone given
In the Pantheon the coffers that appear square to the eye actually have a trapezoidal shape.
“In the Pantheon the coffers that appear square to the eye actually have a trapezoidal shape.”
Quote in the paperNot a substantial claim - Findingown data
A comparison between the ideal and survey models brings to light the surprising uniformity in the distribution of the coffers.
“A comparison between the ideal and survey models brings to light the surprising uniformity in the distribution of the coffers.”
Quote in the paperSubstantial claim- Rests on an assumption: The ideal model built from average measurements is a valid reference for analyzing the original design.
- Findingown data
The average circumferences are approximately concentric.
“The average circumferences are approximately concentric.”
Quote in the paperSubstantial claim - Findingown data
The reduction of the meridian rib is not perceived from the overall view of the dome, where these strips appear to have almost uniform dimensions.
“According to these data, the meridian rib is reduced to almost half of its width from beginning to end, a fact that is not perceived from the overall view of the dome, where these strips appear to have almost uniform dimensions.”
Quote in the paperNot a substantial claim - Findingown data
The main distance between the centre of the circumferences and the centre of the ideal sphere is only 7 cm.
“The main distance between the centre of the circumferences and the centre of the ideal sphere is only 7 cm.”
Quote in the paperSubstantial claim - Findingcitation
The bisector of the North-South axis sector opposite the entrance portal shows a gap with the North-South axis.
“Moreover, as in our previous study (Aliberti et al. 2014), the bisector of this sector shows a gap with the North-South axis.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites Aliberti et al. 2014
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Findingown data
The horizontal bands separating the coffers have very similar dimensions.
“Unlike the coffer width and height variations, the horizontal bands separating the coffers have very similar dimensions.”
Quote in the paperNot a substantial claim - Findingreasoning
If we approximate the form of the inner levels of the coffers to rectangles, it is evident that their proportions change from the horizontal to the vertical.
“If we approximate the form of the inner levels of the coffers to rectangles, it is evident that their proportions change from the horizontal to the vertical.”
Quote in the paperSubstantial claim - Interpretationreasoning
The calculated thermal length change would occur only if the corresponding thermal oscillation affected the entire volume of concrete.
“This change in length would occur when the corresponding thermal oscillation affected the entire volume of concrete.”
Quote in the paperSubstantial claim - Interpretationreasoning
The distribution of the sectors was adjusted empirically to compensate for the irregular position of the coffer sector situated on the North-South axis.
“This fact may indicate that the distribution of the sectors was adjusted empirically to compensate for the irregular position of the coffer sector situated on the North-South axis.”
Quote in the paperSubstantial claim- Rests on an assumption: The current state of the coffers, as registered by the point cloud, sufficiently reflects the original design of the coffers for the geometrical analyses.
- Interpretationreasoning
The design of the inner levels of the coffers seems not to depend on the projection from a hypothetical point, in contrast with some scientific studies.
“Based on these studies, we can state that the design of the inner levels of the coffers seems not to depend on the projection from a hypothetical point, in contrast with some scientific studies.”
Quote in the paperSubstantial claim- Rests on an assumption: In ancient times there was no knowledge of the perspective method or of spherical geometry.
- Interpretationnone given
The greater inclination of inferior transition surfaces serves to open the visual field and leave every edge of the coffers visible.
“The inferior transition surfaces present a greater inclination in order to open the visual field and leave every edge of the coffers visible.”
Quote in the paperSubstantial claim - Premisereasoning
There is no recent and complete graphic restitution of the Pantheon in scientific publications.
“However, in recent scientific publications, no complete graphical restitution of the dome of the Pantheon exists as the surveys used by Valenti (2009) and Belardi (2006) are not yet published; therefore, some authors still use old documents to formulate new hypotheses.”
Quote in the paperSubstantial claim0 of 2 sources checked- cites Valenti (2009)
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- cites Belardi (2006)
- Interpretationown data
The layout of the coffers was adapted to the slight divergences of the North-South sector to determine a uniform distribution using an empirical method.
“The results suggest that the division of the circumference into 28 equal parts could not be controlled by rigid geometrical construction; the layout of the coffers was adapted to the slight divergences of the North-South sector to determine a uniform distribution using an empirical method.”
Quote in the paperSubstantial claim- Rests on an assumption: The current state of the coffers, as registered by the point cloud, sufficiently reflects the original design of the coffers for the geometrical analyses.
- Interpretationown data
The intermediate and deepest levels of the coffers do not adapt to a spherical surface but tend to be flat.
“It can thus be deduced that the intermediate and the deepest levels do not adapt to a spherical surface but tend to be flat, which would undoubtedly make it easier to control the formwork.”
Quote in the paperSubstantial claim - Interpretationcitation
The orientation of the North-South axis is precise compared with other Roman buildings with similar dimensions.
“The accuracy of the orientation of the North-South axis stands out for its precision if we compare it with other Roman buildings with similar dimensions.”
Quote in the paperNot a substantial claim - Premisenone given
The surveys used by Valenti (2009) and Belardi (2006) are not yet published.
“However, in recent scientific publications, no complete graphical restitution of the dome of the Pantheon exists as the surveys used by Valenti (2009) and Belardi (2006) are not yet published; therefore, some authors still use old documents to formulate new hypotheses.”
Quote in the paperSubstantial claim0 of 2 sources checked- cites Valenti (2009)
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- cites Belardi (2006)
- Study design and conductown data
A double verification of the accuracy of the average value was obtained.
“In this way, we obtain a double verification of the accuracy of the average value.”
Quote in the paperNot a substantial claim - Interpretationreasoning
They seem to be traced from the bisectors of coffer sectors that determine the general layout of the coffers.
“They seem to be traced from the bisectors of coffer sectors that determine the general layout of the coffers.”
Quote in the paperSubstantial claim - Premisecitation
The dimensions of the floor squares are visually similar to the image of the dome coffers.
“The dimensions of the floor squares are visually similar to the image of the dome coffers (Waddell 2008: 85) (Fig. 8).”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites Waddell 2008: 85
- Interpretationown data
A large number of survey points are very close to the spherical surface.
“The results indicate that a large number of points are very close to the spherical surface.”
Quote in the paperSubstantial claim - Interpretationreasoning
The arrangement of the vertexes reflects the presence of deformed areas in the North-South zone of the dome.
“If we attempt to establish a relation between this fact and the analysis of the dome surface, it appears that the arrangement of the vertexes somehow reflects the presence of deformed areas in the North-South zone of the dome.”
Quote in the paperNot a substantial claim - Interpretationreasoning
The setting-out on site may have been performed through a practical-constructive technique based on experimentation more than complex geometrical laws.
“The setting-out on site may have been performed through a practical-constructive technique based on experimentation more than complex geometrical laws.”
Quote in the paperSubstantial claim- Rests on an assumption: The current state of the coffers, as registered by the point cloud, sufficiently reflects the original design of the coffers for the geometrical analyses.
- Interpretationreasoning
The third surface follows a different design.
“This fourth surface disappears in the upper level of the coffers; therefore, the third surface follows a different design.”
Quote in the paperNot a substantial claim - Interpretationown data
The division of the circumference into 28 equal parts could not be controlled by rigid geometrical construction.
“The results suggest that the division of the circumference into 28 equal parts could not be controlled by rigid geometrical construction; the layout of the coffers was adapted to the slight divergences of the North-South sector to determine a uniform distribution using an empirical method.”
Quote in the paperSubstantial claim- Rests on an assumption: The current state of the coffers, as registered by the point cloud, sufficiently reflects the original design of the coffers for the geometrical analyses.
- Interpretationcitation
The division of the hemisphere into 28 equal parts was difficult to obtain at the time of construction.
“The division of the hemisphere into 28 equal parts was difficult to obtain at the time of construction.”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites Martines 1989
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Interpretationreasoning
The external limits of the coffers might have been traced from the bisectors according to a system based on the accuracy of the bisector design.
“The external limits of the coffers might have been traced from them according to a system based on the accuracy of the bisector design.”
Quote in the paperNot a substantial claim - Study design and conductown data
The diameter calculated from the ideal sphere matches the result obtained by the point cloud management program.
“The diameter of this calculus matches the result obtained by the point cloud management program.”
Quote in the paperSubstantial claim - Study design and conductown data
This observation has been verified through the study of the point cloud generated from the centre of the room without considering scannings performed on the transversal and longitudinal axes.
“This observation has been verified through the study of the point cloud generated from the centre of the room without considering scannings performed on the transversal and longitudinal axes.”
Quote in the paperNot a substantial claim- Rests on an assumption: The point cloud generated from the centre of the room accurately represents the visual field from that point.
- Classified as probably not a substantial claim. 16
- May combine two claims. 28
Probably not a substantial claim: may not pass S3 (load-bearing).
PremisecitationFernandez-Cabo (2013) used the drawings of Rondelet (1860) to carry out his research.
“In the Nexus Network Journal, Fernandez-Cabo (2013) stressed this evidence and eventually used the drawings of Rondelet (1860) to carry out his research.”
Quote in the paperNot a substantial claim1 of 2 sources checked- cites Fernandez-Cabo (2013) source
- cites Rondelet (1860)
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
May combine two claims.
Findingown dataIn analysing the direction of the transition surfaces between the different levels, the radial tracings were identified, and other tracings approximately converged into certain reference points outside the coffers.
“In analysing the direction of the transition surfaces between the different levels, the radial tracings were identified, and other tracings approximately converged into certain reference points outside the coffers (Fig. 11).”
Quote in the paperSubstantial claimMay combine two claims.
Findingown dataThe upper circumference of the last level of the coffers shows a greater inclination than the average value and is directed towards the North direction.
“The upper circumference of the last level of the coffers shows a greater inclination than the average value, and it is directed towards the North direction.”
Quote in the paperNot a substantial claimMay combine two claims.
Findingown dataThe coffer of the first level of the North-South axis sector opposite the entrance portal (A1) measures 4.00 m in its lower part, whereas the rest of coffers measure A2 3.90 m, A3 3.94 m, A4 3.86 m, A5 3.83 m, A6 3.86 m, A7 3.85 m, and A8 3.92 m.
“(the coffer of the first level of this sector, named A1, measures 4.00 m in its lower part, whereas the rest of coffers measure as follows: A2, 3.90 m; A3, 3.94 m; A4, 3.86 m; A5, 3.83 m; A6, 3.86 m; A7, 3.85 m; A8, 3.92 m)”
Quote in the paperSubstantial claimMay combine two claims.
Findingown dataBased on the study of the North-East quadrant, the average distance between the lowest external points of the first level is 1.02 m, which becomes 0.67 between the upper external points of the last level.
“Based on the study of the North-East quadrant, the average distance between the lowest external points of the first level is 1.02 m, which becomes 0.67 between the upper external points of the last level.”
Quote in the paperSubstantial claimMay combine two claims.
FindingreasoningThe differences between the second and the third level are greater than between the rest of the levels, so the transition seems not to be completely uniform.
“Moreover, the differences between the second and the third level are greater than between the rest of the levels, so the transition seems not to be completely uniform.”
Quote in the paperNot a substantial claimMay combine two claims.
Findingown dataThe external lines of the coffer sectors appear to converge to the upper pole of the sphere but intersect before this point, reflecting some irregularities.
“Another result regarding the general distribution is the analysis of the external lines of the coffer sectors, which appear to converge to the upper pole of the sphere but intersect before this point, reflecting some irregularities.”
Quote in the paperSubstantial claimMay combine two claims.
Findingown dataThe East transversal axis shows a distance from the centre of the sphere of approximately 16 cm and the West transversal axis has a slightly greater value.
“The East transversal axis shows a distance from the centre of the sphere of approximately 16 cm and the West transversal axis has a slightly greater value.”
Quote in the paperNot a substantial claimMay combine two claims.
Findingown dataThe distance from survey points to the ideal surface shows a 10 cm tolerance in 72.5% of the points, 21% under 15 cm, and 6.5% over this measure.
“The data of the outcome show a 10 cm tolerance in 72.5% of the points, whereas 21% are under 15 cm, and 6.5% are over this measure.”
Quote in the paperSubstantial claimMay combine two claims.
FindingreasoningThe external shape can be approximated as a square, but the inner levels have different proportions and change from horizontal to vertical rectangles.
“The external shape can be approximated as a square, but the inner levels have different proportions and change from horizontal to vertical rectangles.”
Quote in the paperSubstantial claimMay combine two claims.
Findingown dataThe analysis of connecting planes makes it possible to identify the radial direction of the upper transition surfaces and the approximate convergence of the inferior transition surfaces to a point at a certain distance from the centre of the space.
“The analysis of connecting planes makes it possible to identify the radial direction of the upper transition surfaces and the approximate convergence of the inferior transition surfaces to a point at a certain distance from the centre of the space.”
Quote in the paperSubstantial claimMay combine two claims.
Findingown dataThis perspective view reproduces an almost square image, and the coffer surfaces seem to be regular and of the same dimensions.
“It is evident that this perspective view reproduces an almost square image, and the coffer surfaces seem to be regular and of the same dimensions.”
Quote in the paperNot a substantial claimMay combine two claims.
Findingown dataThe deviation from perfect orthogonality is 90° 50 0 between the East transversal axis and the longitudinal axis, and 90° 32 0 between the West transversal axis and the longitudinal axis.
“The two parts show a minimum deviation from the perfect orthogonality: 90° 50 0 between the East transversal axis and the longitudinal axis; 90° 32 0 between the West transversal axis and the longitudinal axis.”
Quote in the paperNot a substantial claimMay combine two claims.
Findingown dataThere is special evidence of the irregularity of the sector situated on the North-South axis and the consequent distribution of the sectors of the North-East quadrant.
“We can state that the general layout of the 28 sectors of coffers is approximately uniform, but we must stress the special evidence of the irregularity of the sector situated on the North-South axis and the consequent distribution of the sectors of the North-East quadrant.”
Quote in the paperSubstantial claimMay combine two claims.
Findingown dataIrregularities are highlighted, and the shape and general arrangement of the coffers is related to the spherical geometry of the soffit.
“At the same time, irregularities are highlighted, and the shape and general arrangement of the coffers is related to the spherical geometry of the soffit.”
Quote in the paperSubstantial claimMay combine two claims.
Findingown dataThe angles between vertical axes of the coffer sectors are extremely close to 12° 50 0, equivalent to the subdivision of the 360° ideal model into 28 equal parts.
“The angles between vertical axes of the coffer sectors are extremely close to 12° 50 0 , which is equivalent to the subdivision of the 360° ideal model into 28 equal parts.”
Quote in the paperSubstantial claimMay combine two claims.
Findingown dataA viewer can see a complete view of the coffers from the centre of the space: he can see all the lowest inner edges and many of the upper edges of the coffers from a circular zone at a certain distance from the centre.
“We can confirm that a viewer can see a complete view of the coffers from the centre of the space: he can see all the lowest inner edges and many of the upper edges of the coffers from a circular zone at a certain distance from the centre, and he will have a reduced and changing vision of the interior of the coffers from the area next to the circular wall.”
Quote in the paperSubstantial claim- Rests on an assumption: The point cloud generated from the centre of the room accurately represents the visual field from that point.
May combine two claims.
FindingreasoningThe lowest connecting planes in the first two levels of the coffers are larger than in the upper levels and the inner figure is thus a horizontal rectangle.
“The lowest connecting planes in the first two levels of the coffers are larger than in the upper levels and the inner figure is thus a horizontal rectangle.”
Quote in the paperNot a substantial claimMay combine two claims.
Findingown dataEach coffer generates a different image when the inclination of the perspective axis moves, thus showing its trapezoidal shape.
“Each coffer generates a different image when the inclination of the perspective axis moves, thus showing its trapezoidal shape.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
Findingown dataBy comparing different perspective views, it can be directly noted how the perception of these elements slowly changes.
“By comparing different perspective views, it can be directly noted how the perception of these elements slowly changes.”
Quote in the paperNot a substantial claimMay combine two claims.
Findingown dataWhen calculating these values as arcs of a sphere, the average value is 0.84, with variations of a few centimetres between zones.
“When calculating these values as arcs of a sphere, the average value is 0.84, with variations of a few centimetres between zones.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
PremisecitationThe Coliseum shows a more pronounced gap in the orthogonal direction of the main axis.
“For example, the Coliseum shows a more pronounced gap in the orthogonal direction of the main axis (Pelletti 1989: 15).”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites Pelletti 1989: 15
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Probably not a substantial claim: may not pass S3 (load-bearing).
InterpretationcitationThe coffers may have been slightly modified by the cladding restoration works of Terenzio (1933) in the 1930s and more recently of Belardi (2006), especially if we refer to the smallest surfaces.
“They may have been slightly modified by the cladding restoration works of Terenzio (1933) in the 1930s and more recently of Belardi (2006), especially if we refer to the smallest surfaces.”
Quote in the paperNot a substantial claim0 of 2 sources checked- cites Terenzio (1933)
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- cites Belardi (2006)
May combine two claims.
Study design and conductreasoningThe unique point cloud perfectly describes every part of the coffers and their complex surfaces without detecting any blind areas.
“This unique point cloud perfectly describes every part of the coffers and their complex surfaces without detecting any blind areas.”
Quote in the paperSubstantial claimMay combine two claims.
InterpretationreasoningThe more complex design of the inner levels may be the result of two conditions: the vertical alignment of the coffers and the alteration of the lowest parts of the coffers to correct the perspective perception.
“The more complex design of the inner levels may be the result of two conditions: the vertical alignment of the coffers and the alteration of the lowest parts of the coffers to correct the perspective perception.”
Quote in the paperSubstantial claim- Rests on an assumption: The current state of the coffers, as registered by the point cloud, sufficiently reflects the original design of the coffers for the geometrical analyses.
Probably not a substantial claim: may not pass S3 (load-bearing).
PremisecitationA similar finding of an area of depression along the North-South axis was obtained by Scherer (2009).
“A similar finding was obtained by Scherer (2009: 220-221).”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites Scherer (2009: 220-221)
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Probably not a substantial claim: may not pass S3 (load-bearing).
PremisecitationWaddell (2008) used measurements documented by Piranesi in the seventeenth century to formulate his hypothesis about the distribution of coffers.
“For example, Waddell (2008) used measurements documented by Piranesi in the seventeenth century to formulate his hypothesis about the distribution of coffers.”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites Waddell (2008)
Probably not a substantial claim: may not pass S3 (load-bearing).
PremisecitationThe division of a quarter of the circumference into 7 equal parts was a complicated geometric problem.
“The division of a quarter of the circumference into 7 equal parts was a complicated geometric problem (Martines 1989).”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites Martines 1989
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
May combine two claims.
InterpretationreasoningThis change is probably a result of two conditions of coffer design: the aim to preserve the vertical alignment of the sector in the width of both the external and internal levels; and the need for greater alteration of the lowest coffers to control the perspective view from the centre of the room.
“This change is probably a result of two conditions of coffer design: the aim to preserve the vertical alignment of the sector in the width of both the external and internal levels; and the need for greater alteration of the lowest coffers to control the perspective view from the centre of the room.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
Interpretationnone givenThis divergence from the average value was distributed evenly between the six sectors of the second quadrant in order to generate a uniform image of the soffit frame.
“This divergence from the average value was distributed evenly between the six sectors of the second quadrant in order to generate a uniform image of the soffit frame.”
Quote in the paperNot a substantial claimMay combine two claims.
Interpretationown dataThese data affirm the accuracy of the vault to the ideal model and confirm the uniformity of the general distribution of the coffers.
“These data provide new affirmation of the incredible accuracy of the vault to the ideal model, and also confirms the uniformity of the general distribution of the coffers.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S2 (checkable), S4 (based).
Study design and conductnone givenThe use of contemporary methods of architectural survey assures the correct graphical documentation of the dome in its current state of conservation.
“The use of contemporary methods of architectural survey assures the correct graphical documentation of the dome in its current state of conservation.”
Quote in the paperNot a substantial claimMay combine two claims.
Interpretationown dataThis difference in width has an impact on the radial arrangement of the coffers and generates the divergence of the bisector registered by the comparison of the survey model and the ideal model.
“This difference has an impact on the radial arrangement of the coffers and generates the divergence of the bisector that was registered by the comparison of the survey model and the ideal model.”
Quote in the paperSubstantial claimMay combine two claims.
InterpretationreasoningIt is unlikely that thermal oscillation affected the entire volume of concrete because the building's thermal inertia is very high due to the width of its walls and sections.
“This situation seems unlikely due to the thermal inertia of the building, which is certainly very high because of the width of its walls and sections.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing).
PremisecitationCreating the image of a pure shape, such as a square, is part of the search for regular forms present in the classical Roman culture.
“Creating the image of a pure shape, such as a square, is part of the search for regular forms present in the classical Roman culture (Ferna ´ndez-Cabo 2013: 543).”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites Ferna ´ndez-Cabo 2013: 543
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Classified as probably not a substantial claim.
Study design and conductown dataThe results are based on the current state of the coffers registered by the point cloud.
“In studying this subject, we should consider that the results are based on the current state of the coffers registered by the point cloud.”
Quote in the paperSubstantial claimMay combine two claims.
InterpretationreasoningThe control of perspective correction was inexact and may not have been generated by a difficult process using a projection point.
“The control of perspective correction was inexact and may not have been generated by a difficult process using a projection point.”
Quote in the paperSubstantial claim- Rests on an assumption: In ancient times there was no knowledge of the perspective method or of spherical geometry.
Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.
Interpretationown dataThe present research verifies the ambitious work of the Roman builders based on empirical knowledge of perception and geometry and carried out with the use of ancient tools.
“The present research, performed with sophisticated devices and software, verifies the ambitious work of the Roman builders based on empirical knowledge of perception and geometry and carried out with the use of ancient tools.”
Quote in the paperNot a substantial claim- Rests on an assumption: The current state of the coffers, as registered by the point cloud, sufficiently reflects the original design of the coffers for the geometrical analyses.
May combine two claims.
InterpretationreasoningThis image of a square may be associated with the external shape of the coffers, while the inner levels show some differences.
“This image of a square may be associated with the external shape of the coffers, while the inner levels show some differences (Fig. 14).”
Quote in the paperNot a substantial claimClassified as probably not a substantial claim.
InterpretationreasoningFrom the point of view of construction, such a dependence would be very difficult to achieve due to the great distance and the height of the dome from the floor.
“We consider that from the point of view of construction, such a dependence would be very difficult to achieve due to the great distance and the height of the dome from the floor.”
Quote in the paperSubstantial claim- Rests on an assumption: In ancient times there was no knowledge of the perspective method or of spherical geometry.
Probably not a substantial claim: may not pass S1 (asserted).
InterpretationreasoningRoman constructors designed the external form of the coffers with a square proportion based on the near equivalence between the lowest edge and the vertical edge, adapting to the vertical alignment of the external lines.
“Regarding the coffer shape, we propose the hypothesis that Roman constructors designed the external form of the coffers with a square proportion based on the near equivalence between the lowest edge and the vertical edge, adapting to the vertical alignment of the external lines.”
Quote in the paperNot a substantial claim- Rests on an assumption: The current state of the coffers, as registered by the point cloud, sufficiently reflects the original design of the coffers for the geometrical analyses.
Probably not a substantial claim: may not pass S3 (load-bearing).
Interpretationown dataThe division of the circumference into 28 equal parts might have been started or completed with the sector opposite the entry portal.
“This detail may indicate that the division of the circumference into 28 equal parts might have been started or completed with this sector.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing).
Interpretationown dataThe accuracy of the radial distribution of the coffers is surprising.
“According to the calculations of the present study, the accuracy of the radial distribution of the coffers is surprising (Fig. 5).”
Quote in the paperNot a substantial claim
The paper relies on this without support.
The configuration of the coffers is governed by geometric-constructive laws that exist and can be defined.
“The configuration of the coffers is governed by a complex design that is based on geometric-constructive laws yet to be defined.”
The paper relies on this without support.
The average coefficient of thermal expansion of concrete is 10^-5 °C^-1 and can vary by about ±30% depending on concrete composition and conditions.
“Concrete expands, and the average coefficient of thermal expansion is 10 -5 °C -1 .Test results show that this coefficient can change in a relatively high proportion (on the order of ±30%) depending on the nature of the concrete, sand and gravel, dosage, hygrometry and dimensions of the sections.”
The paper relies on this without support.
Setting out on site was especially difficult at the location of the cornice of the vault.
“Moreover, the setting out on site was especially difficult at the location of the cornice of the vault.”
The paper relies on this without support.
In ancient times there was no knowledge of the perspective method or of spherical geometry.
“Furthermore, as far as we currently know, in ancient times there was no knowledge of the perspective method or of spherical geometry.”
The paper relies on this without support.
The current state of the coffers, as registered by the point cloud, sufficiently reflects the original design of the coffers for the geometrical analyses.
“In studying this subject, we should consider that the results are based on the current state of the coffers registered by the point cloud.”
The paper relies on this without support.
The ideal model built from average measurements is a valid reference for analyzing the original design.
“We used these studies on the average measurement of coffers and their distribution as a first metrical reference to build the complete ideal model.”
The paper relies on this without support.
The point cloud generated from the centre of the room accurately represents the visual field from that point.
“This observation has been verified through the study of the point cloud generated from the centre of the room without considering scannings performed on the transversal and longitudinal axes.”
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
Each contradiction between two passages listed here was confirmed by an independent check.
Meridian rib retains about two-thirds, not half, of its width
MinorThe stated widths change from 1.02 m to 0.67 m. The latter is about 66% of the former, rather than almost half.
Reported 0.5 · recomputed 0.656863
“1.02 m, which becomes 0.67 between the upper external points of the last level.According to these data, the meridian rib is reduced to almost half of its width from beginning to end”
Slope directions are described as both uniformly northwest-southeast and northward
MinorThe text says all maximum-slope lines of the circumference planes run northwest-southeast, then says the upper circumference of the last coffer level slopes toward the north.
“All maximum slope lines of the planes defined by the circumferences are oriented northwest/southeast.”
“The upper circumference of the last level of the coffers shows a greater inclination than the average value, and it is directed towards the North direction.”
Cites
Principles of Roman architecture
(2001) · Choice Reviews Online · doi:10.5860/choice.38-5409 · Cited by 324 · see citing works
Concrete Vaulted Construction in Imperial Rome
Lancaster, L. C. (2005) · Cambridge University Press eBooks · doi:10.1017/cbo9780511610516 · Cited by 242 · see citing works
Concrete vaulted construction in Imperial Rome innovations in context
Lancaster, L. C. (2005) · Cited by 148 · see citing works
The Pantheon: Design, Meaning, and Progeny
Bishop, J. J., & MacDonald, W. L. (1977) · Art Journal · doi:10.2307/776079 · Cited by 94 · see citing works
The Rotunda in Rome: A Study of Hadrian's Pantheon. By Kjeld de Fine Licht.
Frazer, A. (1969) · American Journal of Archaeology · doi:10.2307/504025 · Cited by 41 · see citing works
(2008) · Cited by 27 · see citing works
The Pantheon : design, meaning, and progeny
Mac Donald, W. L. (1976) · Allen Lane eBooks · Cited by 13 · see citing works
Analysis of Different Hypotheses about the Geometric Pattern of the Pantheon’s Coffered Dome
Fernández-Cabo, M. C. (2013) · Nexus Network Journal · doi:10.1007/s00004-013-0165-5 · Cited by 9 · see citing works
Los constructores romanos: un estudio sobre el proceso arquitectónico
Taylor, R. M. (2006) · Dialnet (Universidad de la Rioja) · Cited by 7 · see citing works
(2006) · Cited by 6 · see citing works
Aliberti, L., Canciani, M., & Rodríguez, M. Á. A. (2015) · The international archives of the photogrammetry, remote sensing and spatial information sciences/International archives of the photogrammetry, remote sensing and spatial information sciences · doi:10.5194/isprsarchives-xl-5-w4-291-2015 · Cited by 5 · see citing works
Self-citationDal Pantheon a Brunelleschi : architettura costruzione tecnica
Gambardella, A., Lenza, C., & Borsi, S. (2002) · Cited by 2 · see citing works
The Pantheon in Rome : contributions to the conference, Bern, November 9-12, 2006 : Pantheon I
Graßhoff, G., Heinzelmann, M., & Wäfler, M. (2009) · Cited by 1 · see citing works
Concrete Vaulted Construction in Imperial Rome: Preface
Lancaster, L. C. (2005) · doi:10.1017/cbo9780511610516.001 · Cited by 1
Pantheon y cúpulas clásicas romanas: geometría y construcción
Aliberti, L. (n.d.) · doi:10.20868/upm.thesis.25667
Self-citation
Flagged first, then by citations
Research works printed but not linked: 3
- Graßhoff, Gerd, Michael Heinzelmann and Marcus Wäfler, eds. 2006. The Pantheon in Rome: Contributions to the conference (Bern, November 9–12, 2006). Bern: Bern Studies in the History and Philosophy of Science.
- Saalman, Howard. 1988. The Pantheon coffers: pattern and number. Architectura, Journal of the History of Architecture 18:121–122.
- Valenti, Graziano Maria. 2009. A computing model for the Pantheon’s cupola: from the discrete to the continuous. the ideal continuous model. The Pantheon in Rome. Contributions to the conference (Bern, November 9-12, 2006), Gerd Graßhoff, Michael Heinzelmann and Marcus Wäfler, eds. Bern: Bern Studies in the History and Philosophy of Science, pp. 223–233.
Cited by
Sorted by citations
Graphical Modelling of Hoop Force Distribution for Equilibrium Analysis of Masonry Domes
Paris, V., Ruscica, G., & Roberti, G. (2021) · Nexus Network Journal · doi:10.1007/s00004-021-00556-x · Cited by 15 · see citing works
The New Theory of the Metrological Framework of the Pantheon
Fuchs, W. (2023) · Nexus Network Journal · doi:10.1007/s00004-023-00679-3 · Cited by 7 · see citing works
Geometric Characterization of Late-Baroque Domes in Sicily
Floriano, L., Liuzzo, M., & Margani, G. (2022) · Nexus Network Journal · doi:10.1007/s00004-022-00594-z · Cited by 6 · see citing works
The Linked Geometries of the Roman Pantheon and Hadrian’s Serapeum in Tivoli, Part I: The Pantheon
Aung, M. T., & Bork, R. (2025) · Nexus Network Journal · doi:10.1007/s00004-025-00843-x · Cited by 2 · see citing works
The Pantheon, Eye of Rome, and Its Glimpse of the SkyPreprint
Sparavigna, A. C., & Dastrù, L. (2018) · SSRN Electronic Journal · doi:10.2139/ssrn.3185748 · Cited by 2 · see citing works
Virtual reconstruction of a ghost disco: the Woodpecker in Milano Marittima
Bartolomei, C., Mazzoli, C., & Morganti, C. (2022) · Journal of Physics Conference Series · doi:10.1088/1742-6596/2204/1/012013 · Cited by 1 · see citing works
The Vault and Coffers of S. Bernardo alle Terme in Rome
Aliberti, L. (2020) · Nexus Network Journal · doi:10.1007/s00004-020-00518-9
Self-citationConformality in Hawksmoor's ceiling, the Roman Pantheon and Mercator's projection
Cardy, J. (2026) · Proceedings of the Royal Society A Mathematical Physical and Engineering Science · doi:10.1098/rspa.2026.0076
The Vaulted Apses of the Temple of Venus and Rome: Coffers Design and Visual Alignments
Aliberti, L. (2026) · Nexus Network Journal · doi:10.1007/s00004-026-00889-5
Self-citation
- Authors
- Aliberti, L., & Alonso-Rodríguez, M. Á.
- Affiliations
- Universidad Politécnica de Madrid (ES)
- Corresponding author
- Aliberti, Licinia
- Venue
- Nexus Network Journal
- Published
- 2017-04-25
- Volume
- 19
- Issue
- 2
- Pages
- 363-382
- ISSN
- 1522-4600 (ISSN-L)
- 1590-5896
- OpenAlex
- W2608253481
- Semantic Scholar
- 29c3f9fe7c6b3963f9e8f78f766371bb02d2aa7d
- Cited by
- 10
- References
- 13
- Citations by year
- 2026: 3 · 2025: 1 · 2023: 1 · 2022: 2 · 2021: 1 · 2020: 1 · 2018: 1
- FWCI
- 10.35
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Nexus Network Journal (publishedVersion)
- Funders
- Università degli Studi Roma Tre
- Topics
- Social Sciences › Arts and Humanities › Visual Arts and Performing Arts › Architecture and Art History Studies
- Physical Sciences › Earth and Planetary Sciences › Geology › 3D Surveying and Cultural Heritage
- Social Sciences › Arts and Humanities › Archeology › Historical and Architectural Studies
- Keywords
- Pantheon, coffers, domes, spherical surfaces, architectural geometry, Roman architecture
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Claims read by deepseek-v4.1-flash under definition version 3 (extract-v3) on 2026-10-30.
Classified by jev-1.13-20260917 (gold-guideline-v0.2) on 2026-10-30.
Cited sources are checked by gpt-6-sol.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
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