The correspondence register maps all 75 principal numbers and 26 lettered variants to their recovered operations. It preserves the original pagination and the exact scope of each correspondence.
B. Complete original-equation correspondence
The register covers all 75 principal equation numbers and all 26 printed lettered variants, 101 entries in total. Printed page numbers refer to the original article. A present equation may recover several source forms by the tensor or variation identities proved in the adjoining text; the table is an operation map, not a claim that each historical equation is independent. Unnumbered discrepancies are recorded separately in Appendix A. The machine-readable version is supplied in registers/equation_correspondence.csv.
| Original | Page | Recovered operation and present location | Scope |
|---|---|---|---|
| (1) | 777 | Local Lorentz interval; (3.1) | Inherited local interval. |
| (2) | 778 | Linear calibration of differentials; (3.1) | Invertible calibration. |
| (3) | 778 | Metric and interval readout; (3.1) | Exact. |
| (4) | 778 | Special-relativistic calibration; (3.1) | Exact special case. |
| (5) | 780 | Coordinate tangent transformation; (3.7) | Invertible Jacobian. |
| (5a) | 780 | General contravariant vector transformation; (4.1) | Exact. |
| (6) | 781 | Invariant vector-covector pairing; (4.1) | Arbitrary probes. |
| (7) | 781 | Covector transformation; (4.1) | Exact. |
| (8) | 782 | Contravariant tensor product; (4.1) | Exact. |
| (9) | 782 | Rank-two contravariant transformation; (4.1) | Exact. |
| (10) | 782 | Covariant tensor product; (4.1) | Exact. |
| (11) | 782 | Covariant tensor transformation; (4.1) | Exact. |
| (12) | 783 | Mixed tensor product; (4.1) | Exact. |
| (13) | 783 | Mixed tensor transformation; (4.1) | Exact. |
| (14) | 783 | Contravariant symmetry; (4.1) | Exact. |
| (14a) | 783 | Covariant tensor symmetry; (4.1) | Exact. |
| (15) | 784 | Contravariant antisymmetry; (4.1) | Exact. |
| (15a) | 784 | Covariant tensor antisymmetry; (4.1) | Exact. |
| (16) | 787 | Inverse fundamental tensor; (3.2) | Nondegenerate metric. |
| (17) | 788 | Reciprocal determinants; (3.2) | Nondegenerate metric. |
| (18) | 788 | Invariant volume density; (3.7) | Density convention. |
| (18a) | 789 | Natural volume element; (3.2) | Density readout. |
| (19) | 789 | Determinant-one coordinate transitions; (6.6) | Local oriented chart. |
| (20) | 790 | Stationary interval; (5.1) | Inherited stationarity. |
| (20a) | 791 | Parameterized interval variation; (5.1) | Regular non-null curve. |
| (20b) | 791 | Integrated variation and residual; (5.2) | Boundary term retained. |
| (20c) | 791 | Proper-length Euler equation; (5.3) | Affine normalization. |
| (20d) | 791 | First-kind bracket form; (5.3) | Exact index conversion. |
| (21) | 791 | First-kind Christoffel bracket; (4.10) | Lower first index. |
| (22) | 792 | Geodesic equation; (5.4) | Affine non-null curve. |
| (23) | 792 | Raised Christoffel bracket; (4.10) | Compatible comparison. |
| (24) | 792 | Scalar gradient construction; (5.5) | Derivative intertwiner. |
| (25) | 793 | Hessian along a geodesic; (5.5) | Torsion-free sector. |
| (26) | 793 | Arbitrary covector derivative; (4.12) | Not only gradients. |
| (27) | 795 | Covariant rank-two derivative; (5.6) | All tensor components. |
| (28) | 796 | Determinant differentiation; (5.7) | Nondegenerate metric. |
| (29) | 796 | Log-volume differentiation; (5.8) | Exact. |
| (29a) | 796 | Connection trace identity; (5.8) | Compatible comparison. |
| (30) | 796 | Differentiated inverse identity; (5.7) | Exact. |
| (31) | 796 | Contravariant inverse derivative; (5.7) | Exact. |
| (32) | 796 | Covariant inverse derivative; (5.7) | Exact. |
| (33) | 796 | Metric derivative via first-kind bracket; (5.9) | Compatible comparison. |
| (34) | 796 | Inverse metric derivative via connection; (5.9) | Compatible comparison. |
| (35) | 797 | Vector divergence; (5.10) | Volume retained. |
| (36) | 797 | Antisymmetric covector derivative; (5.11) | Original minus-d sign. |
| (37) | 797 | Cyclic derivative of antisymmetric tensor; (5.12) | Antisymmetric field. |
| (38) | 798 | Contravariant rank-two derivative; (4.12) | Upper-slot plus signs. |
| (39) | 798 | Mixed tensor derivative; (4.12) | Both slot actions. |
| (40) | 798 | Antisymmetric contravariant divergence; (5.13) | Second-index contraction. |
| (41) | 799 | Mixed divergence; (5.14) | Unrestricted tensor. |
| (41a) | 799 | Symmetric-stress divergence via metric; (5.15) | Symmetry required. |
| (41b) | 799 | Symmetric-stress divergence via inverse; (5.15) | Symmetry required. |
| (42) | 800 | Iterated covector derivative difference; (6.3) | Torsion-free form. |
| (43) | 800 | Riemann-Christoffel tensor; (6.2) | Full quadratic terms. |
| (44) | 801 | Contracted curvature and volume split; (6.4) | B equals minus Ricci. |
| (45) | 802 | Negative Christoffel convention; (2.6) | Exact dictionary. |
| (46) | 802 | Free-particle equation; (7.1) | Physical premise retained. |
| (47) | 803 | Vacuum gravitational equation; (7.3) | Unit-volume chart. |
| (47a) | 804 | Source realization of Hamiltonian function; (7.4) | Unrestricted chart extension. |
| (47b) | 805 | Field Euler equation; (7.7) | Variation before gauge. |
| (48) | 805 | Action partial derivatives; (7.9) | Positive derivative sign. |
| (49) | 805 | Canonical energy divergence; (8.3) | Vacuum; raw defect shown. |
| (49a) | 806 | Fixed-region gravitational flux; (8.6) | Inward/outward sign explicit. |
| (50) | 806 | Quadratic gravitational energy; (8.4) | Chart-tagged non-tensor. |
| (51) | 806 | Mixed vacuum field equation; (8.5) | Equivalent residual. |
| (52) | 807 | Total-energy replacement; (9.8) | Same realization. |
| (52a) | 808 | Trace-reversed mixed equation; (10.2) | Trace reversal invertible. |
| (53) | 808 | General gravitational field equation; (9.9) | Coupling inherited. |
| (54) | 808 | Triple-derivative cancellation; (10.3) | General chart identity. |
| (55) | 809 | Double-divergence cancellation; (10.4) | Zero at unit volume. |
| (56) | 809 | Total energy conservation; (10.7) | Coupled unit-volume sector. |
| (57) | 809 | Matter exchange equation; (10.12) | Numbered sign retained. |
| (57a) | 810 | Matter connection-exchange form; (10.13) | Symmetric stress. |
| (58) | 811 | Contravariant fluid stress; (11.2) | Original rho convention. |
| (58a) | 811 | Covariant fluid stress; (11.2) | Inherited constitutive form. |
| (58b) | 811 | Mixed fluid stress; (11.3) | Euler substitution recovered. |
| (59) | 812 | Potential antisymmetric derivative; (12.3) | Field equals minus d phi. |
| (60) | 812 | Homogeneous cyclic equations; (12.5) | Potential contact. |
| (60a) | 812 | Four expanded homogeneous equations; (12.11) | Antisymmetric components. |
| (60b) | 813 | Homogeneous three-vector system; (12.11) | Original component order. |
| (61) | 813 | Lower electric/magnetic components; (12.10) | Original normalization. |
| (62) | 813 | Raise electromagnetic field indices; (12.7) | Metric response retained. |
| (63) | 813 | Sourced Maxwell divergence; (12.8) | Second index; unit volume. |
| (63a) | 813 | Sourced three-vector system; (12.12) | Metric-dependent primed fields. |
| (64) | 813 | Primed upper-index components; (12.10) | Not generally unprimed. |
| (65) | 814 | Field-current transfer covector; (12.14) | Nonzero transfer retained. |
| (65a) | 814 | Transfer spatial and time components; (12.22) | Signature retained. |
| (66) | 815 | Electromagnetic stress balance; (12.20) | Zero transfer only if assumed. |
| (66a) | 815 | Electromagnetic stress tensor; (12.17) | Full residual proof. |
| (67) | 817 | Newtonian particle acceleration; (13.3) | Weak, slow, quasi-static. |
| (68) | 818 | Poisson field equation; (13.6) | Leading low-pressure matter. |
| (68a) | 818 | Green potential and coefficient; (13.7) | Boundary/flux contract. |
| (69) | 818 | Newtonian coupling normalization; (13.9) | Mass-equivalent density. |
| (70) | 819 | First-order central metric; (14.1) | Not an exact metric. |
| (70a) | 819 | Same-mass parameter join; (14.2) | Printed coefficient corrected. |
| (71) | 819 | Radial unit-rod readout; (15.1) | First order; static. |
| (71a) | 820 | Tangential unit-rod comparison; (15.1) | Stated local direction. |
| (72) | 820 | Unit-clock coordinate period; (15.3) | Period, not rate. |
| (73) | 821 | Null interval; (16.1) | Ray law separately supplied. |
| (74) | 822 | Asymptotic light bending; (16.5) | Parameter form recovered. |
| (75) | 822 | Perihelion advance; (17.11) | Cited dependency completed. |
Published source: The Foundations of General Relativity: A Source–Readout Reconstruction of Einstein’s 1916 Theory. Read the original PDF alongside the web treatment.