Follow the light. Question the picture.: sources & model

Inspect the real EHT observation, then choose a direction in a calculated light map. Follow its exterior path, find its source and reveal two images of one tiny patch.

What supports the explanation?

What this model assumes

1. Exterior Schwarzschild geometry only: nonrotating, uncharged, spherical, vacuum and test rays. No accretion, emission, spin, plasma, jets, telescope simulation or fitted astrophysical inference.
2. The source grid and patch are invented labels. Colors and geometric image widths do not predict intensity. The EHT observation is separately credited.
3. Observer at 50 r_g is static, not freely falling. No physical travel time, local speed variation, interior path, observer survival or tidal-injury calculation is offered.
4. Captured backtraces stop at r=2+10⁻⁶. The critical path is a finite approach display. The near-critical interval 1<b/b_c<1.001 is unresolved, not a material shell.
5. Coordinate-path views crop at a stated areal radius; the source sphere lies outside the close view. Guides and markers are display aids. Local angles must not be measured with a flat protractor on that coordinate drawing.
6. The original ESO-served EHT publication JPEG is unchanged with visible EHT Collaboration credit and CC BY 4.0. Model diagrams and exported calculations are separate original teaching material.
7. The paper activity practices interpreting supplied model cards. It is not an empirical light-bending experiment. Specialist review, learner trials and full device/export review remain pending.
8. A one-way causal boundary: In the classical description, the event horizon separates events that can send future-directed light signals to distant observers from those that cannot. It is not a solid surface glowing in the observed image.
9. One explicit geometry: The Schwarzschild exterior is nonrotating, uncharged and spherical. Set r_g=GM/c². The chosen static observer is at 50 r_g and the invented source sphere at 1000 r_g. These are authored positions, not Earth’s location relative to M87*.
10. Areal radius is not every distance: A sphere of areal radius r has area 4πr². Plotting x=r cosφ and y=r sinφ gives a useful coordinate projection, but does not reproduce every proper spatial length or local angle in curved geometry.
11. Exterior null paths: With u=1/r and r_g=1, u″=3u²−u. The first integral is u′²+u²−2u³=1/b². The incoming derivative at the observer is determined by this relation; the code does not use a Newtonian force on a light particle.
12. The critical distinction: The horizon has r=2, the unstable circular null orbit has r=3 and the critical impact parameter is b_c=3√3. For the chosen inward directions, b<b_c is captured, b>b_c returns outward, and b=b_c approaches the unstable orbit asymptotically.
13. Static angle and image radius: The static observer measures sinψ=b√(1−2/50)/50. A local camera uses radius proportional to tanψ. An impact map instead uses radius proportional to b. Switching projection keeps the selected physical ray unchanged.
14. Unwrapped angles matter: The accumulated angle can exceed 360°. First interpolate the full angle, then use its sine and cosine to find a source direction. Interpolating wrapped directions across 360° would produce a false intermediate source.
15. Closest approach: For a returning path, the outer turning radius satisfies b²=r₀³/(r₀−2), with r₀>3. It is not correct to place the turn at r=b. Finite-endpoint accumulated angle is also different from deflection defined at infinity.
16. A bounded lookup: The map uses 512 logarithmically spaced knots over 1.001≤b/b_c≤3.1. Independently checked midpoint angular error is below 4.781×10⁻⁶ radians. Returning mappings closer to criticality are deliberately unresolved; a colored or hatched indication is computational scope, not matter.
17. Two images of a finite patch: For the fixed aligned 2° source patch, centers occur near b=15.337679493438 and b=5.202001640146 r_g. The latter corresponds to an additional winding. Its radial width is about 0.000409681 r_g. Geometry alone does not supply observed radiometric brightness.
18. Shadow and illumination: Under the stated background illumination, captured backward-traced directions lack a returning source connection. An unlit returning direction can also be dark. The independent status label prevents color from being mistaken for proof of capture.
19. Observation is reconstructed evidence: The EHT combined interferometric radio measurements. Independent image reconstructions, tests with synthetic data and comparisons across observing days supported the principal structure. Reconstruction does not make the evidence an arbitrary invented drawing.
20. A measured size is not a direct horizon ruler: The 2019 analysis reports an emission-region diameter of 42±3 microarcseconds. Inferring mass or a horizon scale also uses distance and emission modeling. The published broad structure did not separately resolve every predicted photon subring.
21. Compactness is not unlimited suction: A hypothetical object with the Sun’s same gravitational mass concentrated into a black hole would not automatically pull Earth out of its distant orbit. This is a same-mass thought experiment, not the Sun’s predicted future.

What has been checked

Analytical reference cases, conservation or transition invariants, finite drawing commands, bounded setup parsing, discovery and route integrity are checked automatically. These checks do not establish anatomical fidelity, learner outcomes or browser/device compatibility. Independent subject review, learner trials, comprehensive accessibility review and browser video encoding checks remain pending.

Each source supports the associated claim. Sources do not certify this implementation or its visuals.

About the cover illustration

Original calculated Schwarzschild exterior source map. Colors label an invented numbered background, not predicted brightness. The separately credited EHT Collaboration radio reconstruction appears inside the lesson with its original source and CC BY 4.0 license.