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Animation 20
Phase as the $[\hat X,\hat K]$ commutator
symmetry-ccr-loop-complex.mp4
These are sparse samples decoded from the current MP4, not newly rendered illustrations. They can support checks of the sampled states and labels, but cannot establish continuous motion, timing, transitions, or the absence of problems between samples. Use the full MP4 when judging those properties.
1440 × 900 · 30 fps · 16 s · 480 frames · 12 samples
MP4 SHA-256 4786dad4ba257da869a943a9098907eb5375beed47e425551094e870bdcf7f70
Frame manifest · Context markdown · Download complete review packet
Chapter context
Section: The Heisenberg Symmetry Group. Excerpts are verbatim; line numbers refer to the included chapter markdown.
Caption
Phase as the $[\hat X,\hat K]$ commutator
Image description
A complex spiral follows an x–k loop and returns to its original magnitude envelope with a quarter-turn of phase remaining
Before the animation
Chapter lines 986–990
Chapter lines 992–996
After the animation
Chapter lines 1004–1004
The infinitesimal closed $x$-$k$ loop is generated by $[\hat X,\hat K]$. Because the finite loop leaves a phase translation, and phase translations are generated by $iI$, we have:
Chapter lines 1006–1010
Generation source
Main script --render draws the ordered +k,+x,-k,-x loop and uses the imported packet-phase script for shared artwork, math, and encoding libraries. --check and --encoded-check produce companion checks; there is no input movie.
Mapping evidence and limits
Exact NAME match. Matching validation records the -pi/2 residual phase, 480 frames, 30 fps, 1440 x 900, 16 s, and final hold after 13 s. Matching encoded-validation.json confirms the frame count and renderer comparisons.
Source SHA-256 values identify the exact downloadable bytes in this packet. The source mapping and recorded checks explain the likely generation pipeline; they do not prove that these exact source bytes produced the movie. A GitHub link pinned to a commit is provided only when the delivered source bytes exactly match that path at the build's Git HEAD.
- scripts/generate_symmetry_ccr_loop_complex.py · GitHub at 974f9de35254
SHA-256 2b515b256661caab4a377b29bdbc4d0e384d054039842e8b4b05a432a6947e27 - scripts/generate_symmetry_packet_phase_modes.py · GitHub at 974f9de35254
SHA-256 47fdf5353988db4807c5e9a21545b3f5dc44b097d7a5b077eec2889333f57edb
Existing generator checks (2 reports)
These are existing author-produced generator reports, copied without changes. Their checks were not rerun for this packet and are not independent certification. A report may describe an earlier generation run; inspect its contents before applying its claims to the current movie.
- symmetry-ccr-loop-complex-validation.json
SHA-256 5a2fe33023d8e94ff5b8b4e26893c10a71542b29bfbf7932add277e34c6d5185 - symmetry-ccr-loop-complex-encoded-validation.json
SHA-256 73753f668bb54cbf3a14e22838c462e0d75a134188e956a59b8f203d8c6ce7eb
Decoded contact sheet
Extraction method: Twelve evenly spaced decoded frame indices, including first and last. Native-resolution JPEGs from the encoded MP4; timestamps read from FFmpeg showinfo. No source rerendering. Frame indices are zero-based. Sparse samples do not establish continuous motion or capture every transition.. Frame indices are zero-based.
Full-size sampled frames
