Interaction research sequence

Numbered calculations with their assumptions and subsequent corrections.

1. Question

• Question

  Research record, section 1: Question.

2. Two different notions of encounter

• Two different notions of encounter

  Research record, section 2: Two different notions of encounter.

3. Electron-electron scattering is therefore not the same as electron-electron full-depth contact

• Electron-electron scattering is therefore not the same as electron-electron full-depth contact

  Research record, section 3: Electron-electron scattering is therefore not the same as electron-electron full-depth contact.

4. General depth-mediated interaction rule

• General depth-mediated interaction rule

  Research record, section 4: General depth-mediated interaction rule.

5. First comparison with the observed interaction pattern

• First comparison with the observed interaction pattern

  Research record, section 5: First comparison with the observed interaction pattern.

11. Next proof obligations

• Next proof obligations

  Research record, section 11: Next proof obligations.

14. Central full-depth dynamics does not by itself prove unobserved-visible coincidence

• Central full-depth dynamics does not by itself prove unobserved-visible coincidence

  Research record, section 14: Central full-depth dynamics does not by itself prove unobserved-visible coincidence.

18. A stronger invariant candidate from two complex structures

• A stronger invariant candidate from two complex structures

  Research record, section 18: A stronger invariant candidate from two complex structures.

19. Exchange symmetry and Pauli suppression of full-depth contact

• Exchange symmetry and Pauli suppression of full-depth contact

  Research record, section 19: Exchange symmetry and Pauli suppression of full-depth contact.

20. Generalization to unequal particle depths

• Generalization to unequal particle depths

  Research record, section 20: Generalization to unequal particle depths.

24. Present verdict

• Present verdict

  Research record, section 24: Present verdict.

25. Pair-invariant collapse on the electron sector

• Pair-invariant collapse on the electron sector

  Research record, section 25: Pair-invariant collapse on the electron sector.

26. Direct projection of the current V2 scalar quartic into a two-electron channel

• Direct projection of the current V2 scalar quartic into a two-electron channel

  Research record, section 26: Direct projection of the current V2 scalar quartic into a two-electron channel.

28. Historical quadratic kernel as a candidate pre-contact force

• Historical quadratic kernel as a candidate pre-contact force

  Research record, section 28: Historical quadratic kernel as a candidate pre-contact force.

29. First direct verdict on $K_{66}$ from presently written V2

• First direct verdict on $K_{66}$ from presently written V2

  Research record, section 29: First direct verdict on $K_{66}$ from presently written V2.

30. Electromagnetic pre-contact steering: a dimensional Green-function test

• Electromagnetic pre-contact steering: a dimensional Green-function test

  Research record, section 30: Electromagnetic pre-contact steering: a dimensional Green-function test.

31. A useful decomposition of the electromagnetic problem

• A useful decomposition of the electromagnetic problem

  Research record, section 31: A useful decomposition of the electromagnetic problem.

32. Can a pulled-back depth-two connection reduce unobserved transverse momentum?

• Can a pulled-back depth-two connection reduce unobserved transverse momentum?

  Research record, section 32: Can a pulled-back depth-two connection reduce unobserved transverse momentum?.

33. Consequence for the original electron-beam proposal

• Consequence for the original electron-beam proposal

  Research record, section 33: Consequence for the original electron-beam proposal.

34. Updated verdict after testing the current scalar and electromagnetic sectors

• Updated verdict after testing the current scalar and electromagnetic sectors

  Research record, section 34: Updated verdict after testing the current scalar and electromagnetic sectors.

35. Projector-dynamics audit of the remaining unobserved-steering channel

• Projector-dynamics audit of the remaining unobserved-steering channel

  Research record, section 35: Projector-dynamics audit of the remaining unobserved-steering channel.

37. Next proof obligation

• Next proof obligation

  Research record, section 37: Next proof obligation.

38. Correction: do not extrapolate ordinary 3D field equations into the higher sector

• Correction: do not extrapolate ordinary 3D field equations into the higher sector

  Research record, section 38: Correction: do not extrapolate ordinary 3D field equations into the higher sector.

39. The inverse lifting problem from observed electromagnetism

• The inverse lifting problem from observed electromagnetism

  Research record, section 39: The inverse lifting problem from observed electromagnetism.

40. Compression is not the same as effective reduced dynamics

• Compression is not the same as effective reduced dynamics

  Research record, section 40: Compression is not the same as effective reduced dynamics.

41. The reciprocal pushforward formulation is more faithful to current V2

• The reciprocal pushforward formulation is more faithful to current V2

  Research record, section 41: The reciprocal pushforward formulation is more faithful to current V2.

42. First classification of observationally invisible higher-depth operators

• First classification of observationally invisible higher-depth operators

  Research record, section 42: First classification of observationally invisible higher-depth operators.

43. Implication for visible-unobserved collision correlation

• Implication for visible-unobserved collision correlation

  Research record, section 43: Implication for visible-unobserved collision correlation.

44. Minimal self-adjoint unobserved-visible lock with exactly zero relaxed backreaction

• Minimal self-adjoint unobserved-visible lock with exactly zero relaxed backreaction

  Research record, section 44: Minimal self-adjoint unobserved-visible lock with exactly zero relaxed backreaction.

45. Canonical free-pair operator from two electron complex structures

• Canonical free-pair operator from two electron complex structures

  Research record, section 45: Canonical free-pair operator from two electron complex structures.

46. Quaternionic structure of the free-pair active four-space

• Quaternionic structure of the free-pair active four-space

  Research record, section 46: Quaternionic structure of the free-pair active four-space.

47. Simultaneous commutant and its limited no-mixing theorem

• Simultaneous commutant and its limited no-mixing theorem

  Research record, section 47: Simultaneous commutant and its limited no-mixing theorem.

48. One- and two-vector outer-product mixed ansatzes

• One- and two-vector outer-product mixed ansatzes

  Research record, section 48: One- and two-vector outer-product mixed ansatzes.

49. Beam-adapted $3+3$ frame links recover the pair invariant exactly

• Beam-adapted $3+3$ frame links recover the pair invariant exactly

  Research record, section 49: Beam-adapted $3+3$ frame links recover the pair invariant exactly.

50. Conditional relative-separation theorem under two individual beam locks

• Conditional relative-separation theorem under two individual beam locks

  Research record, section 50: Conditional relative-separation theorem under two individual beam locks.

51. Two individual locks reduce to one exact relative restoring mode

• Two individual locks reduce to one exact relative restoring mode

  Research record, section 51: Two individual locks reduce to one exact relative restoring mode.

54. Electromagnetic two-form alignment: compatibility, circularity, and rank obstruction

• Electromagnetic two-form alignment: compatibility, circularity, and rank obstruction

  Research record, section 54: Electromagnetic two-form alignment: compatibility, circularity, and rank obstruction.

55. Candidate scan for a dynamically selected mixed frame

• Candidate scan for a dynamically selected mixed frame

  Research record, section 55: Candidate scan for a dynamically selected mixed frame.

56. Orthonormalized scattering-frame candidate and exact Schur compatibility

• Orthonormalized scattering-frame candidate and exact Schur compatibility

  Research record, section 56: Orthonormalized scattering-frame candidate and exact Schur compatibility.

57. Variational derivation of the scattering-selected frame link

• Variational derivation of the scattering-selected frame link

  Research record, section 57: Variational derivation of the scattering-selected frame link.

58. Frequency normalization requires the correct lock coordinate and kinetic metric

• Frequency normalization requires the correct lock coordinate and kinetic metric

  Research record, section 58: Frequency normalization requires the correct lock coordinate and kinetic metric.

59. Audit of existing V2 candidates for the dimensionless lock coefficient

• Audit of existing V2 candidates for the dimensionless lock coefficient

  Research record, section 59: Audit of existing V2 candidates for the dimensionless lock coefficient.

60. Maurer--Cartan test: the scattering frame alone cannot generate its own restoring curvature

• Maurer--Cartan test: the scattering frame alone cannot generate its own restoring curvature

  Research record, section 60: Maurer--Cartan test: the scattering frame alone cannot generate its own restoring curvature.

61. Projector-curvature candidate: nonzero geometry beyond the pure-gauge frame map

• Projector-curvature candidate: nonzero geometry beyond the pure-gauge frame map

  Research record, section 61: Projector-curvature candidate: nonzero geometry beyond the pure-gauge frame map.

62. Canonical projector geometry: the rank-three Grassmannian has isotropic Ricci eigenvalue four

• Canonical projector geometry: the rank-three Grassmannian has isotropic Ricci eigenvalue four

  Research record, section 62: Canonical projector geometry: the rank-three Grassmannian has isotropic Ricci eigenvalue four.

63. Grassmannian sigma-model and Jacobi audit: where the eigenvalue four actually enters

• Grassmannian sigma-model and Jacobi audit: where the eigenvalue four actually enters

  Research record, section 63: Grassmannian sigma-model and Jacobi audit: where the eigenvalue four actually enters.

64. Dirac-projector commutator: a conditional sigma-model construction

• Dirac-projector commutator: a conditional sigma-model construction

  Research record, section 64: Dirac-projector commutator: a conditional sigma-model construction.

65. Linear Dirac-action variation does not fix the projector sigma-model coefficient

• Linear Dirac-action variation does not fix the projector sigma-model coefficient

  Research record, section 65: Linear Dirac-action variation does not fix the projector sigma-model coefficient.

66. Orbit-generator spectrum versus the physical mixed block

• Orbit-generator spectrum versus the physical mixed block

  Research record, section 66: Orbit-generator spectrum versus the physical mixed block.

67. Moment maps do not automatically select the frame-lock orbit

• Moment maps do not automatically select the frame-lock orbit

  Research record, section 67: Moment maps do not automatically select the frame-lock orbit.

68. Orbit-rate audit: three electron clocks are distinct until the stationary master generator identifies them

• Orbit-rate audit: three electron clocks are distinct until the stationary master generator identifies them

  Research record, section 68: Orbit-rate audit: three electron clocks are distinct until the stationary master generator identifies them.

71. Axial mixed tensors do not determine the orbit-generator spectrum

• Axial mixed tensors do not determine the orbit-generator spectrum

  Research record, section 71: Axial mixed tensors do not determine the orbit-generator spectrum.

72. Beam-axis spinor decomposition: the orbit generator requires a bilinear lock term

• Beam-axis spinor decomposition: the orbit generator requires a bilinear lock term

  Research record, section 72: Beam-axis spinor decomposition: the orbit generator requires a bilinear lock term.

73. Three-axis contraction test: summing three depth-six channels does not yield the required axial bilinear

• Three-axis contraction test: summing three depth-six channels does not yield the required axial bilinear

  Research record, section 73: Three-axis contraction test: summing three depth-six channels does not yield the required axial bilinear.

74. Orbit generator as a polynomial of the total locked axial spin

• Orbit generator as a polynomial of the total locked axial spin

  Research record, section 74: Orbit generator as a polynomial of the total locked axial spin.

75. Locked-spin gap theorem: the orbit polynomial is uniquely fixed by the existing unit and two-unit projective gaps

• Locked-spin gap theorem: the orbit polynomial is uniquely fixed by the existing unit and two-unit projective gaps

  Research record, section 75: Locked-spin gap theorem: the orbit polynomial is uniquely fixed by the existing unit and two-unit projective gaps.

76. Gap-origin audit: primitive winding and orientation reversal do not derive the two-unit branch

• Gap-origin audit: primitive winding and orientation reversal do not derive the two-unit branch

  Research record, section 76: Gap-origin audit: primitive winding and orientation reversal do not derive the two-unit branch.

77. Extremal-doublet audit: the two-unit gap follows from a primitive signed amplitude charge, but that charge is still an input

• Extremal-doublet audit: the two-unit gap follows from a primitive signed amplitude charge, but that charge is still an input

  Research record, section 77: Extremal-doublet audit: the two-unit gap follows from a primitive signed amplitude charge, but that charge is still an input.

78. Primitive cocharacter norm test: the desired amplitude charge is the unique minimum-norm choice

• Primitive cocharacter norm test: the desired amplitude charge is the unique minimum-norm choice

  Research record, section 78: Primitive cocharacter norm test: the desired amplitude charge is the unique minimum-norm choice.

79. Rejected identification audit: an embedded-$U(1)$ curvature would select $q=1$, but it is not the Hopf connection

• Rejected identification audit: an embedded-$U(1)$ curvature would select $q=1$, but it is not the Hopf connection

  Research record, section 79: Rejected identification audit: an embedded-$U(1)$ curvature would select $q=1$, but it is not the Hopf connection.

81. Beam-axis symmetry leaves the integral charge free

• Beam-axis symmetry leaves the integral charge free

  Research record, section 81: Beam-axis symmetry leaves the integral charge free.

82. Physical $(3,1)\oplus(1,3)$ audit: beam symmetry leaves $q$ free; frame exchange would select $q=1$

• Physical $(3,1)\oplus(1,3)$ audit: beam symmetry leaves $q$ free; frame exchange would select $q=1$

  Research record, section 82: Physical $(3,1)\oplus(1,3)$ audit: beam symmetry leaves $q$ free; frame exchange would select $q=1$.

83. Reciprocity audit: Hermiticity does not force observed-unobserved exchange symmetry

• Reciprocity audit: Hermiticity does not force observed-unobserved exchange symmetry

  Research record, section 83: Reciprocity audit: Hermiticity does not force observed-unobserved exchange symmetry.

84. Locked-sector preservation theorem: invariance of the $\mathbf1\oplus\mathbf3$ split uniquely selects $q=1$

• Locked-sector preservation theorem: invariance of the $\mathbf1\oplus\mathbf3$ split uniquely selects $q=1$

  Research record, section 84: Locked-sector preservation theorem: invariance of the $\mathbf1\oplus\mathbf3$ split uniquely selects $q=1$.

85. Operator-class refinement: the unwanted $q\neq1$ piece is a singlet--triplet vector intertwiner

• Operator-class refinement: the unwanted $q\neq1$ piece is a singlet--triplet vector intertwiner

  Research record, section 85: Operator-class refinement: the unwanted $q\neq1$ piece is a singlet--triplet vector intertwiner.

86. Relative-frame identification: the $q\neq1$ mixer is exactly a broken frame-rotation generator

• Relative-frame identification: the $q\neq1$ mixer is exactly a broken frame-rotation generator

  Research record, section 86: Relative-frame identification: the $q\neq1$ mixer is exactly a broken frame-rotation generator.

87. Fixed-lock compatibility theorem: $q=1$ is the unique zero-drift branch of the selected frame

• Fixed-lock compatibility theorem: $q=1$ is the unique zero-drift branch of the selected frame

  Research record, section 87: Fixed-lock compatibility theorem: $q=1$ is the unique zero-drift branch of the selected frame.

93. Conditional mixed-bilinear singlet selector

• Conditional mixed-bilinear singlet selector

  Research record, section 93: Conditional mixed-bilinear singlet selector.

94. Correction to Section 93: the Levi--Civita mixed connection contracts to mean curvature and does not by itself supply the nine-component lock operator

• Correction to Section 93: the Levi--Civita mixed connection contracts to mean curvature and does not by itself supply the nine-component lock operator

  Research record, section 94: Correction to Section 93: the Levi--Civita mixed connection contracts to mean curvature and does not by itself supply the nine-component lock operator.

95. Quadratic cross-depth route: a first-order $3\leftrightarrow6$ transition can generate the full $(\mathbf3,\mathbf3)$ lock after Schur elimination

• Quadratic cross-depth route: a first-order $3\leftrightarrow6$ transition can generate the full $(\mathbf3,\mathbf3)$ lock after Schur elimination

  Research record, section 95: Quadratic cross-depth route: a first-order $3\leftrightarrow6$ transition can generate the full $(\mathbf3,\mathbf3)$ lock after Schur elimination.

97. Cross-depth channel audit: the canonical factorized normal-spinor contraction does not lock the frames

• Cross-depth channel audit: the canonical factorized normal-spinor contraction does not lock the frames

  Research record, section 97: Cross-depth channel audit: the canonical factorized normal-spinor contraction does not lock the frames.

98. Leading-source orientation no-go: the written scalar and factorized $3\leftrightarrow6$ structures can select $s$ but cannot select the locked frame orientation

• Leading-source orientation no-go: the written scalar and factorized $3\leftrightarrow6$ structures can select $s$ but cannot select the locked frame orientation

  Research record, section 98: Leading-source orientation no-go: the written scalar and factorized $3\leftrightarrow6$ structures can select $s$ but cannot select the locked frame orientation.

99. Correction to the rank-three requirement: a generic rank-two orbital bivector uniquely selects an $SO(3)$ frame by orientation-preserving Procrustes completion

• Correction to the rank-three requirement: a generic rank-two orbital bivector uniquely selects an $SO(3)$ frame by orientation-preserving Procrustes completion

  Research record, section 99: Correction to the rank-three requirement: a generic rank-two orbital bivector uniquely selects an $SO(3)$ frame by orientation-preserving Procrustes completion.