nav: dyn_bike's front slip in its wheel's frame, as dyn_4w's (f_eps = 0) - #852

Follows transfix/libcvc#852: dyn_plant's front slip becomes the wheel-frame
slip dyn4's tires use, alpha_f = -atan2(w_f, u_f) with w_f = cos(delta)
(vy + lf r) - sin(delta) vx (n_f.v) and u_f the floored forward speed in
the wheel's frame, its secant rooted at w_f = 0. The implicit step's
Jacobian takes the front's -S_f cos^2(delta) (1, lf) on the body's y.

In the pH twin, R's front term is S_f n_f n_f^T, f_eps is round-off, and
DynPHParts gains uf and loses w0f.

The three fixtures are regenerated by libcvc#852: dyn_bike_golden.json,
dyn_bike_ph_golden.json, and material_ext_golden.json (its dynamic case;
the surrogate and bicycle cases are byte-identical).

Measured (torch 2.8 CPU), worst relative difference from libcvc: plant 0
(next state) and 2.8e-16 (gradient); pH parts 3.4e-16, rates 3.4e-16,
books 7.1e-14, books gradient 4.4e-14. The floor power is at most 6e-13 W
on the golden's cases. The swerve's residual still falls 3.94x / 3.97x per
halving of the step.

…852), and the pH twin (#138)

The plant's front slip is now measured in its wheel's frame, as the
four-wheel model's: alpha_w = -atan2(n_w.v, sqrt((t_w.v)^2 + eps^2)), each
rooted at n_w.v = 0 (transfix/libcvc#852). The paper follows:
- Section 3: the directions come first, then the slips in the wheels'
  frames; the old front slip is noted.
- Lemma 1 holds at every steering angle (the secant through w = 0, slope
  P C B u_w / (u_w^2 + w^2) at the root); f_eps is the root branch's
  rounding only.
- Section 4.2 and Proposition 1: R's front term is S_f n_f n_f^T, and the
  vehicle is passive from the drive port alone at every floor.
- Section 4.4: S_f ~ C_f / u_f; the front tire's power is exactly its
  dissipation but for the root branch's rounding.
- Section 4.5: the floor reaches only the slips' forward speeds;
  TheFloorTermIsRoundOff measures at most 2.2e-16 of the flow; the old
  remainder and its eps^2 numbers are kept as history.
- Section 4.7: k_f is the wheel-frame slip's exact sensitivity (eq. kf),
  checked by the new TheTangentIsTheTiresDerivative (1.4e-7).
- Section 5.2: braking limiter -358 J, residual 4e-6.
- Section 10: the four-wheel form now carries the single track's over.
- Tables: the plant table gains the renamed floor test and the tangent
  test, with #852's numbers; the live plant's rows move to their own table
  (the plant table no longer fit a page); the twins table and the GRL-SNAM
  validation rows gain #138's pH twin (test_dyn_bike_ph_parity, 18 passed,
  worst 7.1e-14).
- Section 8.2-8.3, Python access and the equation-to-code map: the pH
  form's parts, rates and books are twinned in GRL-SNAM #138.
- Appendix A: #852's and #138's branch commits, and the printed lines at
  1a0acc77 with the c1f104c0 values they replace.
- Versions: #852.

Built with TeX Live pdflatex, three passes: 27 pages, no warnings.

…t slip in its wheel's frame (#138)

Two commits, for Joe to review before merging:
1. a torch twin of libcvc's single-track vehicle in port-Hamiltonian form, with its per-step energy books;
2. `dyn_bike`'s front slip moved into its wheel's frame, following libcvc.

They sit beside `dyn_plant` in `grl_snam/dyn_bike.py`. The whitepaper (#137, `docs/vehicle-ph-plant.tex` §8.2–8.3 and §10) lists the twin as missing.

**1. The pH twin** (held to libcvc's `DynBikePH.Golden`, transfix/libcvc#848). New in `grl_snam/dyn_bike.py`, mirroring libcvc's `dyn_ph_*` in `cvc/nav/detail/dyn_bike.h`:
- `dyn_ph_parts_at`: everything the form is built from at a state:
  - the axle forces (the port);
  - the tires' lateral forces and secant stiffnesses;
  - `u`, `sg`, `uf` and `Dx`;
  - the vectors `n_f`, `n_r`, `t_f`, `t_r`.
- `dyn_ph_rates_at`: the power balance dH/dt = supplied − dissipated + floor + grade.
- `dyn_ph_hamiltonian`: ½ vᵀMv.
- `dyn_plant_books`: `dyn_plant`'s step, unchanged, plus its books:
  - the trapezoid of the rates between the step's start (with the actuators' outputs δ₁, a₁) and the twist the step reached before its limiters;
  - `limiter`: dH across the speed clamp and the low-speed blend;
  - `residual`: the rest.
- `dyn_plant(..., with_free=True)` also returns the pre-limiter twist (libcvc's `dyn_step_free`).
- `dyn_plant`'s step 2 moves into `_axles`, which the parts share.

`tests/test_dyn_bike_ph_parity.py` checks the twin against `dyn_bike_ph_golden.json`, double tier, 1e-9 relative, on eight Humvee cases. Each case checks:
- the parts and the rates;
- one step's next state, pre-limiter twist and books;
- the autograd gradient of a weighting of the books against libcvc's forward-mode duals.

The file also tests that a batch books like its rows. A torch-only gate checks that the books close to second order on a swerve.

**2. The wheel-frame front slip** (follows transfix/libcvc#852, approved by Joe). The front slip becomes the wheel-frame slip `dyn4`'s tires use:
- alpha_f = −atan2(w_f, u_f);
- w_f = cos δ (vy + lf r) − sin δ vx, which is n_f·v;
- u_f is the floored forward speed in the wheel's frame;
- the secant is rooted at w_f = 0.

The implicit step's Jacobian takes the front tire's −S_f cos² δ (1, lf) on the body's y. In the pH twin, R's front term becomes S_f n_f n_fᵀ, and f_ε is round-off. Three fixtures are regenerated from libcvc#852:
- `dyn_bike_golden.json`;
- `dyn_bike_ph_golden.json`;
- `material_ext_golden.json`: only its dynamic case changes; the surrogate and bicycle cases are byte-identical.

**Measured** (torch 2.8, CPU, after both commits):
- Worst relative difference from libcvc:

  | Values | Worst relative difference |
  |---|---|
  | Plant next state | 0 |
  | Plant gradient | 2.8e-16 |
  | pH parts | 3.4e-16 |
  | pH rates | 3.4e-16 |
  | Books | 7.1e-14 |
  | Books gradient | 4.4e-14 |
- On the golden's cases, the floor power is at most 6e-13 W.
- On the swerve, the mean |residual| per step falls 3.94× and then 3.97× per halving of the step.
- `test_dyn_bike_parity`, `test_dyn_bike_ph_parity`, `test_material_ext_parity`, `test_dyn4_parity` and `test_material_bike_parity` give 57 passed and 6 skipped. The skips are live-pycvc checks that this machine's pycvc lacks.
- ruff and black are clean on the changed files.

pycvc has no dynamic binding, so none of this depends on a pycvc release.

… review fixes, links (#140)

* docs(vehicle-ph-plant): reproduce appendix, steering as a modulation, review fixes, links

- Appendix A: the exact setup behind every measured value (libcvc c1f104c0,
  MSVC 19.44, CMake 3.31.7, Ninja 1.12.1, cvcpkg 2.5.6, torch 2.8.0+cpu);
  the Windows commands that were run, with the extra CMake flags and why;
  the Linux/macOS equivalents (not run verbatim here; libcvc's CI runs the
  suites on every platform); each test's printed lines; GRL-SNAM's pytest
  line and its expected 53 passed, 2 skipped.
- Section 6.6 rewritten for the learned plant's steering: the reference
  form books power through steering (13.4% of |y.u| on the golden fit;
  5.6% on a fit to the analytic plant, which books none). The opt-in
  modulated form (transfix/libcvc#851) has D(v, delta) and G(v, delta), with
  the drive alone as the port. A new validation table holds its tests.
- The learned plant's provenance corrected: public CVC-Lab/LieSPHGP has no
  SE(2) vehicle; the port and its golden follow an SE(2) package built on it
  at 65db994. LieSPHGP's own trainers use the EKF ELBO.
- Review fixes:
  - the dynamic plant is 3.7.0 (#714), the learned plant 3.7.1 (#758);
  - psi for the kinematic heading (theta is the grade);
  - a "mixed" parity tier;
  - the sharp check's wording and its 3.5e-5;
  - the health-check range;
  - test totals, the CTest regex and NavPotential.DriveForce*;
  - the GRL-SNAM paper's full title.
- Links from README.md and the guide's "See also".

pdflatex: 26 pages, three passes, no warnings.

* docs(vehicle-ph-plant): the front slip in its wheel's frame (libcvc #852), and the pH twin (#138)

The plant's front slip is now measured in its wheel's frame, as the
four-wheel model's: alpha_w = -atan2(n_w.v, sqrt((t_w.v)^2 + eps^2)), each
rooted at n_w.v = 0 (transfix/libcvc#852). The paper follows:
- Section 3: the directions come first, then the slips in the wheels'
  frames; the old front slip is noted.
- Lemma 1 holds at every steering angle (the secant through w = 0, slope
  P C B u_w / (u_w^2 + w^2) at the root); f_eps is the root branch's
  rounding only.
- Section 4.2 and Proposition 1: R's front term is S_f n_f n_f^T, and the
  vehicle is passive from the drive port alone at every floor.
- Section 4.4: S_f ~ C_f / u_f; the front tire's power is exactly its
  dissipation but for the root branch's rounding.
- Section 4.5: the floor reaches only the slips' forward speeds;
  TheFloorTermIsRoundOff measures at most 2.2e-16 of the flow; the old
  remainder and its eps^2 numbers are kept as history.
- Section 4.7: k_f is the wheel-frame slip's exact sensitivity (eq. kf),
  checked by the new TheTangentIsTheTiresDerivative (1.4e-7).
- Section 5.2: braking limiter -358 J, residual 4e-6.
- Section 10: the four-wheel form now carries the single track's over.
- Tables: the plant table gains the renamed floor test and the tangent
  test, with #852's numbers; the live plant's rows move to their own table
  (the plant table no longer fit a page); the twins table and the GRL-SNAM
  validation rows gain #138's pH twin (test_dyn_bike_ph_parity, 18 passed,
  worst 7.1e-14).
- Section 8.2-8.3, Python access and the equation-to-code map: the pH
  form's parts, rates and books are twinned in GRL-SNAM #138.
- Appendix A: #852's and #138's branch commits, and the printed lines at
  1a0acc77 with the c1f104c0 values they replace.
- Versions: #852.

Built with TeX Live pdflatex, three passes: 27 pages, no warnings.

* docs(vehicle-ph-plant): cite #138's squash commit 2f76ab0

The #138 rows, the reproduction appendix and the versions table now cite main at 2f76ab0, where the dynamic twins' parity tests pass again (57 passed, 6 skipped for pycvc). The PDF is rebuilt: 27 pages, no warnings.

* docs(vehicle-ph-plant): the point-mass books' twin (#139) and pycvc's tick telemetry (libcvc #857)

- Table 9 (the twins) gains the navigator's point-mass books: book_step,
  energy_residual_bound, material_energy and integrate_surrogate_material's
  books hook, held to libcvc's NavPotential.BooksGolden. book_step on
  libcvc's arguments is held to 1e-12 (double tier); the books are held to
  1e-5 of the step's bound, and 2e-5 on the clamped rollout (float tier).
- 8.3, "What is not twinned yet": the point-mass books are twinned. The tick
  telemetry is a running world's, so it has no twin; libcvc #857 binds it in
  pycvc (nav_sim_world_set_capture_drive_telemetry,
  nav_sim_world_drive_telemetry).
- 8.4 gains "Book the navigator's energy": how to ask for the books, the
  measured parity (1.1e-6 and 8.3e-8 of the bound), and the curved-patch
  caveat. On a patch whose gradient channels are not its values' gradients,
  each step books the force/-grad U gap, which fills 99.65% of the bound at
  h = 0.002. It also says where a live world's context work comes from.
- 10, "Python access", and the equation-to-code map: updated to match.

PDF rebuilt with TeX Live pdflatex, three passes: 28 pages, no warnings.

The project version and the cvcpkg recipe family move to 3.7.2. Every recipe is at cvc_revision 1
already, so none restarts.

3.7.2 carries the dynamic plants on the terrain and in a Jolt world, and the four-wheel plant
(#869): --plant dynamic and dynamic4w drive the ground, collide with the
buildings and each other, and book the collisions. It also carries dyn_4w's port-Hamiltonian form
(#850), dyn_bike's wheel-frame front slip (#852), the books goldens for GRL-SNAM's twins (#848,
#849), pycvc's drive telemetry (#857) and keep-alives (#864), the macOS SDK's openssl (#846), and
the state_exec scheduler and evaluator work (#842, #843, #844, #861, #863).