feat: sketch for a Julia template and MWE

[jpbrodrick89]

@dionhaefner I know you're working on your own version of this and I definitely don't want to step on any toes, but I've been playing around with this a bit in the background and thought it better to have in the open to work out what direction we want to go in (both/and is potentially a possibility too). I'm not a Julia expert by any means and this probably needs some more cycles if we go with it, but this seems to work when packages support Enzyme (not all do). Happy to hear how you want play it.

I tried to give an example using a simple linear solver with verifiable gradients that could be useful in a Jax setting as no Jax packages expose modified Cholesky.

[codecov]

Codecov Report

❌ Patch coverage is 20.87912% with 72 lines in your changes missing coverage. Please review.
✅ Project coverage is 69.63%. Comparing base (ea2dbcc) to head (328a661).
⚠️ Report is 9 commits behind head on main.

Files with missing lines	Patch %	Lines
...esseract_core/sdk/templates/julia/tesseract_api.py	11.68%	68 Missing ⚠️
tesseract_core/sdk/engine.py	60.00%	0 Missing and 2 partials ⚠️
...sseract_core/runtime/testing/finite_differences.py	75.00%	0 Missing and 1 partial ⚠️
...seract_core/sdk/templates/julia/julia/Project.toml	75.00%	1 Missing ⚠️

❗ There is a different number of reports uploaded between BASE (ea2dbcc) and HEAD (328a661). Click for more details.

HEAD has 2 uploads less than BASE

Flag	BASE (ea2dbcc)	HEAD (328a661)
	33	31

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #552      +/-   ##
==========================================
- Coverage   77.13%   69.63%   -7.50%     
==========================================
  Files          32       35       +3     
  Lines        4356     4499     +143     
  Branches      717      745      +28     
==========================================
- Hits         3360     3133     -227     
- Misses        712     1082     +370     
  Partials      284      284              

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[PasteurBot]

Benchmark Results

Benchmarks use a no-op Tesseract to measure pure framework overhead.

🚀 0 faster, ⚠️ 0 slower, ✅ 36 unchanged

✅ No significant performance changes detected.

Full results

Benchmark	Baseline	Current	Change	Status
api/apply_1,000	0.495ms	0.495ms	+0.1%	✅
api/apply_100,000	0.498ms	0.498ms	+0.1%	✅
api/apply_10,000,000	0.497ms	0.499ms	+0.4%	✅
cli/apply_1,000	1650.711ms	1657.890ms	+0.4%	✅
cli/apply_100,000	1653.257ms	1645.324ms	-0.5%	✅
cli/apply_10,000,000	1682.491ms	1684.052ms	+0.1%	✅
decoding/base64_1,000	0.029ms	0.029ms	+0.3%	✅
decoding/base64_100,000	0.970ms	0.970ms	+0.0%	✅
decoding/base64_10,000,000	106.318ms	106.556ms	+0.2%	✅
decoding/binref_1,000	0.178ms	0.177ms	-0.5%	✅
decoding/binref_100,000	0.227ms	0.233ms	+2.9%	✅
decoding/binref_10,000,000	8.648ms	8.562ms	-1.0%	✅
decoding/json_1,000	0.100ms	0.100ms	+0.2%	✅
decoding/json_100,000	9.490ms	9.601ms	+1.2%	✅
decoding/json_10,000,000	1119.859ms	1117.219ms	-0.2%	✅
encoding/base64_1,000	0.028ms	0.028ms	+0.1%	✅
encoding/base64_100,000	0.144ms	0.145ms	+0.3%	✅
encoding/base64_10,000,000	22.061ms	21.778ms	-1.3%	✅
encoding/binref_1,000	0.263ms	0.262ms	-0.1%	✅
encoding/binref_100,000	0.430ms	0.427ms	-0.8%	✅
encoding/binref_10,000,000	16.496ms	16.755ms	+1.6%	✅
encoding/json_1,000	0.144ms	0.144ms	+0.4%	✅
encoding/json_100,000	14.514ms	14.551ms	+0.3%	✅
encoding/json_10,000,000	1514.957ms	1512.533ms	-0.2%	✅
http/apply_1,000	2.912ms	3.099ms	+6.4%	✅
http/apply_100,000	8.007ms	8.276ms	+3.4%	✅
http/apply_10,000,000	663.527ms	666.111ms	+0.4%	✅
roundtrip/base64_1,000	0.059ms	0.059ms	+0.7%	✅
roundtrip/base64_100,000	1.126ms	1.123ms	-0.2%	✅
roundtrip/base64_10,000,000	128.577ms	129.030ms	+0.4%	✅
roundtrip/binref_1,000	0.454ms	0.453ms	-0.2%	✅
roundtrip/binref_100,000	0.667ms	0.664ms	-0.5%	✅
roundtrip/binref_10,000,000	25.671ms	25.378ms	-1.1%	✅
roundtrip/json_1,000	0.253ms	0.252ms	-0.5%	✅
roundtrip/json_100,000	21.975ms	21.197ms	-3.5%	✅
roundtrip/json_10,000,000	2630.813ms	2636.945ms	+0.2%	✅

• Runner: Linux 6.17.0-1008-azure x86_64