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fix: preserve DeepSeek system fingerprints in response metadata (#19413)

## Background

DeepSeek callers could receive text and usage, but could not access the
response system fingerprint in provider metadata for generated or
streamed responses.

## Root Cause

The DeepSeek JSON and SSE response schemas omitted system_fingerprint,
and the language model implementation never mapped it into provider
metadata; recorded responses and failing generate/stream assertions
confirmed the field was discarded.

## Summary

Parsed system_fingerprint for JSON responses and SSE chunks, exposed it
as providerMetadata.deepseek.systemFingerprint, retained the latest
non-null streamed value, documented the metadata, and added a patch
changeset.

## Testing

Added generate and stream regression coverage for present, repeated,
changed, null, and missing fingerprints while preserving existing
content and usage snapshots.

## End-to-end Validation

- `pnpm -C examples/ai-functions exec tsx --eval "…"` called the live
DeepSeek generate and stream APIs; both returned text and the same
non-empty system fingerprint in provider metadata.

## Related Issues

Fixes #19386

Closes #19395

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Co-authored-by: ai-sdk-factory <308175966+ai-sdk-factory@users.noreply.github.com>
Co-authored-by: gr2m <39992+gr2m@users.noreply.github.com>
A
ai-sdk-factory[bot] committed
348dacb230ba43ba88e5c98dae4e1ef7dda462fc
Parent: e7fc90e
Committed by GitHub <noreply@github.com> on 8/24/2026, 11:19:11 PM