feat(Order/Causal): add Causal ordering for stream functions

[matthunz]

Adds Causal ordering for stream functions and related theorems:

def Causal (f : Stream' α → Stream' β) : Prop :=
  ∀ (x y : Stream' α) (t : ℕ), (∀ s, s ≤ t → x s = y s) → f x t = f y t

A stream function is causal if the output at time t depends only on inputs up to time t. Causal stream functions are commonly used in signal processing, reactive systems, and semantics of stateful computations, where outputs cannot depend on future inputs.

Future work

• Mealy machines: define Mealy machines as causal stream functions with state, and relate them to standard automata-theoretic constructions.
• Feedback and delay operators: formalize feedback loops and delayed composition, enabling modeling of stateful and recursive stream definitions.

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[github-actions]

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[github-actions]

PR summary 205a0ba54c

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.Order.Causal.Defs (new file)	70
Mathlib.Order.Causal.Basic (new file)	71

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Declarations diff

+ Causal
+ causal_comp
+ causal_id
+ enum_causal
+ map_causal

You can run this locally as follows

## summary with just the declaration names:
./scripts/pr_summary/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh contains some details about this script.

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No changes to technical debt.

You can run this locally as

./scripts/reporting/technical-debt-metrics.sh pr_summary

• The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
• The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).