feat(network): PLP on converging sink-trees via topological relabel (REQ-NC-PLP-CONVERGE-001)

[avrabe]

Summary

Fires PLP (REQ-NC-PLP-001) on single-successor converging sink-trees handed in non-topological order — the many-talkers→one-listener TSN shape that v0.18 shipped rejecting (PlpError::NonTopologicalSinkTree). plp_bound now topologically relabels servers (Kahn, smallest-index-first) as a pure permutation before the sink-tree projection, so the sink lands at the highest index — the invariant the per-flow solve assumes.

Sound with no change to the bound: TFA/PLP are invariant under server renumbering, and a single-successor + acyclic graph is a rooted in-forest that always admits a topological order. The former reject guard is repurposed as a post-relabel invariant (never panics; Errs only if the topo sort is buggy).

This is the converging-tree precursor split out of REQ-NC-PLP-002; the generic/cyclic core remains there (gated on not-yet-generated cyclic fixtures).

Correctness discovery — PLP and TFA are incomparable

This feature's bridge test surfaced that the shipped "PLP ≤ TFA" universal claim was false. Pure polynomial PLP and TFA are incomparable over-approximations — both sound (≥ exact), neither dominates. On the deliberately pathological converging-bridge net (10000-µs-slow-switch), panco's own PLP exceeds its own TFA:

flow	panco PLP	panco TFA	panco EXACT
dataA	1148.33µs	1048.09µs	1035.2µs

spar reproduces panco's PLP to the decimal → the relabel is correct; the sandwich claim was the error. Fixes:

• Bridge test asserts index alignment (slow-stream PLP dominates fast ×5), not a sandwich.
• Per-fixture plp ≤ TFA pins kept, but relabelled as per-fixture regression pins (not a universal law) in check_plp + docs.
• REQ-NC-PLP-001 / BRIDGE-001 text corrected; authoritative per-flow bound min(PLP, TFA) filed as REQ-NC-PLP-MIN-001 (backlog).

Verification

• plp.rs permutation-invariance unit test: relabelled bound == same net presented topologically.
• 3 panco-pinned converging xval fixtures: converge_2to1 (48.89 ≪ 60.39), converge_2to1_tail2 (60.0 ≪ 106.44, the 1.77× wedge), converge_3to1 (70.0 ≪ 74.59 µs).
• Full suites green: spar-network 134, spar-analysis 883. fmt + clippy clean.
• TEST-NC-PLP-CONVERGE oracle step filter corrected (plp_converge_xval matched zero tests → plp_xval::panco_converge).

Falsification

If the topological relabel were not a pure permutation, the converging tree's per-flow bound would differ from the same physical network presented sink-last — the permutation-invariance test would fail. If pure PLP were universally ≤ TFA, the converging-bridge counterexample (panco PLP 1148 > TFA 1048) could not exist.

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Codecov Report

❌ Patch coverage is 98.80952% with 1 line in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
crates/spar-network/src/plp.rs	98.71%	1 Missing ⚠️

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