Restore flow ILP overhead predictions with capacity bit lengths

[isPANN]

Superseded by #1174. This PR’s changes were included in the combined squash commit 8bdddd45 on fix/exact-reduction-parameters. Continue review and fixes in #1174. The original description below is retained for reference.

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Motivation

Stacked on #1180 (base branch: fix/bounded-ilp-variants). That PR makes bounded integer ILP encoding explicit, but four flow reductions still cannot predict ILP numeric magnitude and therefore cannot predict the size of their binary ILP and QUBO targets.

This PR restores those predictions using one intrinsic statistic per flow model and fixes two domain/schema defects found during the audit.

Changes

• Add computed max_capacity_bits to IntegralFlowBundles, IntegralFlowWithMultipliers, UndirectedFlowLowerBounds, and UndirectedTwoCommodityIntegralFlow. It measures existing capacities (bundle capacities for IntegralFlowBundles), with a minimum of one; constructors take no additional input.
• Reuse capacity-based requirement normalization. Requirements beyond attainable flow remain infeasible; oversized demands no longer inflate target coefficients.
• Normalize nonterminal multipliers to min(multiplier, total_capacity + 1), with saturating arithmetic. Above total capacity, positive integral inflow would require impossible outflow, so the replacement preserves feasibility.
• Declare the local bound max_constraint_magnitude_bits <= max_capacity_bits + num_arcs + 1 (or num_edges + 1) in each flow-to-bounded-ILP rule. Every RHS uses only source parameters.
• Propagate capacity bits from DecisionMaximumIndependentSet exactly as 2, and from Partition with the upper bound max_numeric_magnitude_bits + num_elements.

Three flow models previously had no capacity-scale parameter. Multiplier flow already has raw max_capacity, but capacity bits allow the incoming Partition chain to compose without variable-exponent support. The raw capacity field remains available on concrete instances and in the model's complexity expression; its symbolic prediction from Partition remains explicitly unavailable. Downstream ILP size predictions do not depend on it.

API and validation changes

Contract	Before	After
UndirectedFlowLowerBounds construction	Accepted negative lower bounds	Enforces 0 <= lower <= capacity consistently through the shared constructor
Multiplier flow prediction parameters	Included signed requirement, causing a panic when negative	Removes requirement from the canonical parameter schema; preserves the signed construction field, serialization, and getter
Four flow parameter schemas	No capacity bit-length statistic	Add max_capacity_bits

No new variants or model-level inference mechanisms are introduced.

Verified behavior

• For edges (0,1) and (2,3), capacities [1,10], lower bounds [-5,0], and demand 5 from 0 to 1, the base branch reports feasible through source brute force but infeasible through ILP. The new constructor rejects this invalid input.
• Inspecting multiplier flow with requirement -1 previously panicked on conversion to an unsigned parameter. It now succeeds and reports capacity bits; the signed requirement remains instance data.
• CLI reductions through bounded ILP, binary ILP, and QUBO recover a valid lower-bound-flow witness (8 QUBO variables) and a valid two-commodity witness with a negative demand (15 QUBO variables). Corresponding demands of i64::MAX remain infeasible after solving and recovery.
• Tests cover both incoming chains through QUBO: feasible witnesses recover successfully, and odd/even infeasible Partition instances cannot decode a witness.
• Direct ILP rules with incomplete parameter contracts decrease from 26 to 22. This count concerns direct ILP entries, not every possible graph path.

Validation

Regression tests were run failing before implementation, including the validation defect, negative-parameter panic, coefficient normalization, and missing composed predictions.

• cargo test --features example-db --workspace -- --include-ignored: 6,893 passed.
• cargo fmt --all --check: passed.
• cargo clippy --workspace --all-targets --all-features -- -D warnings: passed.
• make paper: passed.
• Focused LLVM coverage: 37/37 changed executable production lines covered.
• CLI checks exercise construction/inspection, explicit reduction routes, solving, and recovered source evaluation. Extreme coefficient tests establish construction and parameter bounds; they do not claim every extreme instance can be solved numerically by the ILP backend.

Stack refresh

Merged the updated parent #1180, carrying the construction-derived bounds and validation fixes from #1174 through the stack. Preserved this PR's bounded ILP types, numeric-magnitude fields, and algorithms; no instance fixtures were added. The PR remains based on its immediate parent.

Validation of the updated head: make check passed (formatting, all-target/all-feature Clippy, and workspace tests including ignored tests). GitHub CI is restricted to PRs targeting main or develop, so these stack branches were checked locally.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 96.76%. Comparing base (05fed6f) to head (2841e0c).

Additional details and impacted files

@@                    Coverage Diff                     @@
##           fix/bounded-ilp-variants    #1182    +/-   ##
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  Coverage                     96.75%   96.76%            
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  Files                          1072     1072            
  Lines                        140481   140656   +175     
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+ Hits                         135928   136103   +175     
  Misses                         4553     4553            

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[isPANN]

Merged to #1174.