Re-run of the package from an extracted copy of release/source.zip (sha256 d275ccfd6b47424a20d9ba7ab4cb7eb85e6fd62bc2e5a91a156f3e4f2281bb06), 2026-10-15, run 2
command: python -I check_note.py > check_note_rerun.out (in reproducibility/ of the extracted copy; nice -n 10)
running time: 10.320 total
diff of the reports without the lines that record running times:
(no differences)

--- the re-run report ---
check_note.py -- exact checks for the note on fare zone assignment with hard cut budgets (record OWR-14298804-012)
python 3.13.5, networkx 3.6.1
(i) Section 3: congestion at most two (Lemmas 3.1, 3.2, Theorem 3.3) and the merge remark
  A1 random trees (3-11 vertices, congestion <= 2): instances=3000, with parallel H-edges=1114, with some u_i=0=1586, with 0<OPT<w(E)=2155, max |E|=10, 0/1 vectors checked for Lemma 3.1=667996, maximal/partial matchings checked for Lemma 3.2=9000
  A2 random set systems (not paths; every element in <= 2 sets; arbitrary w_e >= 0): instances=3000, with parallel H-edges=1327, with some u_i=0=1501, with 0<OPT<w(E)=2333, 0/1 vectors=727104, matchings=9000
  A3 triangle on a star (congestion 2): OPT=2, LP value at y=1/2: 3
  A4 merge remark: 600 random tree instances with repeated paths: edge weights, feasible sets (every 0/1 vector) and congestion counts as claimed
  time: 6.2 s
(ii) Section 4 (stars and independent sets) and Section 5 (column-sparse packing)
  B1 fixed graphs: K4: OPT=3=3*alpha; Petersen: OPT=12=3*alpha; K33: OPT=9=3*alpha; Q3: OPT=12=3*alpha; C5: OPT=4=2*alpha; K5: OPT=4=4*alpha
  B2a Lemma 4.1, both instances, every 0/1 vector, all 2497 pairs (H, d) with H one of the graphs on 1-7 vertices of the networkx graph atlas and d = max(Delta(H),1) or Delta(H)+1
  B2b Lemma 4.1, both instances, every 0/1 vector: 12 random cubic graphs on 4-12 vertices (unit weights, congestion 3) and 1500 random graphs on 1-9 vertices with maximum degree <= d, d in [1, 2, 3, 4, 5, 6, 7]
  B3 Proposition 4.5(a) on 3000 random stars (budgets 0-3, repeated paths, congestion up to 14): feasible <=> forced zeros + independent in H, max degree(H) <= congestion, OPT = MWIS
  B4 Proposition 4.5(c): 5 congestion-1 star instances realizing K_2 (all of them with budgets <= 2, weights <= 4): spoke weights always equal, never proportional to (3,1); w(s_1) <= sum of the other spoke weights on 800 random realizations of K_(k+1), k=2..5
  B5 Remark 4.6: k=1: LP>=1, OPT=1; k=2: LP>=3, OPT=2; k=3: LP>=6, OPT=3; k=4: LP>=10, OPT=4; k=5: LP>=15, OPT=5; k=6: LP>=21, OPT=6
  B6 Corollary 4.4: best single admissible edge feasible and within factor |E| on 1500 random trees
  C1 Theorem 5.1 on 3000 random trees (congestion up to 10): preprocessing keeps OPT, budgets >= 1, column sparsity <= congestion; 1859 unit-budget instances: feasible <=> pairwise disjoint sets (every 0/1 vector), no (k+1)-claw (11407 candidate claws examined)
  time: 3.0 s
(iii) Section 6: total unimodularity (Lemma 6.1) and Propositions 6.2, 6.3
  T1 interval matrices (subpaths of a path; Proposition 6.2(a)): 500 matrices, all totally unimodular
  T2 rooted instances (paths from one vertex; Proposition 6.2(b)): 500 matrices, all totally unimodular
  T3 split matrices of Proposition 6.3 (vertical segments): 500 matrices, all totally unimodular
  T4 arbitrary vertical paths in rooted trees (Lemma 6.1): 500 matrices, all totally unimodular
  T5 negative control: 34 of 500 matrices of arbitrary tree paths are NOT totally unimodular; the star matrix rows {s1,s2},{s2,s3},{s1,s3} has determinant 2
  determinants evaluated exactly in T1-T5: 314536
  G1 Proposition 6.3 chain on 3000 random trees (1227 with all non-vacuous budgets even, 383 with a budget-1 commodity on a longer path made vacuous by blocked edges; congestion up to 7): split-feasible => feasible (every 0/1 vector), y*/t split-feasible, t*OPT(split) >= OPT; largest t = 3; worst OPT/OPT(split) = 3 (all non-vacuous budgets even: 2)
  G2 negative control (budget 1, path of two edges): OPT=1, split optimum=0
  time: 1.0 s
TOTAL failures: 0
RESULT: ALL CHECKS PASSED
time: 10.2 s
