(not-to-merge) kicking the tires: dense subset sum in btsim by bc1cindy · Pull Request #86 · payjoin/tx-indexer

bc1cindy · 2026-06-01T13:23:53Z

wires the dense-subset-sum 4-path subset-sum/coinjoin-mapping counts (brute, radix, sparse, sasamoto) into btsim two ways:

as agent cost: WLowerBoundMetric (W lower bound via brute/sparse) and RadixMappingMetric (k×m! denomination mappings, gated by radix density) plug into the existing PrivacyBundle. With a subset_sum_threshold / radix_threshold set in ScorerConfig, each candidate plan is scored by a linear deficit to the threshold, so agents favor coinjoins with more subset-sum ambiguity.
as measurement: four_counts runs all four paths over the sim's confirmed txs recording CPU, peak RAM (alloc-probe feature), and density regime (kappa via the L bracket). Plus a correctness benchmark against the dep's oracle, a kappa/L sweep, a switch_sweep locating the sparse->Sasamoto handoff, and a CJA comparison (W vs Maurer sub-transaction mappings).

adds denominated funding (standard-denomination UTXOs in a band, via mine_denominated) so the sim can produce dense coinjoins, and fixes a latent over-spend in coin selection that the dense funding exposed (select_all now returns None unless inputs cover the target; session contribution is gated on coverage).

    N | κ    | sparse     | sparse_us | sasa_err% | spearman
    8 | 0.50 | Exact      |    152    |   18.0    |   0.810
   12 | 0.33 | Exact      |    469    |   19.1    |   0.936
   14 | 0.29 | LowerBound |   1179    |    5.3    |   1.000
   22 | 0.18 | LowerBound |   5957    |    2.4    |   1.000


N=14 (κ≈0.29) the sparse convolution stops being exact (its sumset exceeds the budget, CPU climbs 152→5957µs) and precisely there the Sasamoto error drops to ≤5% (spearman→1.0). In other words: where sparse becomes too costly, Sasamoto becomes the good estimator.

the metric is wired + unit-tested, but it doesn't yet steer the sim, emergent coinjoins are still sparse (same-seed runs are identical with the threshold on or off). Driving the sim to produce dense coinjoins is a separate work

BTSIM_CORRECTNESS=1 cargo run - 4 paths vs oracle, κ/L sweep, switch_sweep, CJA

(sparse_mem_budget=4096 entries, dp_max=4000000 cells, radix_max_size=6)
family | N | ground_truth | sparse_kind | sasamoto_err% | spearman | brute_us | radix_us | sparse_us | sasa_us | peakB | lb_ok | aborts | radix_dense | regime
   pow2 |  9 |  exhaustive |    Exact |          7.3 |    0.997 |      144 |       69 |       158 |      88 |         0 |    ok |        - |         yes | κ ∈ [0.3333, 5.3033], κ_c ∈ [0.9849, 0.0000], regime = Transitional
   pow2 | 12 |  exhaustive |    Exact |          6.0 |    0.999 |     1821 |       70 |       356 |     114 |         0 |    ok |        - |         yes | κ ∈ [0.3333, 3.9429], κ_c ∈ [0.9979, 0.0000], regime = Transitional
   pow2 | 15 |  exhaustive |    Exact |          5.5 |    1.000 |        0 |       44 |       687 |      83 |         0 |    ok |        b |         yes | κ ∈ [0.3333, 3.1328], κ_c ∈ [0.9723, 0.0000], regime = Transitional
   pow2 | 18 |  exhaustive |    Exact |          5.4 |    1.000 |        0 |       56 |      2747 |      90 |         0 |    ok |        b |         yes | κ ∈ [0.3333, 2.5961], κ_c ∈ [0.9343, 0.0000], regime = Transitional
   pow2 | 21 |  exhaustive |    Exact |          5.4 |    1.000 |        0 |       57 |      5228 |      87 |         0 |    ok |        b |         yes | κ ∈ [0.3333, 2.2146], κ_c ∈ [0.8939, 0.0000], regime = Transitional
   pow2 | 24 |          dp | LowerBnd |          5.3 |    1.000 |        0 |       51 |     18466 |      93 |         0 |    ok |        b |         yes | κ ∈ [0.3333, 1.9298], κ_c ∈ [0.8549, 0.0000], regime = Transitional
   pow2 | 27 |          dp | LowerBnd |          5.3 |    1.000 |        0 |       51 |     48313 |      89 |         0 |    ok |        b |         yes | κ ∈ [0.3333, 1.7091], κ_c ∈ [0.8187, 0.0000], regime = Transitional
   pow2 | 30 |          dp | LowerBnd |          5.3 |    1.000 |        0 |       54 |    127480 |     106 |         0 |    ok |        b |         yes | κ ∈ [0.3333, 1.5331], κ_c ∈ [0.7857, 0.0000], regime = Transitional
   pow2 | 33 |          dp | LowerBnd |          5.3 |    1.000 |        0 |       79 |    277263 |      93 |         0 |    ok |        b |         yes | κ ∈ [0.3333, 1.3895], κ_c ∈ [0.7557, 0.0000], regime = Transitional
   pow2 | 36 |          dp | LowerBnd |          5.3 |    1.000 |        0 |      234 |    294995 |      93 |         0 |    ok |        b |         yes | κ ∈ [0.3333, 1.2703], κ_c ∈ [0.7284, 0.0000], regime = Transitional
   pow2 | 39 |          dp | LowerBnd |          5.3 |    1.000 |        0 |      269 |    368619 |      93 |         0 |    ok |        b |         yes | κ ∈ [0.3333, 1.1696], κ_c ∈ [0.7036, 0.0000], regime = Transitional
   pow2 | 42 |          dp | LowerBnd |          5.3 |    1.000 |        0 |      654 |    605093 |     114 |         0 |    ok |        b |         yes | κ ∈ [0.3333, 1.0835], κ_c ∈ [0.6810, 0.0000], regime = Transitional
  radix |  9 |  exhaustive |    Exact |         98.7 |    0.277 |      138 |       57 |       137 |      89 |         0 |    ok |        - |         yes | κ ∈ [1.1073, 5.3033], κ_c ∈ [0.8599, 0.0000], regime = Sparse
  radix | 12 |  exhaustive |    Exact |         97.4 |    0.355 |     1371 |       63 |       316 |     128 |         0 |    ok |        - |         yes | κ ∈ [0.8333, 3.9429], κ_c ∈ [0.7907, 0.0000], regime = Sparse
  radix | 15 |  exhaustive |    Exact |         95.4 |    0.346 |        0 |       93 |       869 |      87 |         0 |    ok |        b |         yes | κ ∈ [0.7007, 3.1328], κ_c ∈ [0.9517, 0.0000], regime = Transitional
  radix | 18 |  exhaustive |    Exact |         92.8 |    0.322 |        0 |       93 |      3850 |      86 |         0 |    ok |        b |         yes | κ ∈ [0.6092, 2.5961], κ_c ∈ [0.9921, 0.0000], regime = Transitional
  radix | 21 |  exhaustive | LowerBnd |         90.5 |    0.329 |        0 |       88 |     15555 |     104 |         0 |    ok |        b |         yes | κ ∈ [0.5238, 2.2146], κ_c ∈ [0.9726, 0.0000], regime = Transitional
  radix | 24 |          dp | LowerBnd |         88.8 |    0.430 |        0 |      419 |     39919 |     102 |         0 |    ok |        b |         yes | κ ∈ [0.4623, 1.9298], κ_c ∈ [0.9650, 0.0000], regime = Transitional
  radix | 27 |          dp | LowerBnd |         83.7 |    0.419 |        0 |      731 |    128886 |      95 |         0 |    ok |        b |         yes | κ ∈ [0.4444, 1.7091], κ_c ∈ [0.9817, 0.0000], regime = Transitional
  radix | 30 |          dp | LowerBnd |         88.1 |    0.273 |        0 |     1116 |    369665 |     109 |         0 |    ok |        b |         yes | κ ∈ [0.4032, 1.5331], κ_c ∈ [0.9932, 0.0000], regime = Transitional
arbitrary |  3 |  exhaustive |    Exact |            - |        - |        4 |   124344 |        33 |     101 |         0 |    ok |        - |          no | κ ∈ [7.1722, 16.4381], κ_c ∈ [0.9383, 0.0001], regime = Sparse
arbitrary |  4 |  exhaustive |    Exact |        100.0 |      NaN |        5 |      827 |        27 |      90 |         0 |    ok |        - |          no | κ ∈ [5.4829, 12.2248], κ_c ∈ [0.9657, 0.0001], regime = Sparse
arbitrary |  5 |  exhaustive |    Exact |        100.0 |    0.000 |        8 |   229100 |        67 |     112 |         0 |    ok |        - |          no | κ ∈ [4.4507, 9.7155], κ_c ∈ [0.9782, 0.0002], regime = Sparse
arbitrary |  6 |  exhaustive |    Exact |        100.0 |    0.506 |       16 |    14082 |        71 |      92 |         0 |    ok |        - |          no | κ ∈ [3.7528, 8.0524], κ_c ∈ [0.9849, 0.0002], regime = Sparse
arbitrary |  7 |  exhaustive |    Exact |        100.0 |    0.502 |       32 |   342637 |       122 |      95 |         0 |    ok |        - |          no | κ ∈ [3.2484, 6.8703], κ_c ∈ [0.9889, 0.0002], regime = Sparse
arbitrary |  8 |  exhaustive |    Exact |        100.0 |    0.490 |       72 |       63 |       158 |      92 |         0 |    ok |        - |          no | κ ∈ [2.8664, 5.9874], κ_c ∈ [0.9915, 0.0003], regime = Sparse
arbitrary |  9 |  exhaustive |    Exact |        100.0 |    0.522 |      156 |   469217 |       316 |      98 |         0 |    ok |        - |          no | κ ∈ [2.5668, 5.3033], κ_c ∈ [0.9933, 0.0003], regime = Sparse
arbitrary | 10 |  exhaustive |    Exact |        100.0 |    0.531 |      339 |   518922 |       419 |     116 |         0 |    ok |        - |          no | κ ∈ [2.3253, 4.7577], κ_c ∈ [0.9946, 0.0003], regime = Sparse
arbitrary | 11 |  exhaustive |    Exact |        100.0 |    0.531 |      701 |   567600 |       542 |      98 |         0 |    ok |        - |          no | κ ∈ [2.1265, 4.3127], κ_c ∈ [0.9955, 0.0004], regime = Sparse
arbitrary | 12 |  exhaustive |    Exact |        100.0 |    0.535 |     1503 |      973 |       712 |     102 |         0 |    ok |        - |          no | κ ∈ [1.9597, 3.9429], κ_c ∈ [0.9962, 0.0004], regime = Sparse
random_dense |  8 |  exhaustive |    Exact |         18.0 |    0.810 |       70 |       47 |       137 |      92 |         0 |    ok |        - |         yes | κ ∈ [0.5000, 5.9874], κ_c ∈ [0.9979, 0.0000], regime = Transitional
random_dense | 10 |  exhaustive |    Exact |          9.1 |    0.989 |      324 |       46 |       283 |      93 |         0 |    ok |        - |         yes | κ ∈ [0.3700, 4.7577], κ_c ∈ [0.9988, 0.0000], regime = Transitional
random_dense | 12 |  exhaustive |    Exact |         19.1 |    0.936 |     1503 |       47 |       426 |      92 |         0 |    ok |        - |         yes | κ ∈ [0.3333, 3.9429], κ_c ∈ [0.8686, 0.0000], regime = Transitional
random_dense | 14 |  exhaustive | LowerBnd |          5.3 |    1.000 |     6834 |       47 |      1315 |      94 |         0 |    ok |        - |         yes | κ ∈ [0.2857, 3.3637], κ_c ∈ [0.9859, 0.0000], regime = Transitional
random_dense | 16 |  exhaustive | LowerBnd |          2.9 |    0.999 |        0 |       48 |      2302 |      90 |         0 |    ok |        b |          no | κ ∈ [0.2500, 2.9312], κ_c ∈ [0.9343, 0.0000], regime = Transitional
random_dense | 18 |  exhaustive | LowerBnd |          2.6 |    1.000 |        0 |       53 |      3395 |     103 |         0 |    ok |        b |         yes | κ ∈ [0.2222, 2.5961], κ_c ∈ [0.9915, 0.0000], regime = Transitional
random_dense | 20 |  exhaustive | LowerBnd |          2.7 |    1.000 |        0 |       50 |      3366 |      99 |         0 |    ok |        b |         yes | κ ∈ [0.2000, 2.3289], κ_c ∈ [0.9691, 0.0000], regime = Transitional
random_dense | 22 |  exhaustive | LowerBnd |          2.4 |    1.000 |        0 |       55 |      6241 |      93 |         0 |    ok |        b |         yes | κ ∈ [0.1818, 2.1109], κ_c ∈ [0.9930, 0.0000], regime = Transitional
random_dense | 24 |          dp | LowerBnd |          2.7 |    1.000 |        0 |       59 |     11700 |      93 |         0 |    ok |        b |         yes | κ ∈ [0.1667, 1.9298], κ_c ∈ [0.9979, 0.0000], regime = Transitional

kappa sweep @ N=20 (Sasamoto error vs oracle as density falls):
kappa | regime | sasamoto_err% | spearman
0.15 | κ ∈ [0.1500, 2.3289], κ_c ∈ [0.9584, 0.0000], regime = Transitional |          2.6 |    1.000
0.20 | κ ∈ [0.2000, 2.3289], κ_c ∈ [0.9808, 0.0000], regime = Transitional |          2.7 |    1.000
0.25 | κ ∈ [0.2477, 2.3289], κ_c ∈ [0.9767, 0.0000], regime = Transitional |          2.7 |    1.000
0.30 | κ ∈ [0.2977, 2.3289], κ_c ∈ [0.9809, 0.0000], regime = Transitional |          3.9 |    0.999
0.35 | κ ∈ [0.3471, 2.3289], κ_c ∈ [0.9806, 0.0000], regime = Transitional |          3.0 |    0.999
0.40 | κ ∈ [0.3968, 2.3289], κ_c ∈ [0.9809, 0.0000], regime = Transitional |          3.6 |    0.999

switch sweep @ l_max=16, sparse budget=512 (where sparse stops being exact, Sasamoto takes over):
N | kappa | sparse_kind | sparse_us | sparse_peakB | sasamoto_err% | spearman
8 |  0.50 |       Exact |       180 |            0 |          18.0 |    0.810
10 |  0.40 |       Exact |       340 |            0 |           9.1 |    0.989
12 |  0.33 |       Exact |       498 |            0 |          19.1 |    0.936
14 |  0.29 |    LowerBnd |      1481 |            0 |           5.3 |    1.000
16 |  0.25 |    LowerBnd |      2605 |            0 |           2.9 |    0.999
18 |  0.22 |    LowerBnd |      3791 |            0 |           2.6 |    1.000
20 |  0.20 |    LowerBnd |      3550 |            0 |           2.7 |    1.000
22 |  0.18 |    LowerBnd |      7195 |            0 |           2.4 |    1.000

CJA: W vs sub-transaction mappings (both anonymity facets) on small coinjoins:
label | n_in | n_out | non_derived | entropy_bits | sasamoto_log | w_lookup_log
cja_0 |    4 |     4 |           1 |         0.00 |         -inf |         -inf
cja_1 |    4 |     4 |           7 |         2.81 |         1.19 |         1.10
cja_2 |    3 |     3 |           1 |         0.00 |         0.33 |         0.00

BTSIM_FOUR_COUNTS=1 CONFIG_FILE=dense_small.toml cargo run - 4 paths over the sim's confirmed txs

tx_index | primitive | log2W/count | lower-bound? | status | cpu_us | peak_bytes
     0 |    brute |        0.00 |         true | Computed |     685 |          0
     0 |    radix |       12.08 |         true | Computed |     130 |          0
     0 |   sparse |        0.00 |         true | Computed |     461 |          0
     0 | sasamoto |           - |        false | Computed |   16828 |          0
     1 |    brute |           - |         true | Computed |       6 |          0
     1 |    radix |           - |         true | Computed | 1137067 |          0
     1 |   sparse |           - |         true | Computed |      28 |          0
     1 | sasamoto |           - |        false | Computed |       4 |          0
     2 |    brute |           - |         true | Computed |       6 |          0
     2 |    radix |           - |         true | Computed |   16993 |          0
     2 |   sparse |           - |         true | Computed |      18 |          0
     2 | sasamoto |           - |        false | Computed |     173 |          0
primitive | runs | aborted | with_count | med_cpu_us | max_cpu_us | med_peak_B | max_peak_B
 brute |    3 |       0 |          3 |          6 |        723 |          0 |         0
 radix |    3 |       0 |          3 |      16936 |    1149301 |          0 |         0
sparse |    3 |       0 |          3 |         32 |        459 |          0 |         0
sasamoto |    3 |       0 |          0 |        173 |      16964 |          0 |         0
tx_index | density regime (best/worst-L bracket at midpoint E)
     0 | κ ∈ [8.0548, 12.2248], κ_c ∈ [0.8561, 0.0031], regime = Sparse
     1 | κ ∈ [33.1300, 50.8993], κ_c ∈ [0.0000, 0.0043], regime = Sparse
     2 | κ ∈ [18.0000, 50.8993], κ_c ∈ [0.0000, 0.0000], regime = Sparse
Total payment obligations: 8
Missed payment obligations percentage: 0.625
Total block weight used (wu): 14086
Average fee cost (sats): 1466707716

related to #84

Wires the dense-subset-sum 4-path subset-sum/coinjoin-mapping counts (brute, radix, sparse, Sasamoto) into btsim two ways: - As agent cost: WLowerBoundMetric (W lower bound via brute/sparse) and RadixMappingMetric (k×m! denomination mappings, gated by radix density) plug into the existing PrivacyBundle. With a subset_sum_threshold / radix_threshold set in ScorerConfig, each candidate plan is scored by a linear deficit to the threshold, so agents favor coinjoins with more subset-sum ambiguity. - As measurement: four_counts runs all four paths over the sim's confirmed txs recording CPU, peak RAM (alloc-probe feature), and density regime (kappa via the L bracket). Plus a correctness benchmark against the dep's oracle, a kappa/L sweep, a switch_sweep locating the sparse->Sasamoto handoff, and a CJA comparison (W vs Maurer sub-transaction mappings). Adds denominated funding (standard-denomination UTXOs in a band, via mine_denominated) so the sim can produce dense coinjoins, and fixes a latent over-spend in coin selection that the dense funding exposed (select_all now returns None unless inputs cover the target; session contribution is gated on coverage).

bc1cindy mentioned this pull request Jun 1, 2026

Add radix-ness classifier as first step of the radix lower-bound path #85

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arminsabouri force-pushed the master branch from a9d30e9 to b0ccf7a Compare June 13, 2026 21:42

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(not-to-merge) kicking the tires: dense subset sum in btsim#86

(not-to-merge) kicking the tires: dense subset sum in btsim#86
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bc1cindy commented Jun 1, 2026

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bc1cindy commented Jun 1, 2026

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