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[[300,104,3]] d =
n
300
k
104
d
3
kd²/n
3.12
w
8
X/Z
1
g
0.0023
r
6.0828
layers
2
swaps
1231

Share this result

Distance

X/Z asymmetry 1 · d_X = 3, d_Z = 3 · w_X = 8, w_Z = 8 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)
d_X 3 · witness weight 3 (claimed upper_bound)
witness found by @mathysrennela · research/kit/surrogate.lightest_logical · found at 2000 trials · survived 2000 trials · 2026-10-12
witness operator (support, 3 qubits)
[150, 153, 161]
d_Z 3 · witness weight 3 (claimed upper_bound)
witness found by @mathysrennela · research/kit/surrogate.lightest_logical · found at 2000 trials · survived 2000 trials · 2026-10-12
witness operator (support, 3 qubits)
[90, 113, 130]
certificate exact, d = 3 · CryptoMiniSat 5.14.7 SAT
X: no logical < 3 exists; Z: no logical < 3 exists

Diagnostics

computed by the verifier from the parity checks, the layout, and the stored witnesses; shown as evidence, not used for ranking
girth H_X 4 · H_Z 4 (shortest cycle of each side’s Tanner graph; longer is friendlier to belief propagation)
check weights H_X 8 · H_Z 8
qubit degrees H_X 4 · H_Z 4
trapping sets H_X (1,4)×300 (2,4)×1200 (3,0)×100 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,4): 300 (2,4): 1200 (2,6): 1800 (3,0): 100 (3,4): 4500 (3,6): 15600 (3,8): 15000
trapping sets H_Z (1,4)×300 (2,4)×1200 (3,0)×100 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,4): 300 (2,4): 1200 (2,6): 1800 (3,0): 100 (3,4): 4500 (3,6): 15600 (3,8): 15000
witness diameter X 2.0 · Z 3.0 (Euclidean support diameter of the stored distance witnesses in the layout; an upper bound on the exhibited logicals’ spread, not a minimum over all logicals)

Verified 2D layout

as measured by the verifier: every check drawn over the submitted coordinates; the interaction radius is the longest dashed pair
layout contributed by @MathysRennela · Simulated annealing over integer-grid site assignments with the repo's own research/local2d/fold_layout.search_layout, single layer at radius 4 then two layers at 7, plus a divisor scan of the two-block index convention Z_l x Z_m which gives the tighter embedding here; radius and per-site occupancy re-measured with the verifier's own rule. · 2026-10-13
r = 6.083
X checkZ checkqubit site (158)2 qubits stacked (2 layers)dashed: the pair setting the interaction radiushover a check to isolate its qubits; click to pin — repeated clicks cycle through overlapping checks; click empty space to release
routing cost 1231 nearest-neighbor SWAPs per round in total, at most 12 for one check (heuristic: MST lower bound on the layout, with one lattice step = the minimum qubit spacing 1; not a rank)

Construction & provenance

authors Lee, Gideon
provenance literature baseline
construction Two-block group-algebra code C(a,b) over C5 x D30 = SmallGroup(150, 11) (order 150), elements numbered as in GAP Elements(SmallGroup(order,id)) with element 0 the identity. n = 2|G| = 300; H_X = [L(a)|R(b)], H_Z = [R(b)^T|L(a)^T]; a = {0, 3, 5, 15}, b = {0, 3, 22, 42} as element indices. Check weight 8. Parameters and blocks taken from the public code database of arXiv:2610.13880v1 (Lee, 'Bicycle Race'), github.com/gideonlsx/bicycle-race.
model Mimo-V2.6-Flash (claimed, not verified)
date 2026-10-12
notes Parameters and construction taken from the public database of arXiv:2610.13880v1. Distance is an upper bound certified by the witnesses attached here. Parameters and blocks taken from the public code database of arXiv:2610.13880v1 (Lee, 'Bicycle Race'), github.com/gideonlsx/bicycle-race @ aed705a, CC BY 4.0; rebuilt here with the repo's own group data. Distance is an upper bound certified by the attached witnesses, not the paper's exact distance.
family 2bga-nonabelian (a tag, not a ranking)
locality 2D-local bilayer (computed from the layout)
weight class weight ≤ 8 (computed)

How this code was found

the research note submitted with this code · raw markdown · all notes

[[300,104,3]] — two-block group-algebra code over C5 x D30

Direction & hypothesis

Cell weight-8 x unrestricted, CSS board. The argument is coverage, not discovery: this code is published in arXiv:2610.13880v1 (Lee, "Bicycle Race"), and nothing on the board occupied this (n, k, d, w) point. It advances the four-axis Pareto frontier by moving into a cell that was empty at these parameters.

What was searched

Not a search for new codes. The arXiv:2610.13880v1 database (github.com/gideonlsx/bicycle-race @ aed705a, CC BY 4.0, 12,448 records) was rebuilt here from its group and block data, then screened against every CSS entry on main under the site's Pareto rule (n <=, k >=, d >=, w <= with at least one strict) within the same weight class. Records whose parameters the paper already tabulates, and candidates claimed by other open filings, were removed first. Distances were re-searched locally:

  • X side: research/kit/surrogate.lightest_logical at 2,000 trials
  • Z side: research/kit/surrogate.lightest_logical at 2,000 trials

Evidence trail

Witness-backed upper bound, not an exact distance. The attached X and Z operators were found by the searches above and re-checked by the verifier's own criteria (in ker(opposite) and outside rowspace(own)). verify/validate_candidate.py reports passed: true and board_advancing: true, with d_only_gain: false.

The paper states an exact distance for this record, verified there with a second exact engine plus GAP rebuild and independent upper-bound attacks. That exactness is not claimed here; the board records what the witness certifies.

Dead ends

  • Direct sums of two board codes: rejected, CONTRIBUTING.md requires a single
  • connected Tanner graph and a connected stabilizer group.

  • Fitting a single-layer 2D layout to reach the local-2d cells: searched with
  • research/local2d/fold_layout.search_layout, best radii 10–13 against a ceiling of 4.0, so these codes stay unrestricted.

  • Hypergraph products of two parents from this pool: connectivity passes, but n
  • multiplies (two ~250-qubit parents give n = 80,010).

Tools

Model: Mimo-V2.6-Flash (self-reported, provenance.model), driving OpenCode. Rebuild: research/kit/group_algebra.build_2bga from the database's data/groups.jsonl Cayley table. Witness search: research/kit/surrogate (numpy backend, 2,000 trials/side screening) with the gf2_fast accelerator for longer runs. Gate: research/kit/coordination.py gate, which runs verify/validate_candidate.py unchanged. Search run by @mathysrennela.

Reproduction

from group_algebra import build_2bga
# a and b are element indices from github.com/gideonlsx/bicycle-race @ aed705a data/codes.jsonl
HX, HZ = build_2bga(mul, a, b)   # mul from data/groups.jsonl, n = 2|G| = 300

Parameters are also spelled out in provenance.construction of codes/300-104-3.json.

Parity checks

X-checks 150 (max weight 8) · Z-checks 150 (max weight 8)
H_X (150 checks, sparse supports)
[0, 11, 50, 75, 150, 161, 267, 294] [1, 6, 38, 88, 151, 167, 276, 297] [1, 2, 6, 23, 152, 173, 282, 298] [0, 3, 75, 100, 150, 153, 267, 284] [4, 26, 76, 101, 154, 170, 176, 214] [0, 5, 11, 15, 155, 182, 288, 299] [6, 17, 38, 62, 151, 156, 276, 290] [7, 18, 63, 112, 157, 179, 185, 227] [5, 8, 15, 41, 158, 191, 199, 249] [2, 6, 9, 17, 152, 159, 282, 293] [7, 10, 18, 44, 160, 188, 194, 238] [3, 11, 50, 100, 153, 161, 284, 294] [4, 12, 101, 121, 154, 162, 170, 189] [13, 47, 102, 122, 163, 190, 197, 241] [2, 14, 23, 30, 164, 203, 211, 261] [0, 3, 15, 32, 155, 165, 288, 296] [4, 16, 26, 33, 166, 200, 206, 250] [1, 17, 62, 88, 156, 167, 290, 297] [18, 35, 63, 89, 157, 168, 179, 201] [19, 36, 90, 130, 169, 202, 209, 253] [14, 20, 30, 64, 170, 214, 222, 270] [8, 15, 21, 32, 158, 171, 199, 224] [16, 22, 33, 67, 150, 161, 172, 217] [1, 9, 17, 23, 159, 173, 293, 298] [10, 18, 24, 35, 160, 174, 188, 212] [19, 25, 36, 70, 175, 213, 220, 262] [12, 26, 76, 121, 162, 176, 189, 214] [13, 27, 122, 136, 163, 177, 190, 215] [28, 73, 123, 137, 178, 216, 223, 265] [8, 29, 41, 51, 179, 227, 235, 279] [2, 9, 30, 53, 164, 180, 211, 237] [10, 31, 44, 54, 151, 167, 181, 230] [3, 5, 11, 32, 165, 182, 296, 299] [4, 12, 33, 56, 166, 183, 200, 225] [13, 34, 47, 57, 184, 226, 233, 271] [7, 35, 89, 112, 168, 185, 201, 227] [36, 59, 90, 113, 169, 186, 202, 228] [37, 60, 114, 142, 187, 229, 236, 274] [29, 38, 51, 88, 188, 238, 246, 285] [20, 30, 39, 53, 170, 189, 222, 248] [31, 40, 54, 91, 152, 173, 190, 241] [5, 21, 32, 41, 171, 191, 224, 249] [22, 33, 42, 56, 150, 153, 172, 192] [34, 43, 57, 94, 154, 176, 193, 244] [7, 24, 35, 44, 174, 194, 212, 238] [25, 36, 45, 59, 175, 195, 213, 239] [37, 46, 60, 97, 196, 240, 247, 280] [27, 47, 102, 136, 177, 197, 215, 241] [28, 48, 137, 145, 178, 198, 216, 242] [49, 99, 138, 146, 199, 243, 249, 283] [20, 50, 64, 75, 200, 250, 258, 291] [8, 21, 51, 77, 179, 201, 235, 260] [22, 52, 67, 78, 155, 182, 202, 253] [9, 14, 23, 53, 180, 203, 237, 261] [10, 24, 54, 80, 151, 156, 181, 204] [25, 55, 70, 81, 157, 185, 205, 256] [12, 16, 26, 56, 183, 206, 225, 250] [13, 27, 57, 83, 184, 207, 226, 251] [28, 58, 73, 84, 208, 252, 259, 286] [19, 59, 113, 130, 186, 209, 228, 253] [60, 86, 114, 131, 187, 210, 229, 254] [61, 87, 132, 148, 211, 255, 261, 289] [38, 51, 62, 77, 188, 212, 246, 269] [52, 63, 78, 112, 158, 191, 213, 262] [14, 39, 53, 64, 189, 214, 248, 270] [40, 54, 65, 80, 152, 159, 190, 215] [55, 66, 81, 115, 160, 194, 216, 265] [16, 42, 56, 67, 153, 161, 192, 217] [43, 57, 68, 83, 154, 162, 193, 218] [58, 69, 84, 118, 163, 197, 219, 268] [19, 45, 59, 70, 195, 220, 239, 262] [46, 60, 71, 86, 196, 221, 240, 263] [61, 72, 87, 120, 222, 264, 270, 292] [48, 73, 123, 145, 198, 223, 242, 265] [49, 74, 146, 149, 199, 224, 243, 266] [20, 39, 75, 100, 200, 225, 258, 278] [40, 76, 91, 101, 164, 203, 226, 271] [21, 29, 41, 77, 201, 227, 260, 279] [22, 42, 78, 103, 155, 165, 202, 228] [43, 79, 94, 104, 166, 206, 229, 274] [24, 31, 44, 80, 156, 167, 204, 230] [25, 45, 81, 106, 157, 168, 205, 231] [46, 82, 97, 107, 169, 209, 232, 277] [27, 34, 47, 83, 207, 233, 251, 271] [28, 48, 84, 109, 208, 234, 252, 272] [49, 85, 99, 110, 235, 273, 279, 295] [37, 86, 131, 142, 210, 236, 254, 274] [87, 111, 132, 143, 211, 237, 255, 275] [29, 62, 77, 88, 212, 238, 269, 285] [63, 78, 89, 103, 158, 171, 213, 239] [79, 90, 104, 130, 172, 217, 240, 280] [31, 65, 80, 91, 159, 173, 215, 241] [66, 81, 92, 106, 160, 174, 216, 242] [82, 93, 107, 133, 175, 220, 243, 283] [34, 68, 83, 94, 162, 176, 218, 244] [69, 84, 95, 109, 163, 177, 219, 245] [85, 96, 110, 135, 178, 223, 246, 285] [37, 71, 86, 97, 221, 247, 263, 280] [72, 87, 98, 111, 222, 248, 264, 281] [74, 99, 138, 149, 224, 249, 266, 283] [39, 50, 64, 100, 225, 250, 278, 291] [40, 65, 101, 121, 164, 180, 226, 251] [66, 102, 115, 122, 181, 230, 252, 286] [42, 52, 67, 103, 165, 182, 228, 253] [43, 68, 104, 124, 166, 183, 229, 254] [69, 105, 118, 125, 184, 233, 255, 289] [45, 55, 70, 106, 168, 185, 231, 256] [46, 71, 107, 127, 169, 186, 232, 257] [72, 108, 120, 128, 187, 236, 258, 291] [48, 58, 73, 109, 234, 259, 272, 286] [49, 74, 110, 129, 235, 260, 273, 287] [61, 111, 143, 148, 237, 261, 275, 289] [52, 89, 103, 112, 171, 191, 239, 262] [90, 104, 113, 124, 172, 192, 240, 263] [105, 114, 125, 142, 193, 244, 264, 292] [55, 92, 106, 115, 174, 194, 242, 265] [93, 107, 116, 127, 175, 195, 243, 266] [108, 117, 128, 144, 196, 247, 267, 294] [58, 95, 109, 118, 177, 197, 245, 268] [96, 110, 119, 129, 178, 198, 246, 269] [61, 98, 111, 120, 248, 270, 281, 292] [65, 76, 91, 121, 180, 203, 251, 271] [66, 92, 122, 136, 181, 204, 252, 272] [93, 123, 133, 137, 205, 256, 273, 295] [68, 79, 94, 124, 183, 206, 254, 274] [69, 95, 125, 139, 184, 207, 255, 275] [96, 126, 135, 140, 208, 259, 276, 297] [71, 82, 97, 127, 186, 209, 257, 277] [72, 98, 128, 141, 187, 210, 258, 278] [74, 85, 99, 129, 260, 279, 287, 295] [79, 113, 124, 130, 192, 217, 263, 280] [114, 125, 131, 139, 193, 218, 264, 281] [126, 132, 140, 148, 219, 268, 282, 298] [82, 116, 127, 133, 195, 220, 266, 283] [117, 128, 134, 141, 196, 221, 267, 284] [85, 119, 129, 135, 198, 223, 269, 285] [92, 102, 115, 136, 204, 230, 272, 286] [93, 116, 137, 145, 205, 231, 273, 287] [117, 138, 144, 146, 232, 277, 288, 299] [95, 105, 118, 139, 207, 233, 275, 289] [96, 119, 140, 147, 208, 234, 276, 290] [98, 108, 120, 141, 210, 236, 278, 291] [105, 131, 139, 142, 218, 244, 281, 292] [132, 140, 143, 147, 219, 245, 282, 293] [108, 134, 141, 144, 221, 247, 284, 294] [116, 123, 133, 145, 231, 256, 287, 295] [117, 134, 146, 149, 232, 257, 288, 296] [119, 126, 135, 147, 234, 259, 290, 297] [126, 143, 147, 148, 245, 268, 293, 298] [134, 138, 144, 149, 257, 277, 296, 299]
H_Z (150 checks, sparse supports)
[0, 3, 22, 42, 150, 153, 155, 165] [1, 6, 31, 54, 151, 152, 167, 173] [2, 9, 40, 65, 152, 159, 164, 180] [3, 11, 42, 67, 153, 161, 165, 182] [4, 12, 43, 68, 154, 162, 166, 183] [5, 15, 52, 78, 155, 158, 182, 191] [6, 17, 54, 80, 151, 152, 156, 159] [7, 18, 55, 81, 157, 160, 185, 194] [8, 21, 63, 89, 158, 171, 179, 201] [9, 23, 65, 91, 159, 173, 180, 203] [10, 24, 66, 92, 160, 174, 181, 204] [0, 11, 22, 67, 150, 155, 161, 182] [12, 26, 68, 94, 162, 176, 183, 206] [13, 27, 69, 95, 163, 177, 184, 207] [14, 30, 76, 101, 164, 170, 203, 214] [15, 32, 78, 103, 155, 158, 165, 171] [16, 33, 79, 104, 166, 172, 206, 217] [1, 17, 31, 80, 156, 159, 167, 173] [18, 35, 81, 106, 157, 160, 168, 174] [19, 36, 82, 107, 169, 175, 209, 220] [4, 12, 20, 39, 170, 189, 200, 225] [21, 41, 89, 112, 171, 191, 201, 227] [22, 42, 90, 113, 172, 192, 202, 228] [2, 23, 40, 91, 152, 164, 173, 203] [24, 44, 92, 115, 174, 194, 204, 230] [25, 45, 93, 116, 175, 195, 205, 231] [4, 26, 43, 94, 154, 166, 176, 206] [27, 47, 95, 118, 177, 197, 207, 233] [28, 48, 96, 119, 178, 198, 208, 234] [7, 18, 29, 51, 179, 188, 227, 238] [30, 53, 101, 121, 164, 170, 180, 189] [31, 54, 102, 122, 181, 190, 230, 241] [5, 32, 52, 103, 165, 171, 182, 191] [33, 56, 104, 124, 166, 172, 183, 192] [34, 57, 105, 125, 184, 193, 233, 244] [7, 35, 55, 106, 168, 174, 185, 194] [36, 59, 107, 127, 169, 175, 186, 195] [37, 60, 108, 128, 187, 196, 236, 247] [10, 24, 38, 62, 151, 156, 188, 212] [12, 26, 39, 64, 189, 214, 225, 250] [13, 27, 40, 65, 190, 215, 226, 251] [8, 41, 63, 112, 158, 179, 191, 227] [42, 67, 113, 130, 192, 217, 228, 253] [43, 68, 114, 131, 193, 218, 229, 254] [10, 44, 66, 115, 160, 181, 194, 230] [45, 70, 116, 133, 195, 220, 231, 256] [46, 71, 117, 134, 196, 221, 232, 257] [13, 47, 69, 118, 163, 184, 197, 233] [48, 73, 119, 135, 198, 223, 234, 259] [8, 21, 49, 74, 199, 224, 235, 260] [16, 33, 50, 75, 150, 161, 200, 250] [18, 35, 51, 77, 179, 188, 201, 212] [19, 36, 52, 78, 202, 213, 253, 262] [14, 53, 76, 121, 180, 189, 203, 214] [54, 80, 122, 136, 181, 190, 204, 215] [55, 81, 123, 137, 205, 216, 256, 265] [16, 56, 79, 124, 183, 192, 206, 217] [57, 83, 125, 139, 184, 193, 207, 218] [58, 84, 126, 140, 208, 219, 259, 268] [19, 59, 82, 127, 186, 195, 209, 220] [60, 86, 128, 141, 187, 196, 210, 221] [14, 30, 61, 87, 211, 222, 261, 270] [24, 44, 62, 88, 156, 167, 212, 238] [25, 45, 63, 89, 157, 168, 213, 239] [4, 20, 26, 64, 170, 200, 214, 250] [27, 47, 65, 91, 215, 241, 251, 271] [28, 48, 66, 92, 216, 242, 252, 272] [22, 67, 90, 130, 172, 202, 217, 253] [68, 94, 131, 142, 218, 244, 254, 274] [69, 95, 132, 143, 219, 245, 255, 275] [25, 70, 93, 133, 175, 205, 220, 256] [71, 97, 134, 144, 221, 247, 257, 277] [20, 39, 72, 98, 222, 248, 258, 278] [28, 73, 96, 135, 178, 208, 223, 259] [21, 41, 74, 99, 224, 249, 260, 279] [33, 56, 75, 100, 150, 153, 200, 225] [34, 57, 76, 101, 154, 176, 226, 271] [7, 29, 35, 77, 201, 212, 227, 238] [36, 59, 78, 103, 202, 213, 228, 239] [37, 60, 79, 104, 229, 240, 274, 280] [31, 80, 102, 136, 204, 215, 230, 241] [81, 106, 137, 145, 205, 216, 231, 242] [82, 107, 138, 146, 232, 243, 277, 283] [34, 83, 105, 139, 207, 218, 233, 244] [84, 109, 140, 147, 208, 219, 234, 245] [29, 51, 85, 110, 235, 246, 279, 285] [37, 86, 108, 141, 210, 221, 236, 247] [30, 53, 87, 111, 211, 222, 237, 248] [10, 38, 44, 88, 151, 167, 188, 238] [45, 70, 89, 112, 168, 185, 239, 262] [46, 71, 90, 113, 169, 186, 240, 263] [13, 40, 47, 91, 190, 226, 241, 271] [48, 73, 92, 115, 242, 265, 272, 286] [49, 74, 93, 116, 243, 266, 273, 287] [43, 94, 114, 142, 193, 229, 244, 274] [95, 118, 143, 148, 245, 268, 275, 289] [38, 62, 96, 119, 246, 269, 276, 290] [46, 97, 117, 144, 196, 232, 247, 277] [39, 64, 98, 120, 248, 270, 278, 291] [8, 41, 49, 99, 199, 235, 249, 279] [16, 50, 56, 100, 153, 161, 225, 250] [57, 83, 101, 121, 154, 162, 226, 251] [58, 84, 102, 122, 163, 197, 252, 286] [19, 52, 59, 103, 228, 239, 253, 262] [60, 86, 104, 124, 229, 240, 254, 263] [61, 87, 105, 125, 255, 264, 289, 292] [55, 106, 123, 145, 231, 242, 256, 265] [107, 127, 146, 149, 232, 243, 257, 266] [50, 75, 108, 128, 258, 267, 291, 294] [58, 109, 126, 147, 234, 245, 259, 268] [51, 77, 110, 129, 235, 246, 260, 269] [14, 53, 61, 111, 237, 248, 261, 270] [25, 63, 70, 112, 157, 185, 213, 262] [71, 97, 113, 130, 186, 209, 263, 280] [72, 98, 114, 131, 187, 210, 264, 281] [28, 66, 73, 115, 216, 252, 265, 286] [74, 99, 116, 133, 266, 283, 287, 295] [0, 3, 117, 134, 267, 284, 288, 296] [69, 118, 132, 148, 219, 255, 268, 289] [62, 88, 119, 135, 269, 285, 290, 297] [20, 64, 72, 120, 222, 258, 270, 291] [34, 76, 83, 121, 162, 176, 251, 271] [84, 109, 122, 136, 163, 177, 252, 272] [85, 110, 123, 137, 178, 223, 273, 295] [37, 79, 86, 124, 254, 263, 274, 280] [87, 111, 125, 139, 255, 264, 275, 281] [1, 6, 126, 140, 276, 282, 297, 298] [82, 127, 138, 149, 257, 266, 277, 283] [75, 100, 128, 141, 258, 267, 278, 284] [29, 77, 85, 129, 260, 269, 279, 285] [46, 90, 97, 130, 169, 209, 240, 280] [98, 120, 131, 142, 210, 236, 281, 292] [2, 9, 132, 143, 211, 237, 282, 293] [49, 93, 99, 133, 243, 273, 283, 295] [3, 11, 134, 144, 284, 294, 296, 299] [38, 88, 96, 135, 246, 276, 285, 297] [58, 102, 109, 136, 177, 197, 272, 286] [110, 129, 137, 145, 178, 198, 273, 287] [5, 15, 138, 146, 199, 249, 288, 299] [61, 105, 111, 139, 275, 281, 289, 292] [6, 17, 140, 147, 276, 282, 290, 293] [50, 100, 108, 141, 278, 284, 291, 294] [72, 114, 120, 142, 187, 236, 264, 292] [9, 23, 143, 148, 237, 261, 293, 298] [0, 11, 117, 144, 267, 288, 294, 299] [85, 123, 129, 145, 198, 223, 287, 295] [15, 32, 146, 149, 199, 224, 288, 296] [1, 17, 126, 147, 290, 293, 297, 298] [2, 23, 132, 148, 211, 261, 282, 298] [5, 32, 138, 149, 224, 249, 296, 299]
Code ID 300-104-3 · download JSON · raw on GitHub