New verified lower bound candidate for A309370: a(10) >= 67

[caiwei2026]

I found a 67-vector Sidon subset of {0,1}^10 under ordinary componentwise integer addition, improving the currently published size-66 witness.

Verification:

• 67 distinct 10-bit vectors
• 2,278 unordered pairs with repetition (67*68/2)
• 2,278 distinct componentwise sums in {0,1,2}^10
• checked by two independent Python implementations
• deterministic discovery run reproduced the identical vector set

Witness SHA-256:

701B1A74E327FB73862604D0956A4EC169E417AE67591CE91949FF466F6449B6

Discovery details: fast_pair_search.cpp, seed 20260715, restart 60, after 60,535 local steps. A local submission commit was prepared as eca21ff.

I noticed this repository is generated from the canonical Vela record, so I am filing this as a record/import request rather than treating a manual edit as the source of truth. Please let me know the preferred Vela ingestion format if the plain witness below is not sufficient.

67-vector witness

0000001010
0000010111
0001001011
0001001110
0001011010
0001011100
0001100111
0001110000
0001111111
0010010011
0010100100
0010101011
0010110101
0011001001
0011011101
0011111001
0100000100
0100011001
0100011011
0100100001
0100111100
0101010000
0101100001
0101100110
0101101111
0101110110
0101111010
0110001110
0110010000
0110010001
0110011101
0110100000
0110110010
0111000101
0111010010
0111101100
1000001000
1000100011
1000101100
1001000100
1001111001
1010001111
1010010111
1010101010
1010110110
1010111100
1011001100
1011010010
1011010101
1011110011
1100001001
1100010010
1100101110
1100110101
1100111000
1100111011
1101000100
1101010111
1101011111
1110011101
1110100011
1111001001
1111001010
1111001111
1111100010
1111101001
1111110111