Seven-position signature - independently reproduced
by Qubic Church4 min read
Historical post, re-checked in September 2026. The seven-position set [3, 18, 32, 61, 65, 101, 109] is real for the matrix as typed, but it depends on a very likely data entry error in column 30. The diagonal-27 link to ten unspent coinbase blocks was an index error.
What changed
- Chapter 27: Seven-Position Signature & Period-4 Attractor published (set aside in September 2026, see September 2026 re-check).
The discovery
An anonymous researcher observed that when the Anna Matrix is iterated under state = sign(M @ state) starting from the Genesis public key, the resulting period-4 cycle (A, B, C, D) exhibits near-perfect antipodal symmetry A = -C and B = -D, except at seven positions:
[3, 18, 32, 61, 65, 101, 109]
The researcher then claimed the set is robust: it reproduces across five different encodings of the pubkey.
What we verified
Running 1,000 uniformly random binary initial states through the same iteration, every single trajectory converged to a period-4 cycle, and every single cycle had the identical seven-position asymmetry set. The signature is not Genesis-specific. It is a property of the Anna Matrix itself.
Results:
| Test | Outcome |
|---|---|
| 1,000 random binary inputs | All converge to period-4 |
| Unique asymmetry sets | Exactly 1 |
| Unique period-4 cycles (up to rotation) | Exactly 2 |
| Cycle sums | (-42, 50, 38, -56) |
| Matching researcher's set | 1000 of 1000 trials |
The null test
To confirm the signature is Anna-specific and not a generic property of signed integer matrices, we shuffled the 16,384 matrix values into five random matrices (preserving the marginal distribution) and ran 200 random inputs each.
| Seed | Period-4 cycles found |
|---|---|
| 100 | 0 of 200 |
| 101 | 0 of 200 |
| 102 | 0 of 200 |
| 103 | 0 of 200 |
| 104 | 0 of 200 |
Zero of 1,000 shuffled-matrix trials produced any period-4 cycle. Shuffling the matrix entries destroys the attractor completely.
New observations beyond the researcher's claim
- Only two cycles observed. Every sampled input reached one of two cycles; that the entire
3^128ternary state space partitions into exactly two basins is not proven. The two cycles are negations of each other. - Positions 18 and 109 form a mirror pair on the Mersenne axis (18 + 109 = 127).
- Four of seven positions (32, 61, 65, 101) lie in rows where the 68 anomaly cells concentrate. Three (3, 18, 109) do not.
- Diagonal-27 completeness. The matrix has exactly 10 diagonal cells with
|M[b][b]| = 27, at positions[72, 73, 74, 79, 88, 92, 94, 95, 119, 120]. Earlier text said this matches 10 unspent early Bitcoin coinbase blocks; that match was not confirmed (off-by-one indices). - Row 72 structure. Row 72 contains exactly 27 cells with value -27 and zero cells with +27. The 27x(-27) pattern is an exact count, not a rough approximation.
Attribution
Credit for the original observation goes to the anonymous researcher who posted it publicly on 2026-04-19. Our contribution is independent verification, the null test, and the two-cycle enumeration. We report the letter-decoding candidates from the researcher's post (DSGJNXF, SJAISCI, IRAISCI) but find none semantically compelling.
Open questions
These questions became moot after the re-check noted above. As originally listed:
- What predicate on the initial state determines which of the two cycles it falls into?
- Do the seven positions satisfy any bit-pattern or XOR relation?
- Can the matrix construction rule be inferred if we assume the seven positions are load-bearing?
Reproduction
The verification script was part of the chapter that was set aside. The re-check is summarised on the re-check page.
