adv-mixer: consolidated Q1 verdict and status-board row from the deepening

Internal adversarial pass, not an independent review.

Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>

docs/analysis/cryptanalysis/report-mixer.md

@@ -25,7 +25,7 @@ quoted in public. This is such a pass. It is not an outside review.
 
 | Q | Lane | Method | Known-failed shape | Gate | Result (numbers) | Status |
 |---|---|---|---|---|---|---|
-| Q1 algebraic structure | adv-mixer (this) | fold probe + integral cube-sum degree test | the probes are their own control | affinity violations > 0, dead pairs = 0, key agreements = 0; degree saturates | 1e6/1e6 affinity violations; 0/256 dead word pairs; 0/1e6 key-order agreements; algebraic degree >= 16 after 1 application, saturated (256/512 bits per cube-sum) after 2 | PASS (BOUND: no shortcut, 8x stands) |
+| Q1 algebraic structure | adv-mixer (this) | fold probes (1024 days x 71 key pairs), exact GF(2) affine-relation kernel at full width, integral cube-sum degree (32 days), the 22 line-index bits, a SAT model of two applications | the probes are their own control; the diffusion plant fired | affinity violations > 0, dead pairs = 0, key agreements = 0, kernel = 0, degree saturates | 1,454,080,000/1,454,080,000 affinity violations, 0 dead word pairs, 0 key-order agreements over 1024 days; kernel 0 at K = 1, 2, 8 on 16 days (full width) and on the address bits; degree >= 16 after 1 application and saturated after 2 on 32 days; address bits clean from K = 2 | PASS (BOUND: no composition cheaper than 8x; 9,360 ops per item stand) |
 | Q2 round margin | adv-mixer-3 (courtesy run here) | diffusion avalanche census K=1..8, 2e6 states | diffusion --plant weak (fired) | full diffusion at K | distinguisher reaches K=1 only; K=2..8 clean (0 holes, 0 strong, worst 4.5 to 4.9 sigma) | BOUND (handed to adv-mixer-3) |
 | Q3 weak draws | adv-mixer-2 (courtesy run here) | f4 census over 2^24 days | plant alleq/mul1/mul1all/rc0/rcrk0 (all fired) | any class >= 1.1x on a non-negligible fraction | M1 cost 197 to 263, mean 231.1; best day a 1.17x smaller FPGA multiply datapath, 1 day in 2^24; 0 days DSP or wall-time gain; ROT-all-equal never seen | BOUND+tail (handed to adv-mixer-2) |
 
@@ -221,6 +221,25 @@ and that binary is running on this instance under a one-hour cap at nice 10 (log
 RUNNING; the row lands here. A timeout is the honest expected outcome: the instance is a preimage-shaped search
 on a 2^512 space, and a plain timeout is a bound on solver reach, not evidence either way.
 
+## Q1 consolidated verdict (internal adversarial pass, not an independent review)
+
+Across every probe this lane ran at full 32-bit width with the real day constants, no composition of the 8
+keyed applications between two cache reads costs less than 8 times one application.
+
+| Candidate shortcut from the brief | Evidence | Status |
+|---|---|---|
+| The multiply layer folds or commutes across applications (only rk changes) | adjacent-pair affinity violated on 1,454,080,000 of 1,454,080,000 trials over 1024 days and all 71 seams; key-order commutation 0 of 1,454,080,000 | ruled out at the probe's reach |
+| An exact linear or affine relation across the composition | GF(2) kernel 0 (rank 1025 of 1025) at K = 1, 2 and 8 on 16 days; kernel 0 on the 22 address bits at K = 1 and 2 | ruled out exactly (chance survivor 2^-7167) |
+| A low-degree algebraic form to batch the applications | cube-sums nonzero at every d up to 16 after one application, saturated at 256 of 512 bits after two, on 32 days | ruled out below degree 16; above 16 is owed |
+| A predictable line index that lets a chip prefetch the read early | address bits predictable only after 1 application (incomplete diffusion, no linear leak); clean from K = 2 | at most 1 of 8 applications hides behind the memory latency |
+| An exact commutation witness (SAT model) | 105,652-variable, 361,188-clause instance; cadical 3.0.1 running under a 1 h cap | pending; a timeout bounds solver reach only |
+
+Priced against the chip model: 0 ops saved per item; 9,360 ops per item stand. What a longer pass would add:
+an exact algebraic-degree measurement above 16 (the cube test stops at 2^16 points) and a solver run long
+enough to decide the commutation instance; neither would move the fold or the affine bound, which are exact or
+exhaustive at their reach. The probes cover 1024 consecutive chain days from genesis, about 2.8 years of the
+public calendar.
+
 ## Sibling queue files run by this lane
 
 Per main's rule (claim the next unclaimed sibling file in name order once the own queue is empty), this lane