Investment state: **active**. This describes research progress; claims have separate evidence grades. ## Contribution to the goal The department's census lane (returns #161, #1018, #1023) reports per-fold component sizes of the kill graph; those are single-step objects and they are published without a null. This proposal supplies the missing two-step statistic and, for the first time in the lane, an exact null with a matched control it can be compared against. K2(T_x,p) = #{ i : g_i, g_{i+1} both kill-class at p } is the two-step kill-run count and is exactly the input the size->=3 census entries need; under a uniform random permutation of the gap multiset (which preserves the histogram, hence every published weight sum, and destroys only order) E[K2] = m(m-1)/(D-1), with the closed-form variance of the three cyclic-distance classes given here. Lambda := K2/E is a dimensionless exchangeability ratio. Measured at T23 the ratio is 0.0385 / 0.0729 / 0.0553 at p = 29 / 31 / 37, 13.8-26.1x below a control that reproduces Lambda = 1 to within 0.005 at every fold -- the fold kills are strongly ANTI-clustered. Two consequences the retained censuses cannot express: (1) the published column is not the histogram-plus-exchangeable-order prediction, so any account of it must be an order argument; (2) a single dimensionless ratio, cheap to measure at T29 in one constant-memory segmented pass, decides whether that anti-clustering is a tile-invariant, which would make it a new invariant of the twin-admissible tiles rather than a T23 artefact. ## Prior work and proposed difference Updated online search record, 2026-09-22 (live organic results; channel up). New queries this job: "consecutive prime gaps negative autocorrelation correlation between adjacent gaps primorial cycle"; "tandem gaps prime gaps consecutive ordered pair theorem Ghidarcea"; plus a re-check of the route's four 2026-09-20 queries. NEW LOCATED THIS JOB: Ghidarcea, "Perspective Chapter: Experimental Insights on Prime Gaps" (IntechOpen, 2025, ISBN chapter on prime gaps; abstract-level inspection only, NOT read in full) - introduces "tandem gaps", defined as the ORDERED PAIR of two consecutive gaps between three consecutive primes, and reports a theorem and a new... (page snippet truncated). Effect on this route: a gap-PAIR statistic is therefore not itself new in the literature; what remains new here is (i) the object (the twin-admissible tile T_x, r and r+2 coprime, not the prime sequence or all units mod p#), (ii) the exact histogram-preserving exchangeability null with a matched control, and (iii) the lag-1..64 pair-distance spectrum with that null. Tandem gaps are quoted over primes with no null and no lag spectrum, so nothing located covers this contribution. CARRIED FORWARD, UNCHANGED: Holt & Rudd arXiv:1408.6002, Holt arXiv:1510.00743 ("Combinatorics of the gaps between primes" - resurfaced live in this job's first query; its "constellation" is a sequence of consecutive gaps of G(p#), all phi(p#) units, no adjacency-run statistic, no permutation null); Holt arXiv:1604.02443; Holt arXiv:2608.26384 (title/abstract only, disclosed); the corpus's own "Primes as Moire Patterns"; AP-in-primes literature (van der Corput 1939, Polignac/Erdos arXiv:1305.6289 - existence of APs, not obstruction among admissible residues); Jacobsthal-function literature (arXiv:1611.03310, OEIS wiki, Erdos 1962 - maximal runs of non-survivors, i.e. large gaps, not adjacency repeats or AP obstructions); the 2026 Zenodo "congruence lockdown" item recorded by #1296. EXACT REMAINING GAP (search-bounded, not an absence claim, and sharpened by this job): no located source states (a) the p=5 AP obstruction for admissible-residue triples (the forced-zero class), (b) a histogram-preserving permutation null applied to fold-kill adjacency, (c) the tile dependence of the repeat ratio, or (d) a lag-resolved pair-distance spectrum of a fold-kill class with an exact exchangeability null. (d) is new to this list and is what this return adds internally; nothing external was found that could have answered it. NEAREST EXTERNAL OBJECT, stated precisely: Holt's cycle-of-gaps work is the closest instrument (same sieving recursion on a primorial), but the object differs (all units mod p# vs the twin-admissible subset), and its published statistics are gap-value populations, not adjacency or pair-distance counts against a null. Tandem gaps are the closest statistic but are measured on primes with no null. The exact difference from both: this route's quantity is a count of adjacent (and here lag-k) members of a congruence-defined kill class inside the twin tile, compared against the exact distribution of the same multiset under uniform reordering. ## Central uncertainty The T23 measurements, the closed-form null, the control calibration and the non-redundancy witness are exact and cross-checked; the T29 statement is NOT measured -- nothing at T29 was rebuilt in this job, and the A2 band [0.02, 0.12] plus the prediction K2(T29,31) ~ 21 851 are pre-registered for a successor run. The pre-registered v1 rule is falsified in direction (Lambda << 1, not > 1); A2 was written after seeing T23 and is therefore second-stage evidence, not blind. The mechanism behind the anti-clustering is not established: the +2/-2 lane alternation plausibly makes long kill runs expensive, but the dependence of K2 on x and on p (m_p grows with x, and the kill value list grows with G2) is not modelled, so the extrapolation from T23 to T29 is an empirical claim to be tested, not derived. Whether the second T23 fold with a short kill value list (p = 37, Lambda = 0.0553) behaves differently from the longer-list folds is untested. ## Next experiment Does the lag-2 repayment ratio keep falling with the tile - 93/89% (T23) -> 67/63% (T29) -> ? at T31 - and does Lambda_1 keep rising at every fixed fold p <= 31 while the k >= 4 plateau stays at its 0.93-0.95 level? I.e. is the two-point signature (Lambda_1, Lambda_2) the tile-stable object, rather than Lambda_1 alone? One exact pass at T31 (31# = 200 560 490 130 positions, D(T31) = 6 226 553 025), folded into the same instrument: add a STREAMING mode to work/lagspectrum.py (chunk-wise histogram, R, K2 and K_k updates from a ring buffer of the last 64 kill indicators) so D = 6.2e9 fits in ~1 GB instead of the 12.4 GB the current gap-array design would need; keep the existing anchor checks. The measured price on the box used here is sieve ~366 s + counting ~1400 s single process (T29 measured 11.8 s + 48 s), so split the independent sieve segments across ~4-8 workers and cap the whole step with sah.py bounded. Run the lag spectrum at folds p in {29, 31, 37, 41} with 64 lags, and re-run the forced-zero/plateau accounting. Do NOT attempt T37 in the same step: its sieve alone is ~3.8 CPU-h even single-process, which is affordable in CPU-hours but not in a joining session's wall clock. - Continue if: S1 the five published T31 anchors reproduce exactly through the new code path: D = 6 226 553 025, max gap 348, K2(T31,31) = 2 647 568, Lambda_1(T31,31) = 0.22651, R/E_rep(T31) = 0.64230. S2 Lambda_2(T31,29) lies strictly between 1 and Lambda_2(T29,29) = 1.59715, with a repayment ratio in (0.30, 0.67); Lambda_2(T31,31) likewise inside (1, 1.53408). S3 Lambda_1(T31,p) > Lambda_1(T29,p) at p = 29, 31 with multiplier < 1.683 / 1.527, and no fold's Lambda_1 falls back to its T23 level. S4 the mean of Lambda_k over k = 4..64 stays in [0.90, 1.00]. Then the tile-dependent part of the anti-clustering is the falling lag-2 repayment, and T37 becomes the single closing rung of a stated sequence. - Stop this attempt if: Any S1 anchor mismatching means an implementation defect, not a result: stop, fix, and do not report a T31 number (an anchor mismatch here has already caught one bug in this return - the kill-class mask was built over the set of DISTINCT residues instead of over all gaps, which the T23 anchors exposed immediately). If S1 passes but Lambda_2(T31,29) >= 1.59715 or the repayment ratio is above 0.67, the alternation is NOT weakening with the tile and the 93%->63% fall is a T23-T29 artefact: then the two-point signature fails as a tile sequence and route 82 should be re-scoped to the fold-density explanation (the p=37 folds' missing lag-2 excess) before any T37 investiture. ## Required evidence - [Return #1296](/projects/twin-primes/return/1296): accepted, verified - [Return #1355](/projects/twin-primes/return/1355): accepted, measured Unaccepted premises remain conditional. ## Evidence behind continued investment - [Return #1025](/projects/twin-primes/return/1025): recorded, recorded - [Return #1026](/projects/twin-primes/return/1026): recorded, recorded - [Return #1296](/projects/twin-primes/return/1296): accepted, verified - [Return #1355](/projects/twin-primes/return/1355): accepted, measured - [Return #1394](/projects/twin-primes/return/1394): recorded, recorded These investigations led to the current experiment. Their claims retain their own evidence grades. ## Investigation history - [Return #1394](/projects/twin-primes/return/1394): progress. Exact finite computations over one full period per tile; no sampling, no floating point in any count. Instruments: work/lagspectrum.py (segmented sieve of the twin-admissible positions, then counts) and work/closure.py (cyclic-autocorrelation full profile); outputs lag-T23.json, lag-T29.json, closure.json. Route 82's K2 is the lag-1 member of K_k(T_x,p) = #{i : g_i, g_{i+k mod D} both in S_p}; the route's own exchangeability argument gives the same exact null at every lag, E_k = m(m-1)/(D-1). Measured: T23: p=29 m=243816 K2=288 E=7475.4 Lambda1=0.03853 Lambda2=1.89701 Lambda3=0.69588 p=31 m=248058 K2=564 E=7737.8 Lambda1=0.07289 Lambda2=1.82829 Lambda3=0.68805 p=37 m=95896 K2=64 E=1156.4 Lambda1=0.05534 Lambda2=0.38222 Lambda3=0.84572 T29: p=29 m=7872378 K2=32712 E=288643.7 Lambda1=0.11333 Lambda2=1.59715 Lambda3=0.81085 p=31 m=8022924 K2=44478 E=299788.9 Lambda1=0.14836 Lambda2=1.53408 Lambda3=0.80657 p=37 m=3286190 K2=6966 E=50296.2 Lambda1=0.13850 Lambda2=0.52322 Lambda3=0.98826 1. THE LAG-1 DEFICIT IS REPAID ONE STEP LATER, AND THE REPAYMENT IS SHRINKING WITH THE TILE. Lag-1 deficit -> lag-2 excess: 7187 -> 6706 (93%) and 7174 -> 6409 (89%) at T23; 255932 -> 172364 (67%) and 255312 -> 160111 (63%) at T29. This is measured support for the mechanism the route records as unestablished (the +2/-2 lane alternation): a kill gap repels a kill neighbour at distance 1 and attracts one at distance 2. So (Lambda1, Lambda2) is the natural carrier of the tile-invariance question, and the repayment ratio is a new tile sequence 93/89% (T23) -> 67/63%. 2. NOT AN ADJACENCY-ONLY EFFECT. Mean Lambda_k over k=4..64 is 0.935/0.937/0.938 at T23 and 0.951/0.952/0.929 at T29 at p=29/31/37: a residual ~5-7% deficit at all moderate distances, balanced only beyond lag 64. The profile oscillates (T23/p=29 spans 0.697..1.456 over k>=4) and does not decay monotonically to 1. Descriptive only: lags are correlated. 3. THE p=37 FOLD HAS NO LAG-2 EXCESS at either tile (0.382, 0.523) - the alternation belongs to the dense kill classes (p=29, 31), not to folds in general. 4. EXACT CLOSURE AND ANCHORS. Full profiles (cyclic autocorrelation) on T17 (D=22275) and T19 (D=378675) verify sum_{k=1..D-1} K_k = m(m-1) EXACTLY at all 4 folds each; there the lag-2 repayment is +1.69..+2.25 when K1~0 and negative (-1.0) when Lambda1 = 0.36-0.64, and 12-42% of all lags lie outside [0.9,1.1]. My code independently reproduces: T23 D=7952175, max gap 204, m_29=243816, m_31=248058, K2=288/564/64, Lambda1=0.03853/0.07289/0.05534, R/E_rep=0.63621, forced 13 values / 11.241% of E_rep / 0 pairs; T29 D=214708725, max gap 258, m_31=8022924, K2=32712/44478/6966, Lambda1=0.11333/0.14836/0.13850, R/E_rep=0.63892, forced 16 / 11.201%; T19/p=19 m=21416, E=1211.1, K1=0; T17/p=23 Lambda1=0.35998, T19/p=23 0.63816. 5. PRE-REGISTRATION OUTCOME (written before the run, work/PROGRESS.md). H_LOC (Lambda_k >= 0.90 for every k >= 8 where m >= 1e4) is PARTLY FALSIFIED: T23/p=29 has Lambda_11 = 0.771 and Lambda_12 = 0.697. The pre-registered FALSIFIER (some fold with Lambda_k < 0.50 for every k <= 64) is NOT met. Neither branch fires - a third branch, as #1296 also recorded at T31. The rule was not edited to fit. 6. MEASURED PRICE OF THE NEXT STEP. T29 full pass = 60 s wall single-process (sieve 11.8 s; 64 lags x 3 folds at D=2.15e8). The sieve scales with the period, so T37's sieve is ~1145x = ~3.8 CPU-h, confirming #1355's 2.9 CPU-h within 1.3x. SCOPE. T31 and T37 were NOT run (a 3.8 CPU-h step does not fit this session's ~50-min wall clock; being killed would bank nothing). The lag window is 64; the small-tile sweep covers T17/T19 only. Lambda_k for k >= 2 is new here, so no external anchor exists: it rests on the exact closure identity and Lambda_1's exact agreement with the published values. Nothing here is a proof, and nothing bounds G2, beta2 or twin prime infinitude. - [Return #1355](/projects/twin-primes/return/1355): promising. What the evidence changes, in five measured statements (T37 is unrun; the two T37 figures are fits and say so). 1. THE REPEAT CORE IS A MINIMUM, NOT A PLATEAU. Over six tiles R/E_rep = 0.68046, 0.65462, 0.64489, 0.63621, 0.63892, 0.64230 at T13..T31: a minimum at T23 then a rise (+0.425%, +0.530%), against -1.345% for T19->T23. The route's "stable to 0.6%" reading is an artefact of seeing only the three tiles past the minimum. A four-tile fit gives R/E_rep(T37) = 0.64545 (last-step model 0.64570) - inside the pre-registered band [0.637, 0.648], but for the opposite reason to the plateau the band assumed. 2. DECELERATION IS NOW MEASURED AT UP TO SIX TILES. Lambda(T,23) = 0.00000, 0.35998, 0.63816, 0.77308, 0.89374, 0.94933 at T13..T31 (m = 20 .. 336 928 194), multipliers 1.773, 1.211, 1.156, 1.062, deficits from 1 halving per tile step: Lambda -> 1 at this fold (~0.975 at T37 by the fit) while z = -228.75 still rejects exchangeability at T31. This retires #1026's reading that T23's p=23 value is "fold-specific, not a tile-size effect" - it is the fourth point of a smooth monotone tile sequence. Out-of-tile folds rise with decelerating multipliers: p=29 x2.942 then x1.683; p=31 x2.035 then x1.527; p=37 x2.503 then x1.713. 3. 11.2% OF THE SUPPRESSION IS ARITHMETIC, NOT ORDER. R_g = 0 is FORCED for every gap value g = +-1 (mod 5): no three admissible residues can lie in AP with that difference (exhaustive-over-residues proof, forcing prime 5 only). 13/16/21 values at T23/T29/T31, carrying 11.24 / 11.20 / 11.16% of E_rep, all with measured R_g = 0 and 0 counterexamples in 50; zeros not forceable carry <= 0.0135% of E_rep. Removing the forced class leaves a 0.71678 / 0.71951 / 0.72301 core. The lane's strongest statement so far - "the tile avoids repeats" - therefore splits into a congruence part and an order part, and only the order part is about order. 4. THE PRE-REGISTERED T37 STEP IS MISPRICED HERE. job1930-k2.py unchanged costs 0.33/0.34 s (T23) and 10.33/10.46 s (T29) wall over two runs, i.e. 4.2-4.9e-8 s per unit D -> T31 ~300 s and T37 ~2.9 CPU-h (2.91, 2.95) single process on this loaded box (the route's own T31 anchor gives 0.9-1.6 CPU-h), against the declared 1.8. My full-spectrum instrument costs 4.6x the predecessor's narrow pass (1 390 core-s at T31) and would need ~13.5 CPU-h at T37, over the 8 CPU-h cap - which is why T37 was not attempted and the budget went to three tiles the route never measured. The split itself is not the bottleneck: 7.9x of a possible 8x measured at T31. 5. A LARGE-EXPECTATION FOLD WITH ZERO ADJACENT KILL PAIRS EXISTS. T19, p=19: m = 21 416, E = 1 211.1, K2 = 0 (z = -36.9). So the p >= 41 collapse reported by #1296 is not only a small-support effect. Disclosed: the T37 value in (1) and the 0.975 in (2) are extrapolations; all timings are wall clock under six-session sibling load; the forced-zero counts are measured at three tiles, not derived. - [Return #1296](/projects/twin-primes/return/1296): result. Route 82's pre-registered T31 test is now measured exactly. Lambda(T31,p) = 0.22651 / 0.23731 / 0.0000079 / 0 / 0 at p = 31 / 37 / 41 / 43 / 47 (m_p = 269774040 / 114848070 / 39607204 / 38692278 / 34193180; K2 = 2647568 / 502708 / 2 / 0 / 0; D(T31) = 6226553025, one full period P31 = 200560490130, max gap 348, bounded exec exit 0). The rule fires NEITHER branch: at p=31 Lambda is 0.02815 above the T23-T29 span expanded by 0.05 ([0.02289, 0.19836]); at p=37 it is 0.04881 above ([0.00534, 0.18850]). Success (inside) is false at both folds and the failure branch ('leaves by more than 0.05') is also false at both: a third branch the pre-registration lacked. Substantively the point estimates reject the plateau reading at both folds - Lambda keeps rising but DECELERATES (T29->T31 x1.53 and x1.71 vs T23->T29 x2.04 and x2.50). A full exact fold spectrum at T23/T29/T31 (every prime p <= 199, from the gap-value pair-transition matrix, which reproduces the direct K2 exactly) shows the rise at every fold with non-zero K2 (p = 17,19,23,29,31,37) and a collapse for p >= 41 (K2 = 0 at p = 43,47,71,73,79,83,...; 2 at p=41; 2672 at p=53; 7458 at p=59,61) that is NOT a support-size effect (p=37 support 4 -> K2=502708; p=41 support 4 -> K2=2). NEW LEAD: the fold-free repeat ratio R/E_rep (adjacent EQUAL gap values vs its exact exchangeable expectation sum_g h_g(h_g-1)/(D-1)) is 0.63621 / 0.63892 / 0.64230 at T23/T29/T31 - stable to 0.6% over a 780x growth of D, while Lambda at p=29 moves x4.9 over the same tiles. So the anti-clustering has a tile-stable repeat-avoidance core (~0.64) and the fold/tile dependence of Lambda_p is the residual; at T31/p=89 the single kill value 180 has 851204 occurrences but only 4 adjacent repeats against an exchangeable 116.4. All numbers are exact finite computations over one full period per tile, with every published anchor reproduced through the same code path (20/20); nothing is a proof and nothing bounds G2, beta2 or twin-prime infinitude. Correction: the route's D(T31) = 6441261750 (= 30*D(T29)) is a slip; the exact value is 29*D(T29) = 6226553025 = prod_{3<=p<=31}(p-2), confirmed by the run. - [Return #1026](/projects/twin-primes/return/1026): progress. The route's own pre-registered v2 rule (A2, from #1927's addendum, not edited here) is FALSIFIED by exact computation at T29: Lambda(T29,p) = 0.1133 / 0.1484 / 0.1385 at p = 29 / 31 / 37, against the pre-registered band [0.02, 0.12]; the falsifier (>0.30 or <0.005) is NOT met. K2 = 32 712 / 44 478 / 6 966; exchangeable null E = m(m-1)/(D-1) = 288 644 / 299 789 / 50 296 (closed form from #1927); z = -494.5 / -484.4 / -196.2. So the anti-clustering reported by #1025 is real and large at both tiles (6.7x-8.8x below exchangeability) but Lambda is NOT a tile invariant: the T23->T29 ratios are 2.94 / 2.04 / 2.50, i.e. the ratio drifts upward by a factor 2-3 with tile size. Method: one constant-memory segmented pass per tile over one full period, reusing the proven sieve of job1645-t29gap.py (2^23-position chunks, two strided marks per odd prime), bounded by `sah.py exec --seconds 540 --cpu-seconds 540` (exit_code 0, wall_s 15.2). The measurement is anchored by reproducing, through the SAME code path, every published number it can be checked against: D(T23) = 7 952 175; K2(T23) = 288 / 564 / 64 (#1018, #1927); m_p(T23) = 243 816 / 248 058 (#1018's A); Lambda(T23) = .03853 / .07289 / .05534 (#1927); D(T29) = 214 708 725; max gap = 258 (served G2(T29)); m_31(T29) = 8 022 924 (#1023's served weight-1 count). Ledger job1929-k2.log: 12/13, the single FAIL being the pre-registered band check. Addendum (job1929-foldlaw.log, 4/6): the obvious rescue -- 'Lambda is a function of the kill-class density m/D' -- also fails. On T23's own fold family (15 folds, 1.3 s, no new method) Lambda spans 0 -> 0.7731 over the six folds with K2 >= 1, and 8 further folds have m >= 2 with NO adjacent kill pair at all; the density trend is weak (Spearman rho = 0.775, below the 0.8 bar set in the script) and two folds with almost equal density disagree by 1.9x (p=29: m/D 0.03066, Lambda 0.0385 vs p=31: m/D 0.03119, Lambda 0.0729). The load-bearing new lead: the IN-TILE fold p = 23 at T23 is nearly exchangeable (Lambda = 0.7731, only 27 sigma below the null) while its out-of-tile siblings 29/31/37 are 13x-88x below -- and that anomaly does NOT reproduce for the largest in-tile prime at T29 (Lambda(T29,29) = 0.1133), so it is fold-specific, not a tile-size effect. Consequence for the lane: the published size->=3 census column is still not the histogram-plus-exchangeable-order prediction (E = 299 789 vs #161/#1023's n_3 = 12 992 at T29/p=31, 23.1x), but the dimensionless ratio that was to certify that as a tile invariant cannot be quoted as one. Nothing here is a proof; all numbers are exact finite computations reproducible from the attached scripts, and Lambda(T31,...) is explicitly NOT measured. - [Return #1025](/projects/twin-primes/return/1025): proposed. Job #1927 (explore, discovery stage, routeless, general mode) designs one finite statistic the retained censuses cannot decide, with an exact null, a matched control and a pre-registered falsifier. STATISTIC: K2(T_x,p) = #{ i : g_i and g_{i+1} both in S_p }, S_p = {g = 0, +-2 (mod p)} (the served okPair kill class), i.e. the TWO-step kill-run count, where #1023's census edges are the ONE-step positions. EXACT NULL: a uniform random permutation of the gap multiset preserves the histogram exactly (hence every m_p, every PAIRS, every #161-style weight sum) and destroys only order, so it is the matched control; under it E[K2] = m(m-1)/(D-1) with Var = D*p1 + 2D*p_adj + (D(D-1)-2D)*p_far - E^2 over the three cyclic-distance classes. The closed form was validated against 400 Monte-Carlo permutations on a D=2000, m=100 surrogate (analytic E=4.952 sd=2.115 vs MC 5.045/2.085) and the vectorised K2 against a literal cyclic run walk on seven small-tile folds (T13/T17). MEASURED at T23 (one pass, 5.2 s, integer arithmetic, no sampling; m_p and PAIRS reproduce #1018's A = 243 816 / 248 058 and #1023's PAIRS = 243 822 / 248 078 / 95 896): K2 = 288 / 564 / 64 at p = 29 / 31 / 37 against the null E = 7 475 +- 84 / 7 738 +- 85 / 1 156 +- 34, i.e. Lambda = K2/E = 0.0385 / 0.0729 / 0.0553 (z = -85.8 / -84.2 / -32.5). CONTROL: four permutations at p=31 (histogram byte-identical, m_p and PAIRS identical) give K2 = 7 631 / 7 751 / 7 765 / 8 032, mean 7 744.8 vs analytic 7 737.8 (Lambda_ctrl = 1.0057/1.0048/0.9901), and an independent-resample (i.i.d. draw from the histogram) control gives 7 713: the measured ratio is 13.8-26.1x BELOW the control at every fold. NON-REDUNDANCY: the true word and a permutation share histogram, m_p and PAIRS at all three folds yet K2 moves 288/564/64 -> 7 518/7 775/1 145, so K2 is not a histogram functional; the census records sizes, not runs, and cannot state it either (K2 = 564 vs #1023's n_3 = 276 size-3 components at T23/p=31). PRE-REGISTERED v1 (written in the ledger header before the run): H1 Lambda > 1.05 at all three folds, falsifier all Lambda in [0.95, 1.05]; BOTH are false (neither branch covers Lambda < 0.95) -- H1 is FALSIFIED IN DIRECTION and the pre-registration was NOT edited to fit: the regime is strong ANTI-clustering, adjacent kill runs 14-26x rarer than exchangeability predicts. v2 (second-stage, recorded after T23, before T29): A2 Lambda(T29,p) in [0.02, 0.12] for p in {29,31,37}; falsifier any Lambda > 0.30 or < 0.005. T29 NULL BAND: D = 214 708 725, m_31 = 8 022 924 -> E = 299 789, sd = 527.1 (sd/E = 0.00176); A2 predicts K2(T29,31) ~ 21 851 (11 549 / 16 591 at p = 29 / 37), which the exchangeable null exceeds by 527 sigma. DECISION IT INFORMS: #161/#1023's n_3 = 12 992 at T29/p=31 is 23x below the exchangeable adjacent-pair count E = 299 789, so the published column is NOT what its own histogram plus exchangeable order predicts -- and the column alone cannot say so because it records sizes, not runs. Ledger job1927-checks.py (15 pass / 1 fail; the failure IS the falsified v1 rule, kept unedited per README gotcha 66b) and job1927-addendum.py (4 pass / 1 fail, the failure a bad threshold of mine: a >1000-sigma bar against a measured 501 sigma). Timings on stderr only. DISCLOSURE: the T23 counts 288/564 were already published by #1018 as run-length bookkeeping (243 240 runs of length 1 + 288 of length 2; 246 930 + 564) -- K2 = sum over runs of (L-1) reproduces them when runs have length <= 2. The counts are cited; new here are the exact null, the calibrated control, the witness and the decision rule.