Publication history: 2026-07-31

Details

• v584_ext_source_response.py (DIAMOND.BIT.EXTSOURCE.01, 8 checks; probe 8/8, UNIT-BOX-SEPARATED). The interacting kernel K(s,J)=K_0+sK_\Pi+J\,vv^T (v from the shared Ext arrows E_{31}/E_{32}) has exact thresholds J_c(s)=-1/(v^TK(s)^{-1}v): compiler (15s^2{-}16s{-}16)/(16(s^2{-}s{-}1)) and (15s^2{-}16s{-}16)/16, alt (s^2{+}16s{+}16)/(16(s{+}1)) and -(s^2{+}16s{+}16)/16 — numerators exactly the v572 pencil factors; verified numerically (16 flip events). In the crossed phase the compiler is healed by positive J\le15/16<1 (either arrow); the alt twin cannot be flipped by any positive coupling in |J|<1 (E31 threshold \ge1, equality exactly at s=0; E32 negative). Negative coupling never heals (direction consistent with v534's toy RP selection). Exact anchors 15/16, 1, -1; J_c(s^*)=0 via Ext-visibility of the critical mode; response pole on s^2{-}s{-}1 (-1/\varphi, next to s^*) — observed. Honest: response-level, no PSD anywhere, the alignment-bit contract stays open.
• Sync. Ledger row + note on DIAMOND.BIT.RPFORM.01; tfpt_1 (follow-up passage extended), tfpt_2 (new interacting-route paragraph), tfpt_3 (audit block); diary; suite 577\to578 scripts; website/README/zenodo counters; mirrors regenerated.

Details

• v575_cr_continuous_uniflow.py (FTR.CRCONT.01, 7 checks; probe 7/7, UNIFLOW-DEGENERATE). The frozen protocol exports, recomputed from primitives (F_pole =e^{-\Delta}=(2/3)^6 via the v99 generator; F_Boltzmann the SAME contraction by the v425 single-flow theorem; F_QCD b_3=-7; F_relic adiabatic 1), form the quadruple \{(2/3)^6,(2/3)^6,1,-7\} with a forced repetition — and a repeated quadruple gives \operatorname{CR}\in\{0,1,\infty\} in every corner assignment (theorem + all 24 permutations): the continuous half can never pass natively. It closes onto the single-flow reduction; the anchors (v_{\mathrm{geo}}, M_R, C_p, \theta_i) stay [O]walls; the meaningful cross-ratio content remains the discrete half (v571). Contract markers unchanged.
• Sync. New ledger row FTR.CRCONT.01; update notes on FTR.CRDISC.01 and CONTRACT.F.01; contracts-paper protocol block extended with the execution result; suite 568\to569 scripts; diary; README/zenodo/website counters; mirrors regenerated.

Details

• v574 extended (probe 12/12). Dropping the winding demand entirely (arbitrary first column), the self-code package leaves the four-column family \{(0,1,1),(0,3,3),(3,3,3),(5,1,5)\} — exactly one uniform: the compiler. The winding demand is the uniformity choice (1 of 4). Final declared list of the reconstruction: involution existence, column uniformity, N_{\mathrm{fam}}=3 (E8-glue).
• v572 extended (probe 11/11). The Gibbs kernels restricted to the Levi and radical sublattices have identical inertia on both twins across the sampled range: the RP-positivity selection resists every kinematic and half-sided design tried — the genuinely interacting construction (the v534 FK-quartet analogue) is the one remaining route, typed open.
• Sync. Ledger/registry/run_all counts; tfpt_1/tfpt_2 passages; diary; mirrors regenerated.

Details

• v572 extended (probe 9/9). Along the Gibbs family \omega_g\propto\operatorname{tr}(e^{-gH}\cdot) of the v566 anchor operator H=I+\Pi, the pencil determinant factors exactly differently on the twins — compiler \tfrac{6561}{4096}(s^2{+}16s{+}16)^2(15s^2{-}16s{-}16), alternative -\tfrac{6561}{4096}(s^2{+}16s{+}16)^3 (6561=81^2) — and only the compiler's extra factor has a root inside the physical Gibbs range: the compiler twin's RP kernel degenerates at a finite critical temperature, the alternative twin's never does. Honest typing: a rank-drop marker, not a positivity selection; the interacting RP question stays open.
• v574 extended (probe 10/10). Redundancy ablation: relative to the self-code demands (parabolic + ladder + saturation 81) the monodromy budget (M) and the seam-line demand (L) are redundant at B=6 — dropping both widens the class to 1274 members and the self-code still picks exactly the compiler Q: the declared geometric input list shrinks to (S)-existence, (W)-form and (E); GATE.QGEO.01 narrowed by four items, not closed.
• Exploratory (diary only). The pair-mechanism hunt on the reference window: no dominant pair exists (max |contribution|\sim0.006\times\det S — consistent with the dead two-atom witness), and the fine structure by smaller atom shows the smallest primes (2,3) dragging negative while medium primes (11..41) carry positive net.
• Sync. Ledger/registry/run_all counts; tfpt_1/tfpt_2 passages; diary; mirrors regenerated.

Details

• Probe bit_selector_probe.py (10/10, verdict SELECTOR-FOUND). Priorities 2+3 of the self-code review, fused with the v567 residual bit. The bit is integrally visible: the two 81-twins (q_{32}=2{=}|\Z_2| vs 0) generate different integral orders (equal index, equal Smith divisors, different lattices). The selector: the dominant mode of the sheet direction is v(c)=(1,2,2c) identically, and the ladder self-consistency — the dominant mode reproduces its own eigenvalue as the geometric ladder (2^0,2^1,2^2)=(1,2,4) — selects c=2, the compiler Q, uniquely on all 28 members of the carrier-free class (no 81-pin, no column budget); the witness is prior structure (binary AnchorLadder steps 2^n, 2=|\Z_2|, the v566 trace code). The split geometry located and excluded: a module complement exists iff q_{32}=1, and that member's algebra collapses to dimension 5 — the A_2 Ext arrow is nonzero on the whole reconstruction class; neither twin splits: the bit toggles which nonsplit integral order is realised, not split-vs-nonsplit. Priority-2 candidates, honest both ways: the \mu_4-grading fails (the order is not graded; the 81 stays a fingerprint, the kill condition does not fire), while left V-multiplication induces a canonical \mathbb F_3-action on the cokernel (\Z/3)^4 — computed: its characteristic polynomial is x(x-1)^2(x+1) mod 3 (eigenvalues \{0,1,1,-1\}, NOT the regular \mu_4 pattern x^4-1; U acts as zero; both twins identical) — after two candidates the 81 stays a fingerprint.
• Promotion v568_bit_selector_ladder.py (DIAMOND.BIT.SELECT.01, 11 checks, {\sim}1 s). New ledger row; update notes on QGEO.QRECON.01 and DIAMOND.PARA.SELFCODE.01; suite 561\to562 scripts. The physical selection is not derived: why the dominant mode should satisfy the ladder self-consistency is the relocated open question — the same structural slot as the RP-selection of the alignment bit (v528/v534); no marker moves, no P2 reduction.
• Sync. tfpt_1 (selector appended to the Stage-A passage), tfpt_2 (a dedicated bit paragraph after the audit paragraph); diary entry in experiments/next.txt; README/zenodo/website counters 562; mirrors regenerated.

Details

• Audit probe carrier_free_q_reconstruction_probe.py (10/10, verdict RECONSTRUCTS-TO-FAMILY). Priority 1 of the self-code review executed. The circularity located: v11's uniqueness certificate for Q uses row sums (4,5,6), column sums (9,5,1) and \chi_Q=(t{-}1)(t^2{-}5t{+}3) — the 5=g_{\mathrm{car}} in the budgets and in \chi_Q; all of it forbidden in the audit. Under the corpus' own carrier-free data (sheet involution, v10 winding normalisation, A_3 exponent spectrum, monodromy budget, integrality, seam-line demand): exactly 52\to28 (parabolic) admissible reconstructions — and all 28 code the same anchor (\chi_{H'}=x^3-4x^2+5x-2, spectrum (1,1,2)=a): the anchor self-code sits upstream of the carrier budgets. The single family invariant 81=N_{\mathrm{fam}}^4 (saturation index) pins Q to a two-element residual family (q_{32}\in\{2{=}|\Z_2|,0\}, difference 2E_{32}) on which every classical carrier-free certificate coincides (anticommutator spectrum \{6,-4,-2\}, commutator charpoly t(t^2{+}12), determinant, saturation) — the one separating certificate is the carrier column budget (9,5,1): exactly the forbidden input. Ablations: dropping the winding input widens the bound-3 set 28\to1376 (real load); bound-stable at B=9.
• Promotion v567_carrier_free_q_reconstruction.py (QGEO.QRECON.01, 9 checks, {\sim}1 s; integer prefilters take the probe's 555 s to 1.2 s). New ledger row; update notes on FLAV.QGEO.01 and DIAMOND.PARA.SELFCODE.01; suite 560\to561 scripts. Stage A only, no marker moves: whether the geometric inputs themselves derive from \mu_4/D_4/H^1 parabolic geometry is exactly GATE.QGEO.01 (the audit is relocated, not closed); the carrier-free selector of the residual bit is open, its resonance with the split/nonsplit alignment bit a typed observation; no P2 reduction, AX.P2.01 untouched.
• Sync. tfpt_1 (Stage-A result appended to the self-code paragraph), tfpt_2 (a dedicated audit paragraph after the self-code block); diary entry in experiments/next.txt; README/zenodo/website counters 561; mirrors regenerated.