run 077Settled
../lab/runs/077-order-not-amplitude.mdPrediction(A) Amplitude drops out within a class. Over the 410 pairs of equal C₁ and unequal N₁ (the 62 equal-C₁, equal-N₁ pairs excluded), the partial Spearman of |D| with |Δ ln N₁| controlling for |δ| and for cut class (class as indicator columns in the rank regression) is below 0.15 in absolute value. Cut-2 pairs all have |Δ ln N₁| = ln 4 and contribute through class only; A is also reported on cut 4 alone. (B) Amplitude drops out across classes. Over the 704 pairs of unequal C₁, the partial Spearman of |D| with |Δa| controlling for |δ| and |ΔC₁| is below 0.15 in absolute value (|Δ ln N₁| in its place is reported, not scored). (C) Order does not drop out. Over the same 704 pairs, the partial Spearman of |D| with |ΔC₁| controlling for |δ| and |Δa| is at least 0.3. Confirmed if A, B and C all hold.
Falsifier(A) the within-class partial Spearman exceeds 0.3 in absolute value: the amplitude matters at fixed separation, and the order-and-amplitude reading fails inside a class. (B) the across-class one exceeds 0.3 in absolute value. (C) the order partial is below 0.1, including any negative value: once amplitude and separation are held, cut class carries nothing. Falsified if any clause is falsified; confirmed if all hold; otherwise unanticipated. Each clause is scored at its point value; a clause whose function-bootstrap 5th–95th range spans both its confirm and its falsify bands is reported as unresolved beside its score. Power rule for A, applied first: if Spearman(|Δ ln N₁|, |δ|) over the 410 pairs exceeds 0.8 in absolute value, or if the positive control, the partial of |D| with |Δy₉| given |δ| and class over the same pairs, is itself below 0.15, then A has no resolving power and is scored unanticipated whatever its value.
Sealed 2026-09-30, after run 076 was scored and before any correlation of D with N₁ was computed (codifier). Known at sealing: everything in RESULTS076.md, including the equal/unequal-C₁ bins, the partial Spearman of |D| with |ΔC₁| over all pairs (+0.60), the twenty largest |D| (all cut 5 or 4 against cut 2) and the seat-record items. Not known: any statistic of D against N₁. Read at sealing, from the census and the polynomials only: N₁ per class (cut 2: 4 or 16; cut 3: 16, 24, 36, 64; cut 4: fifteen values from 4 to 324; cut 5: 36, 54), the set counts above, and the control, which already holds (degree C₁ and coefficient N₁ on all 49 functions).
Where the analogy is weak, stated before the data. In Feigenbaum's setting the amplitude does not move δ. Here N₁ does move the exponent inside a class: run 068 found N₁ sub-bands in measured 1/ν, and y₉ tracks them. So the claim sealed is narrower than full universality: not that N₁ is irrelevant, but that once the separation δ is fixed, the composition deviation no longer cares about N₁ while it still cares about C₁. The live risk is that D tracks the exponent gap Δy₉ beyond δ (run 076: Spearman 0.81 with |Δy₉|), and Δy₉ tracks N₁ inside a class; if so, clause A fails, and the order-and-amplitude reading with it.
Reported, not scored. Spearman(|Δ ln N₁|, |δ|) within cut 4, cut 3 and cut 2 and pooled over the 410 (reported first, for the power rule); per-class counts of the 410 and of the 62 excluded; a leave-one-function-out jackknife range for A, B and C. The same partials with |Δy₉| in place of |Δ ln N₁|; within each class with at least 15 pairs (cut 4: 378, cut 2: 78, cut 3: 15), Spearman of |D| with |δ| and with |Δ ln N₁|; the partial of |D| with |Δ ln N₁| given |δ| for cut 4 and cut 2 separately; and a table of |D| against |δ| per class.
The reductio this seal passed first. By construction: the control is known to hold. Clause C is not run 076's clause D restricted: over unequal pairs |ΔC₁| takes 1 (302 pairs), 2 (376, of which 364 are cut 4 against cut 2) and 3 (26), so C loses the equal-versus-unequal contrast that carried 076's +0.60 and asks whether cut-4-against-cut-2 pairs deviate more than the rest at fixed separation and amplitude; it can fail on data 076 passed. Pooling: classes differ in their |D| level and in their spread of N₁, so A controls for class and B uses the per-order amplitude, to keep class identity from passing or failing them. Null: if D depended on N₁ as strongly as on C₁ at fixed δ, A and B would read near 0.5 or above. Negation: a world where N₁ is a second order parameter, not an amplitude, shows A above 0.3. Cost: seconds, stored data.
Reviewed before commit by a second reader (OPS.md); its seven edits are folded in: a function-level bootstrap stratified by class (pairs share functions); class controlled in A, with cut 2's single amplitude gap named; the per-order amplitude (ln N₁)/C₁ across classes in B and C; a power rule for A with |Δy₉| as its positive control; C's sign stated; the by-construction note on C corrected; and the jackknife and per-class counts reported.
unanticipatedScored by the codifier from RESULTS077.md (0f143f7), as written. Control passes: the lowest-order term of 1 − R(1 − q) is N₁·q^{C₁} on all 49 distinct functions.
Power rule for A, first — triggered. Spearman(|Δ ln N₁|, |δ|) over the 410 pairs is +0.49 (below 0.8), but the positive control, the partial of |D| with |Δy₉| given |δ| and class, is −0.099, below 0.15. By the seal, A has no resolving power and is scored unanticipated. (Its value, −0.256, would have been unanticipated anyway: between 0.15 and 0.3 in size. It comes from cut 4, −0.274; cut 2 has only one amplitude gap.)
(B) Amplitude drops out across classes — confirmed. +0.015 over 704 pairs (function bootstrap −0.13 to +0.19; jackknife −0.03 to +0.06).
(C) Order does not drop out — confirmed. +0.722 (function bootstrap +0.66 to +0.78).
Outcome. Unanticipated (A unresolved, B and C hold). Across cut classes the composition deviation keeps the order of contact C₁ and forgets the per-order amplitude completely, as the Feigenbaum reading says. Inside a class nothing tested resolves: once separation is fixed, neither the amplitude nor the exponent gap moves |D| by much.
Reported, read. With |Δy₉| in place of the amplitude, B reads +0.544 and C +0.367: across classes the exponent gap carries information beyond C₁ and δ that the amplitude does not, and it takes about half of C's weight. Since y₉ depends on both C₁ and N₁ while the amplitude alone is silent, the extra information in Δy₉ is not amplitude; what it is is open. Within classes, |D| tracks |δ| strongly (Spearman 0.70 cut 4, 0.96 cut 2, 0.73 cut 3).
generated 2026-10-25the lab index