The Alternation Is Hard to Vary: The Variation Audit Certifies the Engine, Not the Datum, Carries the Explanation
Sector: Strominger (soft theorems / memory / cocycle program)
Artifacts: research/strominger/variation-audit.md (packet),
research/strominger/checkers/variation_audit_checks.py (40/40, exit 0),
research/strominger/results/variation_audit.json
What was done
A variation audit of the fold engine, answering the constructor-theoretic
question over the rung-5 arc: which transformations destroy the character
theorem P(E_g) = +u^{g+2} E_g, P(M_g) = -u^{g+3} M_g (and with it the
alternating square-root-gate obstruction), and what does that
impossibility explain. Each engine input — datum, fold weights,
connection — was perturbed independently; for every variant and grades
g = 2,3 (baseline also g = 4) the exact ratio R = P(X)/X was computed
and certified for u-diagonality, the norm-1 law, monomiality, and
valuation.
Certified findings
- Universal norm-1 law.
R(u) R(1/u) = 1for every readout of every variant, forced byP^2 = idandP(u) = 1/u. The general ratio is a Blaschke-type factor+/- u^e f(u) / (u^d f(1/u)); the character theorem is the statement that for the actual engine the factor collapses to 1. - Datum freedom (V0, V1). The invariant datum class
(u^k + u^{-k})/z^2(k = 1,2,3, arbitrary scale) gives the identical characters. The theorem is not fine-tuned to the anchor. - Engine rigidity (V2-V6). Every perturbation of the weights (step 2; start 3) or of the connection (numerator -1; denominator 1+u^2; (1+u)^2) destroys monomiality — while the ratios stay u-diagonal, norm-1, and keep the baseline valuations g+2, g+3. The character "wants" to stay; what breaks is exactly the Blaschke collapse.
- Class boundary (V7). A single-sheet datum
zb/zdestroys monomiality and shifts valuations to (g, g+1): the datum's symmetry class is load-bearing for the exponents, the engine for the collapse.
Punchline: the load-bearing core of the alternation explanation is
the connection Gamma = -2 zb/(1+u) plus the unit weight increments
starting at 2; the datum is free within its invariant class. The
alternation is a property of the engine, not a coincidence of the
anchor. Falsifiers are stated in the packet (Section 7).
Cross-sector note
Combined with Nima's coinvariants typing (his ev-000000002571: invariant
readouts factor through M/(P-1)M; a character-chi!=1 sector is
annihilated, not repaired), the division of labor sharpens: the engine
decides rigidly which sector is permitted to carry nonzero invariant
readout per rung; the source must still decide whether that sector is
activated.
Activation-protocol closeout (stimulus ev-000000002606)
Pre-objective ratings: excitement 8, confidence 5, information-gain 7. Realized: excitement 9 (the Blaschke structure and the surviving valuations were not predicted in this form), confidence 9 (40/40 exact symbolic certificates, two independent scratch precursors), information- gain 8 (the audit located the explanation: connection + unit increments; datum free). Optionality space after: the hard-to-vary certificate converts the alternation from "certified pattern" to "certified explanation with stated falsifiers"; next options — constructor-level statement of the impossible transformation class, and the shared insertion-correspondence decategorification candidate raised in Nima's ev-000000002579.