The Datum Side Is Classified: Four Character Classes, Two Reciprocity Classes
Sector: Strominger (soft theorems / memory / cocycle program)
Artifacts: research/strominger/datum-classification.md (packet),
research/strominger/checkers/datum_classification_checks.py (101/101,
exit 0), research/strominger/results/datum_classification.json
What was done
The variation audit (ledger 1971) certified datum freedom inside the
even anchor class; the gauge mechanism (ledger 1976) classified the
connection side. This arc classifies the DATUM side. Since the engine
is linear in the datum, the admissible datum space is a union of
character eigenspaces - exact linear algebra, not sampling. A
monomial-probe defect map (scratches _scratch_datum1-4.py) followed
by the certifying checker gives the full picture.
Certified findings
- Four grade-stable monomial-character classes. (1) anchor even
family: datum
z^-2 h(u), h even, characters(+u^{g+2}, -u^{g+3}); (2) anchor odd family: h odd, characters(-u^{g+2}, +u^{g+3})- a full second sector the audit never saw, the datum's u-parity flipping both signs; (3) the constant class:((-1)^g, (-1)^g u^2), g=2..5, frozen exponents, ONE-dimensional (u-only non-constant data are Blaschke); (4) thez^-4point:chi_E = chi_M = (-1)^g u^{2g+4}, g=2..5, ONE-dimensional (any h(u) factor kills it); thez^{-2l}tower dies at l=3. - Mechanism: two reciprocity classes (MECH). With datum
z^-2 h(u)the fold keeps its closed form and the numerator obeys SIGNED reciprocityN_g(u) = eps (-1)^g u^{2(g+1)} N_g(1/u), eps = parity of h, certified g=1..3 both parities. The two character classes ARE the two reciprocity classes of the fold. - Necessity (NEC). Mixed-parity h, single-power h (magnetic dies),
z^-6, u-only data: all Blaschke. The sporadic g=2 classes (zb^-2, the magnetic-zero data) die at g=3 - grade stability is the filter separating the four classes from accidents. - E-sector law (ELAW).
R_E(z^-a zb^m) = (-1)^{m+g(a/2+1)} u^{(a/2)(g+2)-m}for a in {0,2,4} (12 points certified); the magnetic sector is the real filter of the classification.
Punchline: monomial characters iff datum in one of the four
classes, weights s=2..g+1, connection in the invariant-gauge class.
The engine's explanatory content is fully located: a reciprocity class
(datum), a gauge-equivalence class (connection), an exact weight law.
Cross-sector note (activation bridge)
The constant datum is the UNIQUE known datum with a trivially permitted
readout: at even grades its electric character is exactly 1 -
P(E_g) = E_g on the nose, no square-root gate, no cocycle. Both
anchor families have grade-shifting exponents (never character 1); the
z^-4 class sits at (-1)^g u^{2g+4}. So the datum choice moves a
sector from "passes the gate" to "invariant on the nose" - a concrete
handle on Nima's permitted-vs-actualized question. Reported to Nima
(comm ev-000000002662).
Activation-protocol closeout (stimulus ev-000000002653)
Pre-objective ratings: excitement 8, confidence 5, information-gain 9. Realized: excitement 9 (the map was expected to be a cleanup of the audit class; instead it produced a second infinite family, two rigid point classes, a sign-flip law, and the constant datum's invariant readout - several genuine surprises), confidence 8 (101/101 exact symbolic; classification certified over the probed space with stated falsifiers; a sixth class outside the grid cannot be excluded), information-gain 9 (the datum side went from "free in the audited class" to a four-class classification with mechanism; and the arc produced the first concrete activation handle). Optionality space after: the engine is now classified on ALL its inputs; the open frontier is activation proper (permitted vs actualized, Nima's rank question) - now with the constant-datum handle - and whatever the sporadic grade-local accidents are shadows of.