Moonshine junction to the frontier-physics target set

Date: 25 October 2026

Status: corpus crosswalk and ranked theoretical work programme; no physical promotion

Authority: frontier target set Evidence: machine-readable crosswalk Certificate: crosswalk verifier

Result

The Moonshine programme now touches seven maintained frontier targets, but it does so at three different distances. FPT-002 and FPT-019 can move immediately by computation: the scalar/genus-one quotient is already known, and the cost of each proposed refinement can be audited. FPT-007, FPT-009 and FPT-022 have exact finite carriers but still require either a physical source or an intertwiner. FPT-010 and FPT-017 remain comparisons only: the current chain does not produce a new positivity bound or a renormalization-group flow.

This prevents two opposite errors. Moonshine is no longer isolated from the frontier lane, but neither is its mathematical closure counted as experimental or four-dimensional physical closure.

Target map

target	exact asset contributed by the Moonshine branch	distance to target	next gate	stop rule
FPT-002 inverse detector design	explicit losses: \(23A/B\to T_{23}\), 22 charges to one charged character, \(\mathrm{Dic}_{11}\to D_{11}\), \(\chi_5\to\chi_{10}\)	immediate computational	find the least additional trace/insertion that separates the desired orientation after nuisance quotients	stop if every candidate is constant on the same fibres
FPT-007 defects and boundaries	order-23 Tambara--Yamagami defect channel; order-46 2A/2B junction; ten-sector genus-two seam carrier	mathematical near, physical far	construct the twisted--twining/genus-two junction and state what it transports beyond quantum dimension or sector count	stop if equal defect indices admit scrambled orientation and seam data
FPT-009 quantum-code and synthetic-gauge emulators	529-label finite quadratic module, Fourier quarter-turn and order-44 \(\mathrm{Dic}_{11}\) instruction set	emulator-near	realize \(D_5\) and \(S\) from source-native controls and predict forbidden/reachable words	stop if only an arbitrary universal compiler realizes the group
FPT-010 scattering, causality and positivity	explicit admissibility quotients and no-goes constrain what an observable may retain	comparison only	derive an inequality excluding an otherwise unitary, causal and passive response	stop if it is standard positivity in new notation
FPT-017 scale-stable admissibility	a composable chain from characteristic-two code through number field, lattice and VOA	translation-near, RG-far	define pushforward measures/errors at three actual physical scales and test direct versus staged descent	stop if arrows are changes of mathematical category without coarse-graining
FPT-019 computational admissibility	finite certificates for Rule 60, quadratic forms, modular label orbits, transition groups and carrier counts	immediate audit	publish input size, arithmetic cost, source dependence and missing analytic tables for every next calculation	stop any claim hiding full VOA construction or unrestricted character data as an oracle
FPT-022 quotient scars	exact central-sign loss \(\mathrm{Dic}_{11}\to D_{11}\), orientation loss \(23A/B\to T_{23}\), and order-eight 2B-lift kernel	strong comparative asset	test whether an oriented record resolves the central/lift residue while scalar records remain identical	do not identify this \(C_2\) quotient with \(D_4\to G_2\) triality

The closest no-new-experiment tranche

The next work should stay entirely on the mathematical side until it either produces a discriminator or fails:

enumerate the four oriented order-46 cases and their power-map labels;
modularly transport the known order-46 Hauptmoduln to \(Z(h^2,h^{23};\tau)\) and normalize them compatibly;
group the 46A/B and 46C/D results by their Conway and Baby-Monster centralizer lifts;
record the resulting no-go: fifth power fixes the involution and leaves each orientation pair scalar-degenerate;
identify the complete \(C_{23}\times S_4\) centralizer and place the \(Q_{46AB}\cong C_2^2\), \(Q_{46CD}\cong C_2\) quotient labels inside its five insertion classes;
close every single-insertion scalar route: the product orders \(23,46,46,69,92\) are cyclic and all A/B scalar series pairs agree;
construct the smallest matrix kernel from the surviving order-23 branches to the ten even genus-two characteristics;
reject the join if the modular representations or anomaly lines cannot intertwine.

Steps 1--6 close the scalar part of FPT-002. The projective-centralizer audit then closes the remaining genus-one \(S_4\) representation route: the transgressed cocycle is trivial and the five class traces determine the module. Step 7 is therefore the FPT-007 higher-genus junction. Step 8 is useful even when negative: it converts a speculative bridge into a typed no-go.

The finite emulator tranche

The defect plane already supplies a compact synthetic-gauge target:

\[ A=\mathbb F_{23}^2, \qquad q(a,b)=ab/23, \qquad S(a,b)=(b,-a), \qquad D_5(a,b)=(5a,14b). \]

An emulator need not realize a Monster VOA. It must realize these two operations with independently calibrated controls, preserve the declared quadratic data, and demonstrate the predicted 44-element closure before projective readout and the 22-element closure after it. The decisive record is the central sign: coherent label readout must see it; projective readout must not. That is a source-restricted FPT-009/FPT-022 experiment. A generic qudit compiler reproducing the matrices on demand would verify software, not the proposed physical provenance.

Where the physical path stops

No present arrow maps the VOA grading variable to laboratory time, the Monster defect to a material defect, or the genus-two sewing modulus to a spacetime metric component. The Spin adjacency also remains finite and arithmetic:

\[ \mathrm{Dic}_{11}<SL(2,23)<Sp(4,23)\cong Spin(5,23), \]

whereas the corpus's physical carrier uses the real form \(Sp(4,\mathbb R)\cong Spin_0(2,3)\). A physical promotion requires a lift choosing real signature, positive energy, time orientation, dynamics and a detector map. None follows from reduction modulo 23.

Ranked continuation

Mixed-level genus-two intertwiner: use the exact \(Sp(4,2)\times Sp(4,23)\) CRT carrier; a direct order-11 action on the ten characteristics is impossible. The unique projective \(C_2\) sign coupling survives, while the scalar metaplectic \(C_4\) lift is ruled out for the one-block embedding. The genuine eta line instead gives \(v_\eta(K)=i\), while \(K\) permutes the ten even characteristics with cycle type \(3^3\,1\). The eta-normalized free-Majorana action is now complete: its three cycle products are \(1\), its fixed odd--odd eigenvalue is \(-1\), and its determinant is \(-1\). Arf conjugation fixes the Baby-Monster multiplier to the inverse phase, so the complete \(2A\) action is the pure \(3^3\,1\) permutation with determinant \(+1\). Construct an amplitude vector carrying it and test degeneration.
Cross-grade VOA/defect composition: test fusion or intertwining data not determined by the now-exhausted graded \(S_4\) characters.
Finite \(\mathrm{Dic}_{11}/D_{11}\) emulator: conventional but sharp test of quotient scars and detector equivalence.
Scale/RG and Spin lift: hold until a physical carrier and action exist.

This ranking makes the programme useful either way. A successful intertwiner would be new mathematical structure close to the corpus's central seam. A failed intertwiner would remove a large speculative branch. The emulator would still demonstrate, in an ordinary platform, the exact information-loss geometry that motivated the admissibility language.

Moonshine junction to the frontier-physics target set

Route into this page

Moonshine junction to the frontier-physics target set

Result

Target map

The closest no-new-experiment tranche

The finite emulator tranche

Where the physical path stops

Ranked continuation

Corpus links

Inbound corpus links

Outgoing corpus links