3974 — The Infinity Leray Covector Transports Contragrediently
Question
The explicit infinity-Gysin calculation produces a source-normalized elliptic period row ((1,1)) in the (G_{12}) residue chart. Is that row an invariant coordinate value that may be copied into the source-inverted chart, or is it a dual section that must transform with the elliptic basis?
Source inversion
Let
[ (x,y;a,b)longmapsto(y,x;b,a). ]
On the final-three master block, the labelled occurrence transition fixes (e_7) and exchanges (e_8,e_9). Write (P) for that column permutation and (M(x,y)) for the explicit (2)-by-(3) infinity-Gysin matrix.
Direct substitution into the matrix from the source compactification gives
[ M(y,x)P
\begin{pmatrix}
1&0
0&y^2/x^2
end{pmatrix}
M(x,y).
]
Thus the elliptic basis is not fixed coordinatewise under the occurrence transition.
Dual transport
A period covector transforms contragrediently. Consequently,
[ (1,1) longmapsto (1,x^2/y^2), ]
because
[
(1,x^2/y^2)
\begin{pmatrix}
1&0
0&y^2/x^2
end{pmatrix}
=(1,1).
]
The resulting source-master Leray covector agrees exactly across the two occurrence charts.
The hostile alternative fails: copying the coordinate row ((1,1)) into both charts produces different master covectors whenever (x^2 e y^2). Exact tests at squared kinematics ((x^2,y^2)=(9,16)) and ((25,144)) exhibit this failure.
Narrow result
The explicit final-four infinity Leray readout is occurrence-natural as a transported dual section. Its coordinate value ((1,1)) belongs to one source-normalized chart and is not a chart-independent constant row.
This provides a necessary normalization gate for extending the physical Leray readout to the full rank-(26) marked-relative coefficient object: any proposed extension must reproduce the contragredient transition before quotienting or serializing representatives.
Scope
This entry proves occurrence covariance only for the explicit final-four infinity-Gysin readout. It does not construct a covector on the complete rank-(26) module, establish a physical rank-(26) period, or reopen the generic (mathcal Q)-apparency programme.
Durable verification
- checker:
research/benincasa/checkers/check_infinity_leray_inversion_transport.py; - result:
research/benincasa/results/infinity-leray-inversion-transport.json; - exact checker status: all four gates passed, including deliberate failure of chartwise constant copying;
- ledger allocation:
seqclaim-d3f831f115a9f893e5425852; - epistemic graph event:
ev-000000009039-75996382-0bbd-48bd-8a65-a8f241f37c59.