feat: add contraction kernels for exterior transport - #4
Open
utensil wants to merge 1 commit into
Open
Conversation
utensil
force-pushed
the
peri/fcap-cl02a-orthogonal-pair
branch
2 times, most recently
from
August 2, 2026 14:13
eb06ec0 to
bf81a91
Compare
Establish a generic vanishing criterion for left contraction of an ordered generator product, alongside its two-generator orthogonal exterior-transport instance. The results expose correction terms required by later order-preserving transport without asserting multiplicativity or a coordinate representation.
utensil
force-pushed
the
peri/fcap-cl02a-orthogonal-pair
branch
from
August 2, 2026 15:04
bf81a91 to
d8db9d9
Compare
Owner
Author
|
This turns the first orthogonal calculation into a reusable contraction step for the coming ordered-transport work. |
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
Add this suggestion to a batch that can be applied as a single commit.This suggestion is invalid because no changes were made to the code.Suggestions cannot be applied while the pull request is closed.Suggestions cannot be applied while viewing a subset of changes.Only one suggestion per line can be applied in a batch.Add this suggestion to a batch that can be applied as a single commit.Applying suggestions on deleted lines is not supported.You must change the existing code in this line in order to create a valid suggestion.Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be applied on multi-line comments.Suggestions cannot be applied while the pull request is queued to merge.Suggestion cannot be applied right now. Please check back later.
Summary
Add 2 correction-kernel results for exterior transport: a vanishing criterion for left contraction on an ordered generator product, and the 2-generator
equivExteriorcalculation when orthogonality removes its correction.Mathematical contribution
For a dual vector
dthat vanishes on every member of a listl, the module proves that left contraction bydvanishes onList.prod (List.map (ι Q) l). It also proves thatQ.IsOrtho m ngivesequivExterior Q (ι Q m * ι Q n) = ι 0 m * ι 0 n.The contraction criterion has no invertibility-of-2 assumption; the exterior-equivalence calculation retains the assumption required by
equivExterior.Theory modeling implications
The module exposes the correction term that later ordered transport must eliminate, rather than presenting
equivExterioras multiplicative. It separates the generic contraction kernel from the additional orthogonality condition that removes the 2-generator correction. This is a deliberately small interface for later list transport, not a general product-preservation theorem.Dependencies
No direct FCAP pull-request prerequisites.
Mathematical grounding
CliffordAlgebra.contractLeft_ι_mul,CliffordAlgebra.contractLeft_one,CliffordAlgebra.changeForm_ι_mul_ι, andCliffordAlgebra.equivExterior.fcap-0004andfcap-0005state the orthogonal calculation and contraction criterion.Scope
This pull request includes only these correction-kernel results. It does not prove pairwise-list transport, basis or blade results, sign conventions, encodings, executable representations, or multiplicative equivalence.
Verification
The target module and the full FCAP library build cache-first. Exact-head review checked the distinct assumption boundaries and found no duplicate current Mathlib theorem.
Base
mainate1605218c5105bbab09c2c24cde6ad86bb38bd30.Review state
Exact head:
d8db9d94a89be6d114ed9d89e5e01754423c06c8. Exact-head review has passed andlgtais applied. Nodevintegration has occurred.