This directory owns the computational companion and release closure for Paper XX, All-Depth Carrier Accessibility for Routed Composition. The routed factorization, survivor recursion, and cutwise statements are proved in the manuscript. The exact shared-carrier census is a finite Computational Certificate; the numerical censuses remain bounded companions.
This is the paper-owned package for the post-protocol carrier/route line. Its mathematical antecedents are Paper III's all-length disjoint-block obstruction and Paper VII's carrier-resolved incidence geometry. Its retained results do not depend on earlier experiment archives or numerical logarithm diagnostics. The package also does not certify Paper XXI or make that paper a corollary; a cross-paper bridge would require an explicit Paper XX carrier-hypothesis registration for the marked finite-field family.
The engine records:
- direct support norms and support-edge count;
- explicit routed products at each enumerated depth;
- carrier support of every sector;
- active-route counts and first active depth within the declared search bound.
- carrier-restricted path pairs, exposing the sandwich
composition <= carrier-path <= support-path.
The computational engine requires a complete orthogonal sectorization. It stores orthonormal sector bases and multiplies the corresponding rectangular transport blocks; these are basis representations of the same routed operators, not Boolean substitutes.
Endpoint pairs and source->target keys use source-first order. The stored
direct-support matrix follows the operator convention
matrix[target][source] = max_g ||Q_target R_g Q_source||_F.
The current adapters are:
z2_double_regular_engine(): a 4-dimensional regular-plus-regular Z2 model with exactly representable 0/1 input matrices, a pure--hybrid--pure graph path, and a mathematically exact all-depth carrier obstruction;s3_natural_regular_engine(): a 9-dimensional natural-plus-regular S3 control model with an A-only endpoint, an A+B hybrid intermediate, and B-only endpoints;rubik_engine(): the canonical 228-dimensional Rubik realization.
| Model | Carrier dimensions | Sectors | Final depth | Support / carrier-path / composition pairs |
|---|---|---|---|---|
| Z2 regular + regular | 2 + 2 | 3 | 3 | 9 / 7 / 7 |
| S3 natural + regular | 3 + 6 | 6 | 2 | 36 / 28 / 28 |
| Rubik canonical | 64 + 144 + 8 + 12 | 9 | 2 | 53 / 43 / 43 |
Counts are for ordered endpoint pairs and include diagonal pairs when present. In these bounded runs every strict support/composition difference is explained by cross-carrier stitching. This is not a general claim that shared-carrier image--kernel obstructions cannot occur; the exact strict control below gives eight such obstructions in one carrier.
The strict shared-carrier control is separate from the thresholded adapters. It uses one carrier, integer permutation/projector matrices, and a complete depth-two route enumeration:
python experiments/paper20/within_carrier_census.py
python experiments/paper20/validate_within_carrier_census.py
The retained result contains 24 supported labelled candidates, 16 active products, and eight exact within-carrier image--kernel obstructions. No disjoint endpoint carrier support occurs in this model.
The manuscript's carrier-support decision diagram is presentation-only and is rebuilt from its renderer without consuming a scientific result record:
python figures/paper20/render.py
Run the small control census:
python experiments/paper20/census.py --model z2 --max-depth 3
python experiments/paper20/census.py --model s3 --max-depth 2
Validate the retained census artifacts and their declared source digests:
python experiments/paper20/validate_results.py
With no explicit paths, the validator checks only the registered Z2, S3, and Rubik census artifacts. The exact within-carrier obstruction and image--kernel artifacts retain their dedicated validators below.
Run the active post-release hostile controls with:
python experiments/paper20/validation/validate_hostile_controls.py
The historical tests/test_paper20_carrier_accessibility.py bytes remain
available at their published path in the paper20-v1.0 release tree. The
active maintenance gate above replaces that top-level test in current HEAD; it
is not retroactively inserted into the published closure.
Add --recompute to replay every retained artifact from its registered
producer closure. The Rubik depth-2 replay is intentionally slower.
The Rubik adapter is intentionally bounded:
python experiments/paper20/census.py --model rubik --max-depth 1
Increasing the depth enumerates actual routes and can grow exponentially.
Every output declares its depth bound, tolerances, and computational_observation
status. It does not claim an all-depth classification from finite enumeration.
minimum_active_depth_within_bound: null means only that no active route was
observed through max_depth_enumerated; the theorem supplies an all-depth
conclusion only when its carrier-disjointness hypotheses apply. In particular,
the 12 Rubik pairs with overlapping carrier support that are null through
depth 2 are not decided by endpoint carrier support alone. Their separate
image--kernel audit closes the bounded depth-two mechanism as factor-zero
obstruction while leaving exact all-depth status unestablished:
python experiments/paper20/image_kernel_census.py
python experiments/paper20/validate_image_kernel.py --recompute
The audit exhausts 12 * 9 * 18^2 = 34,992 depth-two route indices. It
classifies 19,008 routes with both projected factors below tolerance, 7,992
with only the prefix below tolerance, and 7,992 with only the suffix below
tolerance; it observes no route with two active factors and a zero product and
no active product. A carrier-restricted replay covers 40,824 route/carrier
indices with the same qualitative result. Index-space coverage is exact, but
factor and product norm classifications are bounded numerical observations.
Exact projected-factor zero, exact absence of nontrivial image--kernel
cancellation, and exact all-depth vanishing are not established. Exact pair
and route records remain in the registered result JSON files.
The retained census is computed in complex128, including the Z2 control.
For Z2, exactness of the all-depth conclusion comes from the theorem and its
0/1 construction, not from treating a floating-point validator PASS as an
exact-arithmetic certificate.
Lean formalization is optional and is not a release prerequisite for this elementary block-factorization paper. The release receipt binds the manuscript, declared environment, implementation, retained results, Rubik source closure, the exhaustive depth-two image--kernel audit, and hostile regression tests.
The v1.0 receipt was generated after replaying all registered producers and is now immutable. Validate its published artifact closure with:
python experiments/paper20/validation/validate_release.py
To run the current producer implementations as a separate maintenance replay, use:
python experiments/paper20/validation/validate_release.py --recompute-results
Receipt PASS establishes the declared local release closure and conformance
only. It is not a machine proof of the manuscript, an independent validator of
its own implementation, or an exact-arithmetic certificate for the
complex128 census.
The README is a downstream navigation and digest index, not an artifact in the receipt's ordered closure. This permits it to bind the exact receipt bytes without creating a receipt-to-README-to-receipt cycle. The release manifest is upstream of validation and likewise does not contain the receipt digest.
- Receipt:
experiments/paper20/results/carrier_accessibility_v1.release-receipt.json - Exact-file SHA-256:
befaee58cd9d8561faa08ff4de870cb23939d52f2373911a377125940055604b - Receipt content SHA-256:
ad746f6ff7626b0e6a3a2b74d08f31bf50be952dfed354dd35c7dbabbb54ba7d - Artifact closure SHA-256:
eecca10fe115d9a12be2b250021aa3ba9aba6c82c7124ea9db21fdebc57aee1b - Validation mode:
LOCAL_CLOSURE_VERIFICATION - Independent validation:
false - Receipt included in its own closure:
false