Uniformly bounded centered iid local steps with uniformly nondegenerate covariance share standard Gaussian finite-dimensional limits after exact covariance whitening.
Research alpha · deterministic finite instruments
Global Geometry II
The Universality and Inverse-Design Atlas
local rules→global worlds
global target→local compiler
partial traces→hidden geometry
Current scientific boundary
Square and triangular one-skeleton refinements retain different four- and six-corner norm balls.
Deterministic topology and transport records are available; universality remains NOT_EVALUATED.
One engine · six interrogations
What survives scale?
Every panel states its evidence ceiling. Passing a finite check never promotes a continuum, physical, or universality claim.
finite deterministic carrier
Local construction → filled global disk
Four microscopic triangulation rules are measured under one closed topology and transport contract.
Carrierexact finite
——Topologyexact finite
——Curvature closurebinary64 audit
——Transportfinite solve
——Ready.
proved finite-dimensional basin
One diffusion limit, two metric worlds
Universality is typed: a shared process law does not erase a distinct intrinsic metric.
Uniform after centering, nondegeneracy, bounded support, and covariance whitening.
Four versus six extreme points obstruct an isometry of the normed limits.
Not established here: path-space tightness, semigroup convergence, boundary/disorder invariance principles, or object-level universality.
finite classifier
Partial observations → candidate microscopic worlds
Masking observables exposes ambiguity rather than forcing a single geometric identity.
Recognition uses one bounded preview matrix; it is not an identifiability theorem or learned model.
ordered theorem gates
Desired intrinsic geometry → certificate or obstruction
The compiler never turns a necessary condition, an incomplete search, or an intrinsic witness into a physical-shape claim.
Choose a closed finite target.
No report proves an embedding, actuator design, material response, or unique shape.
| Gate | Status | Evidence | Finding |
|---|
No certificate selected.engineering emulator · virtual HIL
Local defect budget → programmable intrinsic phase
The emulator is observation-bound, in-memory only, and incapable of accessing hardware.
- Center defect
- —
- Total defect
- —
- Plant state
- —
- Virtual actuation
- not initialized
- Protocol
- —
No virtual command has run.
Engineering ceiling: intrinsic finite model and virtual HIL only. No physical sheet, camera calibration, actuator force, shell equilibrium, or safety certification is claimed.
closed-schema evidence ledger
Claims you can replay
Each ledger claim has a status, basis, scope, falsifier, assumptions, tests, limitations, and content digest.
Proved-here recordsledger
—Finite propositions and precisely scoped limitsGenerated / verified artifactsSHA-256
4 layersCalibration, atlas, inverse, and virtual sheetEvaluation checkpointpartial evidence
UNRESOLVEDOnly Gate 1 is closed; Gates 2–8 are unresolved; decision authority is NONERelease-v2 macOS / Windows replayexternal attestation
Read scoped statusOnly the release and deep-test surface declared by this addressed record is compared.Physical validationapproval gate
NOT_RUNCamera validation is also NOT_RUN; the dry preflight is not a physical testEvaluation boundary: screening v3 completed 3,840/3,840 records on each host, but its exact raw comparison is FAIL and every confirmatory decision gate is outside screening authority. The strict partial campaign has exact cross-platform replication FAIL; its 10−12 diagnostic comparison is PASS with decision authority NONE. The full confirmatory campaign is NOT_RUN.
Failure and normalization disclosure: the screening ledger contains 112 estimator-unavailable records (9 comb, 103 small-world). The strict normalization artifact is validated and bound, but its fitted values are not consumed by the partial campaign's numerical measurements; those channels are not calibration-normalized.
| ID | Claim | Scope / principal limitation |
|---|
Calibration artifact
Atlas preview artifact
Inverse certificates
Virtual sheet HIL artifact
U2 evaluation report
Evaluation-v2 index
Strict partial · macOS compact
Strict partial · Windows compact
Strict partial comparison
Screening-v3 comparison
Strict campaign archive · macOS
Strict campaign archive · Windows
Screening raw archive · macOS
Screening raw archive · Windows
Release-v2 evidence index
Release-v2 reproducibility manifest
Release-v2 macOS / Windows comparison
Sheet experiment manual
Passive-sheet dry preflight
Fabrication manifest
q=5 template
q=6 template
q=7 template
Historical v1 release index
Historical v1 manifest
Historical v1 platform comparison
Local reproduction programs are retained in the offline archival source package and are not served by this public website.
The v1 index, manifest, and platform comparison are retained for historical inspection only; they do not certify release v2.