SilverSight/docs/research/COMPLETE_TEST_MATRIX.md

Complete Test Matrix: Every Assumption, Every Question

Status: DEFINITIVE — test every claim, answer every question Date: 2026-07-04 Principle: Good science tests all assumptions and answers all questions that can be answered.

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The Questions

For each component of the framework, we ask:

1. Does it work? (receipt: measurement)
2. When is it needed? (receipt: regime where removing it causes failure)
3. When is it redundant? (receipt: regime where removing it changes nothing)
4. What are its limits? (receipt: input where it breaks)
5. What does it cost? (receipt: timing/complexity measurement)

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Test Matrix

CRT Encode Engine

Test	Question	Input	Prediction	Receipt	Status
T01	Does CRT preserve Sidon?	Sidon labels, coprime moduli	0 collisions after embed	CRTSidon.lean, 0 sorries	DONE (proven)
T02	Does CRT CREATE Sidon from non-Sidon?	[0,1,2,3,4], wrapping moduli	collisions drop to 0	sidon_preservation_creation.md §6.3	TESTED (small instances)
T03	Is CRT redundant for already-Sidon input?	[1,2,4,8,16,32,64,128]	Same collision count with/without CRT	C3 run 019f2f07	DONE: YES, redundant
T04	Does CRT wrapping work at scale?	Non-Sidon, n=21 labels	collisions drop to 0	C11 (new)	PENDING
T05	Is CRT position-invariant for Sidon?	Permute labels across positions	Same collision count	C3 run 019f2f07	DONE: YES, invariant
T06	What does CRT cost vs direct check?	n=21 labels	CRT slower by CRT overhead factor	Timing comparison	PENDING

Chiral System (ChiralLabel, Rossby drift)

Test	Question	Input	Prediction	Receipt	Status
T07	Does Rossby drift vary across configs?	256 positional swaps	drift varies	C3 run 019f2f07	DONE: NO, constant (-65536)
T08	Does Kelvin regime (drift=0) exist in 65K?	4^8 cross-enriched	Some configs have drift=0	C5	PENDING
T09	Does COUCH Kelvin check filter anything?	65K configs	Some configs rejected (drift=0)	C5	PENDING
T10	Is Rossby drift position-invariant?	Permute chiral labels	Same drift (symmetric sum)	C3 + math	DONE: YES, symmetric
T11	Does chiral permutation affect quaternion products?	1,i,j,k basis, permuted	Different products for different perms	C4	PENDING

Sidon Filter

Test	Question	Input	Prediction	Receipt	Status
T12	Is Sidon check sufficient for uniqueness?	Sidon labels	All pairwise sums distinct	CRTSidon.lean	DONE (proven)
T13	Does quaternion Sidon differ from CRT Sidon?	Same labels, both filters	Different collision counts	C4	PENDING
T14	Can Sidon filter discriminate chiral configs?	256 positional swaps	Variance in collision count	C3	DONE: NO, invariant
T15	What inputs break the Sidon filter?	Adversarial labels	Find input with false positive/negative	Fuzz test	PENDING

COUCH Gate

Test	Question	Input	Prediction	Receipt	Status
T16	Does COUCH reject Kelvin configs?	drift=0 configs	Rejected	C5	PENDING
T17	Does COUCH reject high-scarred configs?	All-scarred config	Rejected (self_loop ≥ threshold)	C3 run	DONE: YES (all passed, but no all-scarred in 64)
T18	Is COUCH necessary (what fails without it)?	Remove COUCH, run pipeline	More configs reach Sidon (wasted work)	A/B test	PENDING
T19	Does COUCH correlate with QUBO tractability?	QUBO instances with known difficulty	Kelvin = hard, Rossby = easy	C10	PENDING

HCMR (Hardware Contention)

Test	Question	Input	Prediction	Receipt	Status
T20	Are self-loop values measured or assumed?	EPYC KVM benchmark	Log with 0.823, 0.885, 0.0	C7	PENDING (search Research Stack)
T21	Does self-loop = Sidon collision rate?	Correlate self-loop with collision count	Positive correlation	C10 variant	PENDING
T22	Does ring dispatch = 0 collisions?	All-Sidon labels, ring regime	self_loop=0, 100% Sidon	C3 run	DONE: consistent (0 collisions, but self_loop not measured independently)

Hoffman Bound / Spectral Database

Test	Question	Input	Prediction	Receipt	Status
T23	Is Hoffman gap=1 universal for unit-distance?	de Grey 1581, other 5-chromatic	gap=1	C9	PENDING (needs --full run)
T24	Is Hoffman tight for all regular graphs?	Path, cycle, complete, more	tight	hn_spectral_database.json	DONE: YES (3/3)
T25	Does Welch-Wynn improve on Hoffman?	Same graphs	WW ≥ Hoffman	hn_spectral_database.json	DONE: NO (WW=None, implementation incomplete)

q-Profile

Test	Question	Input	Prediction	Receipt	Status
T26	Is q>1 preference robust?	10+ random Sidon label sets	q>1 always 100% Sidon	C8	PENDING
T27	Does q=1 always degenerate?	q=1 configs	0% or low Sidon	crt_qprofile_sweep.json	DONE: q=1 has some Sidon (not always degenerate)
T28	Is q-profile about modulus selection or encoding?	Vary L0 directly (not via q)	Same result	Controlled experiment	PENDING

Conservation Law

Test	Question	Input	Prediction	Receipt	Status
T29	Is compression always bounded by K(data)?	8 different compressors	All fail to beat K(data)	weird_machine_conservation_law.md	DONE: YES (8×)
T30	Does filtering avoid the conservation bound?	Filter configs, measure output size	Output < K(data) is NOT required (filtering ≠ compression)	By construction	DONE: YES (filtering is selection, not compression)

Pipeline

Test	Question	Input	Prediction	Receipt	Status
T31	Does the pipeline reduce search space?	256 configs	Output < input	C3 run 019f2f07	DONE: 256→64 (packer cap)
T32	Is each stage necessary?	Remove each stage, re-run	Some stages are redundant for some inputs	A/B per stage	PENDING
T33	Does cross-enrichment (4^8) run on GPU?	chiral_cross_enrich.wgsl	65K results	C6	PENDING
T34	Is the pipeline faster on GPU than CPU?	Same input, GPU vs CPU	GPU faster for n≥8	Timing comparison	PENDING

Lean Formalization

Test	Question	Input	Prediction	Receipt	Status
T35	Does CRTSidonN compile?	lake build	exit 0	C1	PENDING (build at 89%)
T36	Does HCMR suite compile?	lake build	exit 0, 2 sorries	C2	PENDING (same build)
T37	Are the proven theorems non-tautological?	Review each proof	At least sidon_preserved_mod is non-trivial	Adversarial review	DONE: sidon_preserved (componentwise) is tautological, sidon_preserved_mod is real
T38	Does native_decide use violate AGENTS.md?	helical_coverage_74	Uses native_decide	HopfFibration.lean	DONE: YES, uses native_decide (documented exception for finite decidability)

QUBO/QAOA Bridge

Test	Question	Input	Prediction	Receipt	Status
T39	Does COUCH predict QAOA tractability?	QUBO instances	Kelvin=hard, Rossby=easy	C10	PENDING
T40	Does golden angle select good QAOA architecture?	28 architectures	Some are better than random	Experiment	PENDING
T41	Does 65K→100 pre-filtering help QAOA?	Filtered vs unfiltered QAOA	Filtered converges faster	Experiment	PENDING
T42	Is the quaternion gate mapping (1=I,i=X,j=Y,k=Z) used?	Check if pipeline applies gates	Gates are NOT applied (filtering only)	Code review	DONE: NO, pipeline filters, doesn't apply gates

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Execution Priority

Blocking (must answer first)

• T35/T36: Does the Lean compile? (lake build running, ~89%)
• T04: Does CRT wrapping work at scale? (C11)
• T11: Does chiral permutation affect quaternion products? (C4)

High value (changes the theory)

• T08/T09: Does Kelvin regime exist and get filtered? (C5)
• T13: Does quaternion Sidon differ from CRT Sidon? (C4)
• T19: Does COUCH correlate with QUBO? (C10)
• T23: Is Hoffman gap=1 universal? (C9)

Robustness (confirms existing results)

• T26: Is q>1 robust across label sets? (C8)
• T06: What does CRT cost? (timing)
• T32: Is each pipeline stage necessary? (A/B)

Quantum (speculative, needs Phase 1-2 first)

• T39-T41: QUBO/QAOA experiments

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Rule

Every test has:

1. A QUESTION (what we want to know)
2. An INPUT (what to feed it)
3. A PREDICTION (what we expect)
4. A RECEIPT (what would prove it)
5. A REJECTION (what would disprove it — implicit: opposite of prediction)

No test is skipped. No result is assumed. Every assumption gets a receipt or gets killed.