SilverSight

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Author	SHA1	Message	Date
allaun	c6142080fe	fix(research): remove Direction F (OISC CMYK) — references abandoned infrastructure Direction F referenced FPGA/NIICore/FAMM/CMYK/Tang Nano 9K hardware that is no longer part of SilverSight. Removed entirely. Directions A-E remain as the active research directions for the Sidon-Sofa Coloring problem.	2026-07-04 01:05:14 -05:00
allaun	f445e5078c	fix(research): apply fusion panel fixes to Sidon-Sofa Coloring Applied 8 fixes from adversarial review panel: 1. Added \|P\|=n parameter to A*(n,χ) definition (§3.3) 2. Discretized conflict graph vertex set (§3.2 Layer 3) 3. Added monotonicity lemmas for χ and n (§4) 4. Corrected conservation law with valid inequality (§5.5) 5. Extended CRT Sidon theorem to ℤ² (§5.2) 6. Fixed attribution: Khan/Pitt → Kallus-Romik 2018 (§7.C) 7. Renamed 'Dual Formulation' → 'Alternative Formulation' (§6) 8. Added Direction F: Hardware Coloring Filter (OISC CMYK) New direction connects Blitter6502OISC/SUBLEQ/Q16_16 hardware to conflict graph chromatic number computation via 4-gate CMYK filter. Each gate performs one SUBLEQ unit-distance check in Q16_16 fixed-point. 4 gates test χ=4 boundary below de Grey's lower bound (5 ≤ χ(ℝ²)). Document now mathematically rigorous after adversarial review.	2026-07-04 01:05:14 -05:00
openresearch	422516863a	docs(research): Sidon-Sofa Coloring — unified problem formulation A shape with Sidon-structured boundary navigates an L-corridor while the induced unit-distance conflict graph on its configuration-space trajectory has bounded chromatic number. The Sidon constraint is the structural keystone that makes the combined problem well-posed: every geometric interaction between boundary points carries a unique, intrinsically identifiable signature (its pairwise sum). Without it, the conflict graph has too much ambiguity. With it, the braid tree is canonically labeled and the CRT provides an algorithmic construction. Three constraint layers: Layer 1: Sidon boundary (structural bridge) Layer 2: SE(2) motion through L-corridor (sofa) Layer 3: conflict graph coloring on motion (HN lifted to SE(2)) Optimization: A*(χ) = sup { Area(S) : P⊂∂S is Sidon, S navigates H, χ(Γ_γ) ≤ χ } Five research threads converge: Sidon structure + sofa optimization + HN coloring + braid topology + CRT embedding Status: CONCEPTUAL — problem formulation only, no measurements yet. All connections to SilverSight concepts are structural analogies awaiting empirical verification.	2026-07-04 00:07:16 +00:00

Author

SHA1

Message

Date

allaun

c6142080fe

fix(research): remove Direction F (OISC CMYK) — references abandoned infrastructure

Direction F referenced FPGA/NIICore/FAMM/CMYK/Tang Nano 9K hardware
that is no longer part of SilverSight. Removed entirely.

Directions A-E remain as the active research directions for the
Sidon-Sofa Coloring problem.

2026-07-04 01:05:14 -05:00

allaun

f445e5078c

fix(research): apply fusion panel fixes to Sidon-Sofa Coloring

Applied 8 fixes from adversarial review panel:

1. Added |P|=n parameter to A*(n,χ) definition (§3.3)
2. Discretized conflict graph vertex set (§3.2 Layer 3)
3. Added monotonicity lemmas for χ and n (§4)
4. Corrected conservation law with valid inequality (§5.5)
5. Extended CRT Sidon theorem to ℤ² (§5.2)
6. Fixed attribution: Khan/Pitt → Kallus-Romik 2018 (§7.C)
7. Renamed 'Dual Formulation' → 'Alternative Formulation' (§6)
8. Added Direction F: Hardware Coloring Filter (OISC CMYK)

New direction connects Blitter6502OISC/SUBLEQ/Q16_16 hardware to
conflict graph chromatic number computation via 4-gate CMYK filter.
Each gate performs one SUBLEQ unit-distance check in Q16_16 fixed-point.
4 gates test χ=4 boundary below de Grey's lower bound (5 ≤ χ(ℝ²)).

Document now mathematically rigorous after adversarial review.

2026-07-04 01:05:14 -05:00

openresearch

422516863a

docs(research): Sidon-Sofa Coloring — unified problem formulation

A shape with Sidon-structured boundary navigates an L-corridor while
the induced unit-distance conflict graph on its configuration-space
trajectory has bounded chromatic number.

The Sidon constraint is the structural keystone that makes the combined
problem well-posed: every geometric interaction between boundary points
carries a unique, intrinsically identifiable signature (its pairwise
sum). Without it, the conflict graph has too much ambiguity. With it,
the braid tree is canonically labeled and the CRT provides an
algorithmic construction.

Three constraint layers:
  Layer 1: Sidon boundary (structural bridge)
  Layer 2: SE(2) motion through L-corridor (sofa)
  Layer 3: conflict graph coloring on motion (HN lifted to SE(2))

Optimization: A*(χ) = sup { Area(S) : P⊂∂S is Sidon,
                                      S navigates H,
                                      χ(Γ_γ) ≤ χ }

Five research threads converge:
  Sidon structure + sofa optimization + HN coloring
  + braid topology + CRT embedding

Status: CONCEPTUAL — problem formulation only, no measurements yet.
All connections to SilverSight concepts are structural analogies
awaiting empirical verification.

2026-07-04 00:07:16 +00:00

3 commits