CKey locator format v0.1.0 (draft)

Status: experimental implementation profile. Wire and geometry constants are versioned as format=1, profile=1; interoperability is not promised until decoder fixtures pass in independent implementations.

1. Coordinate system and symbol shape

The canonical symbol field is 29 × 29 module units. The origin is the upper-left; x increases right and y increases down. Its center is (14.5, 14.5). A 0.65-unit rounded square boundary runs from (0.5,0.5) to (28.5,28.5) with radius 3.5. At each corner, local finder coordinates (u,v) range 0–4 from that finder's upper-left. A finder cell is dark iff u=0 || u=4 || v=0 || v=4 || (u=2 && v=2) || (left-side finder && u<2) || (right-side finder && u>2). “Left-side” means the two finders occupying columns 0–4; “right-side” means those occupying columns 24–28. Thus perimeter, center, and asymmetric stripe precedence are exact, and finder sites are never payload sites. The boundary and all finder cells are structural and take precedence over any other layer. These dimensions remain fixed for profile 1.

The polar angle a is clockwise from 12:00. There are 72 angular slots per turn, each exactly 5 degrees. Polar point (ring, slot) has radius 4.5 + ring for rings 0 through 5, and center

x = 14.5 + radius × sin(2π × slot / 72)
y = 14.5 − radius × cos(2π × slot / 72).

The symbol is monochrome. Dark means mark, light means background. Color never changes interpretation.

2. Permanent calibration keys

These are reserved structures and cannot be payload sites.

• Grid Key: At Cartesian column 2, rows 10 through 17, the fixed word 10110100 is rendered as centered circular marks in the corresponding cells. It calibrates Cartesian pitch and verifies local grid alignment.
• Ray Key: At slot 0 (12:00), a ray reaches 100% of the 9.5-unit polar radius. At slot 54 (9:00) it reaches 50%, and the immediately adjacent slot 55 (9:05) reaches 75%. The angular slots and radius are normative.
• Ring Key: On ring 5, slots 18 and 19 are individual dots; slot 20 is explicitly empty; slot 21 is one individual dot; slots 22–25 are one connected, continuous four-slot arc. A dot is a circular mark centered in one angular slot. An arc is one connected stroke spanning four slot intervals, with no internal gaps or dot caps. It is not encoded as four dots.

Reference mark dimensions in profile 1 are normative for rendering: Grid Key dot radius 0.29 units; payload polar-dot radius 0.16; Ring Key dot radius 0.16; Ray Key stroke width 0.22; Ring Key arc stroke width 0.32 with butt ends; rounded-square boundary stroke width 0.65. Finder cells occupy one full Cartesian unit each. A future decoder profile must specify measurable tolerances around these nominal dimensions before claiming camera support; v0.1.0 does not yet define those tolerances.

The three keys are jointly required for calibration/orientation validation. A missing or inconsistent key must be a decode failure, not treated as an empty payload site.

3. Locator framing and integrity

The locator payload is exactly 16 arbitrary bytes. Its 26-byte data frame is:

CRC-32C uses reflected Castagnoli polynomial 0x82F63B78, initial value 0xFFFFFFFF, reflected input/output, and final XOR 0xFFFFFFFF.

The frame is encoded as a shortened systematic Reed–Solomon code RS(42,26) over GF(256), primitive polynomial 0x11D, primitive element 2, generator roots α^0 through α^15, transmitted high-degree coefficient first. Append 16 parity bytes after the frame. This code has the algebraic bound 2e + s ≤ 16 (up to 8 unknown byte errors or 16 known erasures). The v0.1.0 implementation corrects unknown byte errors through the full e ≤ 8 bound in 32 deterministic test patterns. Erasure decoding is not implemented, so the s portion is a code capability, not a current decoder claim.

4. Placement and reserved geometry

The 42-byte codeword is read MSB-first, yielding 336 bits. A dark site represents 1, a light site 0. Payload/ECC bits are mapped over eligible Cartesian and polar sites in alternating coordinate-system order: take the next Cartesian candidate, then the next polar candidate, and repeat until one list is exhausted; then continue through the remaining list. Cartesian eligible cells are in row-major order; polar eligible sites are in ring-major/slot-major order. The current profile has 316 Cartesian and 406 polar eligible sites (722 total); remaining sites are unused background in v0.1.0. No payload-bearing site may overlap a finder, boundary, Grid Key, Ray Key, or Ring Key.

Cartesian candidates are cell centers in rows and columns 1–27, excluding the four 5 × 5 finders, the 8-cell Grid Key, and every cell center at radius ≤10.4 units from the symbol center. Polar candidates are all ring/slot centers except the three Ray Key bearings on every ring and Ring Key slots 18–25 on ring 5. Candidates beyond bit 335 remain unassigned and light. The logo-safe area is not implicitly the polar center: no logo may cover any required structure or assigned payload/ECC mark. A future profile may define explicit reserved-empty/logo-safe sites only after damage limits are specified.

The normalized geometry is shared; vector rendering uses continuous polar coordinates while matrix elements remain square cells. The native image decoder must rectify the outer square before sampling both coordinate systems. v0.1.0 does not yet define a camera-validity envelope or decoder tolerances.

5. Example

For payload bytes 00 01 02 … 0F, the first 26 frame bytes end with CRC-32C AF 88 C6 03; the independently generated RS parity is 85 0F 0D 71 E9 DD F1 43 28 EE 45 C2 9D 7A 02 AA. The full fixture is in tests/vectors/locator-v1.json.

6. Known omissions before stabilization

The next format revision must specify decoder tolerances for line width, dot diameter, arc connectivity/gap, geometric fit residuals, reflections, and distortion; full RS decode and erasures; every-version capacity accounting; and independent implementation fixtures. This draft has one locator profile only. It does not claim a general 2,048-byte profile.