Core Definition

FP-META stands for:

Fingerprint for Metameric Relation Topology

It is not a color fingerprint. It is a pair fingerprint.

The central local quantity is the spectral difference curve:

ΔR_AB(λ) = R_B(λ) − R_A(λ)

This curve describes how the reflectance spectrum of reference B differs from the reflectance spectrum of reference A at each wavelength.

While ΔE₀₀ describes how close two references appear under one defined colorimetric condition, FP-META describes how their spectra are structurally related.

ΔE₀₀ describes appearance proximity under one condition.
FP-META describes spectral relation topology.

Why FP-META?

Metamerism is commonly discussed through colorimetric similarity: two samples may appear very close under a given illuminant and observer condition, even though their spectral reflectance curves are not identical.

FP-META adds a structured spectral layer to that discussion. It documents:

local ΔR_AB(λ) topology
+
global ARBE structure differences

This makes the pair relation more transparent than a single color-difference value alone.

FP-META does not replace classical color measurement. It does not “solve” metamerism automatically. It provides a structured, atlas-bound way to document metamerically relevant spectral pair relations.

Atlas-Bound Reference Pair

A valid FP-META record requires two valid atlas references:

A = H230_L010_C005
B = H235_L010_C005

The identity of each reference is always the atlas code of the form:

Hxxx_Lxxx_Cxxx

Without two valid atlas references, no valid FP-META object exists.

Local Spectral Relation

For two atlas spectra:

R_A(λ)
R_B(λ)

FP-META computes the local spectral relation as:

ΔR_AB(λ) = R_B(λ) − R_A(λ)

This local difference curve is used to detect and describe the topology of the pair relation.

The key topology fields are:

XNODE
XSIGN
XEQUAL
XPOS

XNODE, XSIGN, and XEQUAL

FP-META separates different types of ΔR = 0 events.

XNODE = all detected ΔR = 0 nodes

XSIGN = interpolated sign-change crossings

XEQUAL = equality nodes on the atlas grid

This distinction is important because not every ΔR = 0 node has the same topological meaning.

Example: H230_L010_C005 vs H235_L010_C005

For the example pair:

A = H230_L010_C005
B = H235_L010_C005

FP-META reports:

XNODE = 8
XSIGN = 3
XEQUAL = 5

The detected ΔR = 0 positions are:

382.5, 400.0, 513.3, 550.0, 560.0, 570.0, 585.0, 600.0 nm

The topology is split into:

XSIGN positions:
382.5, 513.3, 585.0 nm

XEQUAL positions:
400.0, 550.0, 560.0, 570.0, 600.0 nm

This means that the pair relation contains three interpolated sign-change crossings and five equality nodes on the atlas grid.

Local ΔR Metrics

FP-META also records local metrics of the difference curve:

AREAABSΔR
AREASIGNEDΔR
MAXABSΔR
RMSΔR
MEANABSΔR

For the example pair:

These values describe the local spectral relation between the two atlas references. They do not replace the atlas identity of either reference. They are descriptive attributes of the pair relation.

Colorimetric Condition

FP-META may include a colorimetric distance under a declared condition.

For the example pair:

Illuminant: D50
Observer: 2°
ΔE₀₀ = 0.507639

This means that the two references are colorimetrically very close under the specified D50 / 2° condition.

However, FP-META does not stop at this colorimetric value. It also documents the spectral structure behind the pair relation.

Global ARBE Structure Differences

In addition to the local ΔR_AB(λ) topology, FP-META records pairwise differences of global ARBE structure attributes.

These values do not describe the local difference curve directly. They describe the difference between the global structure attributes of reference A and reference B.

The core definitions are:

ΔλPAIR = |Δλ*_B − Δλ*_A|
Δμ2    = |μ2_B − μ2_A|
Δσ     = |σ*_B − σ*_A|
Δμ3    = |μ3_B − μ3_A|

with:

Δλ* = λ*_V2 − λ*_EE

λ*_V2 must be computed using the Brent method.

For the example pair:

The workflow priority remains:

Δλ* > Δμ2 > Δσ*

Δμ3 may be reported as an explanatory asymmetry descriptor but does not override Δλ*.

FP-META Status

The field:

STATUS_META_REPORTED

means that the FP-META report was validly generated and recorded.

It is a procedural status. It is not a quality class.

A future classification field may be added separately:

META_CLASS

For v0.1, META_CLASS may remain null until calibrated thresholds are defined from atlas pair distributions.

Machine-Readable FP-META Code

The complete FP-META v0.1 code for the example pair is:

FP-META::V_0.1::A_H230_L010_C005::B_H235_L010_C005::SRC_decision_ready_v1::λV2METHOD_Brent::REL_metameric_relation_topology::ΔR_RB_minus_RA::GRID_380_730_10nm::XNODE_8::XSIGN_3::XEQUAL_5::XSIGNPOS_382.5_513.3_585.0::XEQUALPOS_400.0_550.0_560.0_570.0_600.0::XPOS_382.5_400.0_513.3_550.0_560.0_570.0_585.0_600.0::AREAABSΔR_0.075500::AREASIGNEDΔR_0.061500::MAXABSΔR_0.000600::RMSΔR_0.000268::MEANABSΔR_0.000219::ΔE00D50_0.507639::ΔλPAIR_0.136400::Δμ2_59.898100::Δσ_0.277600::Δμ3_1113.756200::STATUS_META_REPORTED::META_CLASS_NULL

A shorter communication form is:

FP-META::V_0.1::A_H230_L010_C005::B_H235_L010_C005::REL_metameric_relation_topology::ΔR_RB_minus_RA::XNODE_8::XSIGN_3::XEQUAL_5::ΔE00D50_0.507639::ΔλPAIR_0.136400::Δμ2_59.898100::Δσ_0.277600::Δμ3_1113.756200::STATUS_META_REPORTED

3D Interpretation

FP-META can also be represented as a 3D relation topology.

The axes are:

x = λ
y = R_A(λ)
z = R_B(λ)

The equality plane is:

R_A = R_B

When the FP-META relation curve touches this plane, an equality node is present. When it passes through the plane with a sign change, an XSIGN crossing is present.

This makes the pair relation visible not only as two spectral curves, but as a spatial topology of their relationship.

What FP-META Is Not

• FP-META is not a color generator.
• FP-META is not a replacement for colorimetric measurement.
• FP-META is not a recipe or mixing model.
• FP-META is not a claim that metamerism has been solved.

It is a structured, atlas-bound method for documenting the spectral relationship between two valid references.

Summary

FP-META v0.1 serializes the metameric relation topology of two valid atlas references.

It combines:

local ΔR_AB(λ) topology
+
global ARBE structure differences
+
declared colorimetric condition

This makes metamerically relevant pair relations reproducible, auditable, and machine-readable within the ARBE-λ* system.