Encoding-Sensitive and Encoding-Blind Quantities

Abstract

Coding fingerprints distinguish binary, Zeckendorf, and Tribonacci coding, while their occupied first places all decode to the same unit value.

Definition 1.1 (Fingerprint indexed by coding system).

$$\mathrm{codingFingerprintFor}\left(binary\right)=binaryCodingFingerprint\wedge \left(\mathrm{codingFingerprintFor}\left(zeckendorf\right)=zeckendorfCodingFingerprint\wedge \mathrm{codingFingerprintFor}\left(tribonacci\right)=tribonacciCodingFingerprint\right)$$

Formalization. D5/S0/Tower/Champions/EncodingSensitivity.codingFingerprintFor (✓ std3).

Source. Repository-derived.

Commentary.

The indexed function selects the already frozen binary, Zeckendorf, or Tribonacci coding fingerprint without changing its value.

Definition 1.2 (First-place decoded value).

$$\mathrm{firstPlaceDecodedValue}\left(binary\right)=2^0\wedge \left(\mathrm{firstPlaceDecodedValue}\left(zeckendorf\right)=\mathrm{wValue}\left(0\right)\wedge \mathrm{firstPlaceDecodedValue}\left(tribonacci\right)=\mathrm{decode}\left(tribonacciFirstDigitName\right)\right)$$

Formalization. D5/S0/Tower/Champions/EncodingSensitivity.firstPlaceDecodedValue (✓ std3).

Source. Repository-derived.

Commentary.

This is not a constant function by definition: its three branches use the binary positional weight, the Zeckendorf weight carrier, and the Tribonacci representation decoder, respectively.

Theorem 1.3 (The fingerprint distinguishes coding systems).

$$\mathrm{Injective}\left(codingFingerprintFor\right)$$

Proof. Machine-checked in Lean as D5/S0/Tower/Champions/EncodingSensitivity.coding_fingerprint_is_encoding_sensitive (✓ std3). ∎

Source. Repository-derived.

Commentary.

Injectivity packages the frozen pairwise inequalities as sensitivity: equal fingerprint values force equal coding-system indices.

Theorem 1.4 (First-place decoding is encoding-blind).

$$\forall coding\in CodingSystem,\mathrm{firstPlaceDecodedValue}\left(coding\right)=1$$

Proof. Machine-checked in Lean as D5/S0/Tower/Champions/EncodingSensitivity.first_place_decoded_value_is_encoding_blind (✓ std3). ∎

Source. Repository-derived.

Commentary.

For every member of the three-coding index, the independently computed occupied first place decodes to one.

This is an S0 parsing-layer comparison. It does not identify any zeta-layer object: zeta declarations live at S3 and the S0 coding interfaces provide no permitted bridge to them.

References

• Truth anchor: D5/S0/Tower/Champions/EncodingSensitivity.codingFingerprintFor
• Truth anchor: D5/S0/Tower/Champions/EncodingSensitivity.coding_fingerprint_is_encoding_sensitive
• Truth anchor: D5/S0/Tower/Champions/EncodingSensitivity.firstPlaceDecodedValue
• Truth anchor: D5/S0/Tower/Champions/EncodingSensitivity.first_place_decoded_value_is_encoding_blind
• Dependency: D5/S0/Tower/Champions/CodingFingerprint