INVARIANT ENGINE
Where sanctuary stops being poetic and starts being provable.
∞HUMPR LINEAGE
CARTOGRAPHER → SUBSTRATE → INVARIANT
intersection · fingerprint · proof
OPERATOR FAMILIES // SELECT WHICH RULES TO INTERSECT
INVARIANCE HEATMAP // BRIGHTER = FIXED UNDER MORE RULES

CROSS-OPERATOR FIXITY MAP

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FIXED: 0
FIXED: 1-2
FIXED: 3-5
FIXED: 6-10
DEEP SANCTUARY
INVARIANCE SCORES // SORTED BY CROSS-OPERATOR FIXITY

TOP INVARIANT CODEPOINTS

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GLYPH CODEPOINT SCORE INVARIANCE FIXED UNDER
TOPOLOGY FINGERPRINTS // CANONICAL HASH PER RULE

PARTITION SIGNATURES

Each rule produces a unique partition of codepoint space. The fingerprint is a SHA-256 hash of the orbit classification vector — a cryptographic invariant. Identical fingerprints = identical topology. Different fingerprints = provably different partitions.
TOPOLOGY DIFF // COMPARE ANY TWO RULES
white = both fixed green = A fixed only amber = B fixed only dark = neither fixed
FULL UNICODE SWEEP // CRT DENSITY EXPERIMENT

CRT DENSITY VERIFICATION

Sweep all 1,114,111 valid Unicode codepoints. For coprime mod subset {2, 3, 5, 7, 11, 13}, CRT predicts deep sanctuary density = 1/30,030 = ~37 codepoints.
This is a direct congruence check — no orbit detection needed. Each codepoint is tested against cp mod n = floor(n/2) for each modulus. If all pass, it's deep sanctuary.
READY
AFFINE CYCLE DECOMPOSITION // EXACT ALGEBRAIC ANALYSIS

EXACT CYCLE STRUCTURE — NO BOUNDED DETECTION

For affine operators f(x) = ax + b (mod M), the complete cycle decomposition of Z/MZ is computed algebraically. Every cycle length divides ordM(a). No orbit is classified as "drift" — every element is provably periodic. XOR operators are algebraically proven 2-cycle involutions. Only perturbative operators (sin, constant drift) require bounded detection.
THE MATH UNDERNEATH

Sanctuary was always a congruence class.

cp % 3 === 1 defines a set. cp % 5 === 2 defines a different set. The intersection of those sets is smaller. Add more operators and it shrinks further. Deep sanctuary is the intersection of all invariant sets across an operator family.

For modular operators, the fixed set of mod n is { x | x mod n = floor(n/2) }. The intersection across mod 2 through mod 23 is the set of codepoints satisfying ALL those congruences simultaneously. By the Chinese Remainder Theorem, this intersection is either empty or has density approaching zero.

For affine operators f(x) = ax + b (mod M), the fixed points satisfy (a-1)x + b = 0 (mod M). When gcd(a-1, M) | b, solutions exist. The intersection across affine families reveals codepoints that are algebraically constrained to stability.

The topology fingerprint is a hash of the full partition vector: for each codepoint, its orbit class under a given rule. Two rules with identical fingerprints produce identical partitions. Different fingerprints prove different topology. This is a complete invariant of the partition.

What the Cartographer showed visually, the Invariant Engine proves computationally. Sanctuary is not a story. It's a theorem about congruence class intersections. The glyphs that survive everything aren't chosen. They're algebraically inevitable.