TECHNICAL MONOGRAPH // FIELD SPECIFICATION NO. 05 [FIG. 00]

The Variable-Pin Web Lock

An order-sensitive, deterministic cryptographic puzzle that maps any arbitrary character string $S$ of length $L$ into a configurable $N$-digit mechanical combination ($D_1 D_2 \dots D_N$) without collisions on simple transpositions.

INPUT DOMAIN ASCII / UTF-8 ($L \ge 0$)

OUTPUT LENGTH ($N$) 5 PINS (1–32 CONFIG)

PARITY & CASCADE MOD-10 SEALED

01 // PASSPHRASE TERMINAL ($S$) & PIN COUNT ($N$) STANDARD EVALUATION

IN>

INPUT LEN L = 5

OUTPUT DIGITS ($N$)

PINS:

CALIBRATION VECTORS:

02 // CHARACTER VALUATION MATRIX $V(c_i)$ HOVER ANY CHAMBER BELOW TO ISOLATE ACTIVE TOKENS

||| TOKENS: c₁–c₅ // FULL TAPE |||

03 // VERNIER SIGHTLINE ALIGNMENT N = 5 PINS

LOCK AXIS →

D₁ Handshake

D₂ Anchor

D₃ Payload

D₄ Wave

D₅ Parity

← MOD 10

||| SPAN: D₁–D₅ // FULL LOCK |||

04 // LIVE CHAMBER DERIVATION TRACE (D₁–D₅)

[INTERACTIVE] HOVER OVER ANY CHAMBER TO INSPECT INPUT DEPENDENCIES

SECTION 1.0 // LEXICAL PRE-PROCESSING [EQ. 1.1 – 1.3]

Character Valuation Function $V(c)$

Given an input string $S = c_1 c_2 \dots c_L$ of length $L$ and a target output pin count $N \ge 1$, every character $c_i$ is first normalized into a discrete non-negative integer $V(c_i)$. Alphabetical characters are case-insensitive and mapped to their 1-indexed Latin alphabet position ($1\text{–}26$).

Numeric characters retain their literal integer value ($0\text{–}9$), while punctuation, symbols, and whitespace are folded into $[0, 9]$ using their ASCII codepoint modulo $10$. If $S$ is empty ($L = 0$), all $N$ pins default immediately to $0^N$ (e.g. $\mathbf{00000}$ for $N=5$).

Character Class	Domain	Formal Rule	Sample Evaluations
Alphabetical	A–Z, a–z	$$V(c) = \text{ord}(\text{lower}(c)) - 96$$	'a' → 1, 'h' → 8, 't' → 20, 'z' → 26
Numeric Digits	0–9	$$V(c) = \text{int}(c)$$	'0' → 0, '3' → 3, '9' → 9
Symbols / Other	ASCII \ Alnum	$$V(c) = \text{ASCII}(c) \bmod 10$$	'-' (45) → 5, '.' (46) → 6, ' ' (32) → 2

SECTION 2.0 // MECHANICAL REDUCTION & ARBITRARY-LENGTH EXTENSION [EQ. 2.1 – 2.6]

The Chamber Equations ($D_1 \dots D_N$)

Pin	Chamber Name	Mathematical Definition	Structural Purpose
D₁	The Handshake	$$D_1 = \big(V(c_1) + L\big) \bmod 10$$	Binds the leading character $c_1$ additively to total string length $L$.
D₂	The Anchor	$$D_2 = \big(V(c_L) \times L\big) \bmod 10$$	Binds the trailing character $c_L$ multiplicatively to total length $L$.
D₃	The Payload	$$D_3 = \text{dr}\!\left(\sum_{i=1}^{L} V(c_i)\right) = 1 + \big((\Sigma - 1) \bmod 9\big)$$	Recursive digital root ($\text{dr}$) of the total character sum $\Sigma$ (0 if $\Sigma=0$).
D₄	The Wave	$$D_4 = \left\|\sum_{i=1}^{L} (-1)^{i+1} V(c_i)\right\| \bmod 10$$	Alternating difference ($c_1 - c_2 + c_3 - c_4 \dots$) to detect internal swaps.
D₅	The Parity Seal	$$D_5 = (D_1 + D_2 + D_3 + D_4) \bmod 10$$	Modular checksum verifying the integrity of primary pins $D_1 \dots D_4$.
D_k (k>5)	Harmonic Rotor	$$D_k = \big(V(c_m) + k \cdot D_{k-1} + m\big) \bmod 10$$	For $N > 5$, cycles over $m = ((k-1)\bmod L)+1$ to expand output to any length $N$.

SECTION 3.0 & 4.0 // CANONICAL PROOF & ANAGRAM RESISTANCE [VERIFICATION]

Canonical 5-Pin Proof for $\text{"https"} \to \mathbf{35211}$

Stage	Input Parameters	Step-by-Step Arithmetic	Pin Result
Vector	$S = \text{"https"}, \quad L = 5$	$V = [\text{h}:8,\; \text{t}:20,\; \text{t}:20,\; \text{p}:16,\; \text{s}:19]$	—
Pin 1 ($D_1$)	$V(c_1) = 8, \quad L = 5$	$(8 + 5) \bmod 10 = 13 \bmod 10$	3
Pin 2 ($D_2$)	$V(c_5) = 19, \quad L = 5$	$(19 \times 5) \bmod 10 = 95 \bmod 10$	5
Pin 3 ($D_3$)	$\Sigma = 8+20+20+16+19 = 83$	$83 \to 8 + 3 = 11 \to 1 + 1$	2
Pin 4 ($D_4$)	$8 - 20 + 20 - 16 + 19$	$\|11\| \bmod 10$	1
Pin 5 ($D_5$)	$D_1=3, D_2=5, D_3=2, D_4=1$	$(3 + 5 + 2 + 1) \bmod 10 = 11 \bmod 10$	1

CLICK ANY PERTURBATION TEST CASE BELOW TO LOAD INTO THE INSTRUMENT ACTIVE LENGTH: N = 5

BASELINE

"https" 35211

Canonical 5-character protocol string.

FULL REVERSAL

"sptth" 40217

Same payload ($D_3=2$), but boundary & cascade pins shift.

INTERNAL SWAP

"htpts" 35233

Same ends & sum, caught by Wave ($D_4$).

TRUNCATION

"http" 24141

Dropping 's' alters all chambers simultaneously.