This revision explains normal authorized-key operation and keeps the calculator as abstract sequence counting, without key-cutting, manipulation or bypass instructions.
Pin-Tumbler Abstract Sequence Explorer
Choose an abstract position count, symbol count and maximum adjacent symbol step. The worksheet counts sequences; the animation separately illustrates normal shear-line alignment with a generic authorized key.
Equation Used
- Each of P abstract positions independently uses one of D integer symbols for the raw count.
- The adjacency-valid count applies only the declared maximum neighboring symbol difference M.
- Dynamic programming counts every permitted sequence exactly once.
- The animation is a generic normal-operation schematic and is not driven by a real code.
- Manufacturing rules, reserved codes, master-keying, tolerances, security ratings, decoding, manipulation and bypass are excluded.
Keeps exact abstract sequence counting and normal-operation shear-line alignment while removing physical key, bypass and unsupported security claims.
Authorized-key operation aligns every pin interface
WO 1996/025574 describes a shell, turnable plug, keyhole, aligned passageways, spring-loaded driver pins and tumbler pins, with the plug/shell boundary defining a shear line. With the authorized key inserted, each tumbler-pin/driver-pin interface meets that line so the plug can rotate.
The animation shows only this normal operation. It does not show lock manipulation or bypass.
A documented cylinder-lock topology
EP 2,228,507 documents the conventional housing, plug, driver pins, key pins and springs. US patent 8,166,783 likewise states that an authorized key raises tumbler pins and driver pins so their interfaces clear the plug/shell shear line.
This page is educational and does not provide servicing, rekeying or access instructions.
An abstract constrained-sequence count
P positions with D symbols each produce D to the P raw sequences. The valid count is computed exactly by dynamic programming, retaining only adjacent symbols whose difference is at most M.
The calculation does not generate a physical key, dimensions or a compatible lock code.
An abstract counting example
With five positions and ten symbols there are 100,000 raw sequences. Applying the declared neighboring-step rule removes sequences that violate that mathematical rule; it does not model all rules of any manufacturer.
Sequence count is not security strength
The former random-match output used the raw count even when the displayed adjacency rule excluded codes. It is replaced by the exact valid share. Unsupported master-key case studies, tolerances, maintenance, troubleshooting, rekeying and security claims are removed.
Pin-tumbler worksheet questions
Does this generate a working key code?
No.
Does the count measure lock security?
No.
What does the animation show?
Only normal authorized-key alignment at the plug shear line.
Pin-tumbler references
- WO 1996/025574: shell, plug, passageways, driver/tumbler pins, springs and shear line.
- EP 2,228,507: conventional housing, plug, driver pins, key pins and springs.
- US patent 8,166,783: authorized-key alignment of pin interfaces at the shear line.
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