The anchor sift algorithm

What the method is
Measure how far something sits from the most disordered arrangement of its own parts.

That is the whole construction. Every domain below is that one sentence with a different answer to what counts as a part: atoms in a cell, symbols in a corpus, bytes in a file, coordinates in a board layout. The reference is built from the object's own parts, so there is no prior to estimate, no training set to collect and no model of the domain to write.
Building a reference by maximizing entropy under the constraints the object supplies is Jaynes's principle, and the departure from it is the free energy above equilibrium.

I have tried posting the algorithm and math to a few different communities but the automod deletes them. I’m busy researching and I know there are other curious people are here. I would put the link to the research here but it’s my github and I don’t want it to get auto removed so. Your use falls under AGPL as stated in the repository.

I’m tired of trying to jump social media gates designed for bots.

2. Theory
2.1 Definitions
Let $\Sigma$ be a set of symbols. No structure on $\Sigma$ is assumed: no order, no metric, no finite cardinality, and no way to enumerate its members. The only operation available is a decidable equality between two positions.
Let $(G,+)$ be an additive group of displacements and let a domain be a map $x$ from a subset of $G$ to $\Sigma$. A pattern is a finite set $D \subset G$ of displacements together with the symbols a chosen base position carries at them. For a base $t$ and a candidate base $s$, define
$$\mathrm{Occ}(s) \iff \forall d \in D:; x(s+d) = x(t+d)$$
An anchor set is any subset $A \subseteq D$, and
$$\mathrm{Anc}_A(s) \iff \forall a \in A:; x(s+a) = x(t+a)$$
Nothing in either definition requires $G$ to be the integers, $D$ to be contiguous, or $\Sigma$ to be known.
2.2 Proposition 1: soundness
For every $A \subseteq D$, every domain, and every base,
$$\mathrm{Occ}(s) ;\Longrightarrow; \mathrm{Anc}_A(s)$$
The proof is that $A$ is a subset of $D$, and a conjunction over $D$ contains the conjunction over $A$. The search runs the contrapositive:
$$\neg,\mathrm{Anc}_A(s) ;\Longrightarrow; \neg,\mathrm{Occ}(s)$$
A position an anchor rejects is settled exactly and permanently, with no verification, and no later stage revisits it.
2.3 Proposition 2: no completeness
For every proper subset $A \subsetneq D$, the converse
$$\mathrm{Anc}_A(s) ;\Longrightarrow; \mathrm{Occ}(s)$$
is not entailed, in any domain and in any state. A witness is any $s$ agreeing with the base on $A$ and differing on some $d \in D \setminus A$, and the definitions permit such an $s$ whenever $|\Sigma| > 1$. The only $A$ for which the converse holds is $A = D$, where the filter has become the verification.
A matching anchor establishes nothing. The exact compare cannot be removed by any amount of knowledge about the domain, and adding anchors reduces the survivors without ever reaching certainty.

Please contact me from your .org or .edu if you want an educators license. This is part of my research body. It accidentally exploded in scope and the conjecture will take years of proofing from all physical disciplines.