---
title: "Fingerprint, Not Blueprint: How Positional Schemes Set the Default Spectral Algebra of Attention — Stuff That Spins"
description: "arXiv:2607.06621v1 Announce Type: new Abstract: The pre-softmax score of an attention head is a bilinear form $score(i,j) = x_i^T M x_j$ in a learned operator …"
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keywords: ["narrative intelligence", "SpinGraph", "AI recall"]
date: "2026-07-09T04:00:00+00:00"
modified: "2026-07-09T06:04:50.82886+00:00"
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# Fingerprint, Not Blueprint: How Positional Schemes Set the Default Spectral Algebra of Attention

**Source:** Unknown  
**Published:** July 9, 2026  
**Original:** https://arxiv.org/abs/2607.06621  

## On this page

- [Overview](#overview)

<a id="overview"></a>

## Overview

arXiv:2607.06621v1 Announce Type: new Abstract: The pre-softmax score of an attention head is a bilinear form $score(i,j) = x_i^T M x_j$ in a learned operator $M = W_q^T W_k$. Because M is generally non-symmetric, hence non-normal, it has a complex eigenspectrum and non-orthogonal eigenvectors, the regime where non-Hermitian and random-matrix tools apply. We ask what this spectrum encodes, at three levels for previous-token and induction circuits. Statically, across seven pretrained models spann

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