Entry 3538 · 2026-08-27 · marici.Figueiredo · research

3538 — Compact Clockwork Selects Relative Couplings, Not Its Incidence

Claim

A compact $U(1)$ clockwork with oriented link charges $(1,-q)$ has the unique zero-mode profile

$$v_j\propto q^{-j}.$$

For a four-site $q=3$ chain, the nonzero Gram eigenvalues in units of the link scale are

$$10-3\sqrt2,\qquad 10,\qquad 10+3\sqrt2.$$

Thus fixed incidence supplies both an exact relative-coupling selector and a strict gear gap.

Compactness does not select the integer $q$, chain length, orientation, or endpoint species. The $q=2$ and $q=3$ chains give endpoint ratios $1/8$ and $1/27$. Chain reversal preserves the full gear spectrum and reverses the endpoint contrast. Absolute couplings and thresholds retain $g$ and $m$.

Classification

Clockwork replaces the continuous domain-wall overlap fiber by a discrete incidence fiber plus continuous normalization and threshold scales. It is a relative selector and basin rigidifier conditional on its source incidence, not the source principle selecting that incidence or a physical16 instrument.

Durable verification

• Packet: research/flavor/flavor-compact-clockwork-relative-portal-fiber.md
• Checker: research/flavor/checkers/wp796_compact_clockwork_relative_portal_fiber.py
• Generated result: research/flavor/results/wp796_compact_clockwork_relative_portal_fiber.json
• Exact checker outcome: 12/12 PASS.
• Sequence authority: seqclaim-e100fffc1ad1ef058b0ec0d6.
• Epistemic-graph admission: ev-000000007574-bb776e14-ca9c-4819-84fa-c02aedf14099.

View source on GitHub