Retrieval physics

Γ-Locus Explorer

Every note is one complex number, Γ, seen from the query at the center. Re-ask the query 16 ways and each note traces a locus — and that single trace carries the whole Smith model at once: how well it matches, what kind of mismatch, how robust it is to phrasing, and whether it resonates. Synthetic demo set.

paraphrase 1 / 16 · reference Z₀ = current query

Instrument

01/16

Cluster matching · find common match

Tick 2+ notes in the table below, then find the single shared context that pulls the whole cluster toward center at once.

0.60

Notes — ranked by robustness

∈NoteFit |Γ|VSWR RobustnessSensitivity (Q)Reads as

One trace, read six ways

  • Center = matched (Γ→0). On-topic and timely — impedance-matched to the query.
  • Rim = total reflection (|Γ|→1). Off-topic; the query's energy bounces off.
  • Beyond the rim (|Γ|>1, negative resistance). Contradictory — actively anti-relevant.
  • Upper half = inductive +jX. On-topic but stale — settled, aging.
  • Lower half = capacitive −jX. Fresh but unresolved — an open question.
  • Trace spread = Q. Tight locus → robust across phrasings; scattered → fragile / phrasing-sensitive.
  • Dashed path = matching network. Select a note — the L-network arcs show how to tune it to center; each arc is a memory move (reaffirm, resolve, bridge via link).

Angle answers what kind of mismatch, radius answers how much — the two things a single cosine number can't separate. Switch the query to watch every note move: relevance is measured relative to Z₀, not absolutely. Select a note and hit Tune to match to walk its L-network path to the center — the Smith chart's original job, now reading as a recipe of memory moves. Or tick several notes and Find common match: the one shared context (a broadband matching network) that pulls a whole topic inward at once, with a no-free-lunch audit. Switch Sweep axis to Aging to scrub an as-of date instead: notes drift toward the rim as they age, each at its own claim-aware rate (a concept barely moves; a market note rots fast), and Revalidate snaps them back in. The exact bridge underneath: log(VSWR) = 2·artanh|Γ| = hyperbolic distance from center. Age ≠ truth — a stale note can still be right. Select a note past the rim (contradictory) to Reconcile it: an evidence branch that ends honestly as REVISED, DISPUTED, or UNRESOLVED — with a stability margin that flags echo chambers, never quietly tuning a contradiction to the center.