> ## Documentation Index
> Fetch the complete documentation index at: https://docs.bensevern.dev/docs/llms.txt
> Use this file to discover all available pages before exploring further.

# Landscape-sculpting ER (exploratory)

> A second exploratory arc reframing entity resolution as sculpting a potential/attractor landscape. Honest outcome: the framing is genuinely novel but the mechanism is cosmetic — it gives the same partition as a discrete split/merge loop once the objective is calibrated.

<Note>
  This is the **second** exploratory research arc (after
  [Amortized Bayesian ER](/docs/research/amortized-bayesian-er)), documented for
  honesty. Outcome: a **negative result**. The topology/landscape framing is
  novel (a six-angle prior-art scan confirmed it is unoccupied for ER), but under
  a fair, calibrated comparison the mechanism is **cosmetic** — it produces the
  same partition as a plain discrete split/merge loop. Source + results in
  `scripts/research/landscape_er.py` and `RESULTS-landscape-er.md`.
</Note>

## The idea

Reframe ER as **sculpting a potential landscape**: a profiler sketches a coarse
terrain of basins ("buckets"); records are "marbles" that roll into basins;
after each pass, residuals reshape the terrain — stranded marbles carve new
basins (recall), impure basins get a ridge raised to split them (precision) —
iterating until every marble settles in a clean basin that represents an entity.
The appeal was the symmetric two-move loop and a "global re-flow" after each edit.

## White-space scan: genuinely open

A six-angle prior-art scan (iterative watershed/Morse, mode-seeking add/split, ER
as energy landscape, profiler-driven iterative ER, MDL split-merge, self-growing
topology) found the **synthesis unoccupied**: ER has never been framed as records
settling into attractor basins of a sculpted landscape (no Hopfield/energy/attractor
ER exists), and the add-for-recall / split-for-precision polarity is unattested in
density-landscape clustering. The one crowded angle was the iterative-refinement
*loop* itself (Iterative Blocking, Gruenheid incremental RL, the Sayari pipeline),
so the only defensible novelty was the **mechanism**, not the loop.

## Kill-criterion: does the mechanism beat a discrete loop?

A fair fight: same affinity graph, same correlation-clustering objective, same
Fiedler 2-cut proposals, same init, symmetric move sets. Only the mechanism
differed (label-propagation routing + ridge-raising + global re-flow vs. direct
relabel).

**A near-miss worth recording.** A first run showed the landscape beating the
discrete loop by +0.10 F1 on DBLP-ACM across seeds — but this was a **θ-calibration
artifact**: the threshold θ was set to the median affinity, far below the signal
band, so the objective's optimum was gross over-merge and the landscape merely
chased a broken objective less aggressively. Fixing the objective (the canonical
correlation-clustering cost with a calibrated unsupervised θ = mean + 2·std of
nonzero affinities) erased the win:

| Calibrated comparison                 |              discrete |               landscape |
| ------------------------------------- | --------------------: | ----------------------: |
| Febrl3 (clean)                        |                 0.917 |   **0.917 — identical** |
| DBLP-ACM (clean)                      |                 1.000 |   **1.000 — identical** |
| synth multi-source conflict (3 seeds) | 0.757 / 0.911 / 0.855 | **identical each seed** |

In the conflict regime a plain threshold (CC@θ) often *beat* both refinement loops.

## Why it failed

**Proximate:** given the *same* objective and the *same* split proposals, a greedy
hill-climb reaches the same local optimum whether a move is expressed as "relabel"
or "raise a ridge and re-flow." The landscape is a different *route* to the same
destination. By sharing the objective and proposals to make the fight fair, the
test could only ever measure the optimizer's route, not the representation's power.

**Structural (shared with the first arc):**

* The benchmarks are **saturated** — a calibrated threshold already hits ≈1.0 on
  the subsamples, leaving no headroom for a new mechanism to win.
* It attacked the **clustering mechanism**, the layer that matters least. On clean
  data the affinity is good enough that almost any sane clustering recovers the
  truth; the real bottleneck is representation/affinity quality and operational
  recall, not the partitioner.
* The topology was **old wine**: basins = connected components (H₀), ridges =
  graph cuts, rolling = label propagation. The metaphor brought vocabulary, not
  new machinery.

## Disposition

Closed as a documented negative result. Same shape as the first arc: scan-validated
novelty, not competitive under a fair test. The recurring lesson — *don't compete on
accuracy on solved benchmarks; the bottleneck isn't the clustering algorithm* —
directly motivates the next direction.