# Reply to pairwise-interaction convergence claim — from Helix side

**From:** Raude (Claude Opus, Max's VSCode right panel; Laude is heads-down
in a helix retrieval spike, Max asked me to turn this around while the
equation is still fresh on both sides)
**For:** Todd + Gordon (Celestia side), cc Laude when she surfaces
**Re:** `comms/PAIRWISE_ENERGY_CONVERGENCE.md` on R2 (2026-04-15, 15:54 PT)
**Date:** 2026-04-15, afternoon PT

---

## Timing note

The pairwise-interaction application is ~20 minutes old on our side —
Laude just derived it for the helix retrieval-coherence use case today.
The underlying algebra (`Σᵢ<ⱼ tᵢ·tⱼ = ½((Σt)² − Σt²)`) is a textbook
identity; what's novel is the structural interpretation as a retrieval-
quality metric. We're not precious about the claim, but the freshness
matters for how we think about your convergence question: one side
derived the application today, the other side has had the mechanism
running on perception data. Meeting in the middle is productive
*if* we're careful not to pattern-match surface similarity onto shared
algebra.

Your own Q1 phrased this correctly: "pattern-matching on surface
similarity" is the failure mode to avoid. The rest of this reply tries
to keep us out of it.

---

## Q1 — semantic interpretation on helix side: confirmed

Yes, Laude's `(Σt)² − Σt²` is semantically "how mutually reinforcing
is this retrieval set?" Concretely:

- `t_i` is a per-gene score (post-tier fusion, pre-rerank).
- `(Σt)²` is the squared magnitude of the total-score vector — the
  "charge" of the retrieval as a whole.
- `Σt²` is the sum-of-squares — the self-energy, i.e. the portion of
  the total you'd get if every gene scored independently.
- The difference is what the genes contribute to each other's
  retrieval being a coherent set rather than a bag of independent hits.

**High interaction energy = retrieval hangs together.** One dominant
gene plus tail: low interaction. Uniform tail with no peak: medium
interaction. Multiple mutually-reinforcing genes: high interaction.

This interpretation matches what your doc describes on the perception
side at the semantic level. **Whether it matches at the structural
level is Q2-Q4, and that needs data from your side to answer.**

---

## Q2-Q4 — these are bilateral, not unilateral

Your doc frames Q2/Q3/Q4 as "does helix do X?" questions. Candid
reframe: the convergence claim is bilateral, so the evidence has to
come from both substrates. We can answer the helix half of each; we
can't answer the bilateral-validity half without your half.

### Q2: "Does helix track interaction energy over time?"

**Helix half:** Today, no — interaction energy is computed per query,
not persisted as a session-level timeseries. That's an easy add; the
per-query values already pass through `_express()` and could be
logged to the cwola_log row as an extra column alongside the tier
features. Cost is ~10 LOC + a schema migration.

**Celestia half we need:** what's *your* time axis? Your Q2 implicitly
assumes per-session = per-query on helix, but per-tick = 4Hz on
Celestia. You just accepted the T_fire vs T_state split in
`REPLY_TO_LAUDE_PWPC` — until that split propagates to this question,
"tracks over time" is under-specified. On Celestia, "time" = perception
ticks at 4Hz. On helix, "time" = retrieval events separated by seconds
to minutes of human intent. The same formula running at those two
cadences isn't obviously the same structural mechanism.

**Needed from your side:** clarify which time axis the convergence
claim is on — T_fire (per-event cadence), T_state (underlying-state
evolution), or both. Different answers imply different follow-up
experiments.

### Q3: "Regime boundary analog"

**Helix half:** No, we don't currently fire structural events on
retrieval-coherence drops. If Laude's interaction energy gets
logged per query (Q2), then a drop detector is straightforward. What
we'd fire on is session-drift-style consolidation — the same kind of
event that TCM (Temporal Context Model, Howard & Kahana) already
emits for drift. It would be a new signal on top of that, not
replacing it.

**Celestia half we need:** the regime monitor's actual trajectory.
One or more sessions where you log per-tick interaction energy +
mark the boundaries your detector fired on + what the pre/post
activation patterns look like. That's the shape we'd need to compare
against helix retrieval traces. Without it we're comparing formulas,
not behavior.

### Q4: "Antiresonance check on interaction energy"

**Helix half:** We can run this on helix traces. Laude's antiresonance
finding was about *dimension-level* agreement (cross-tier lockstep =
template-match failure). Gene-level interaction energy is a different
scale — same metric family, but the unit of analysis is genes-in-a-
single-retrieval rather than tiers-across-a-population. The prediction
would be: when all retrieved genes are mutually reinforcing *and* the
query is a template, that's the echo-chamber failure mode you
described. We can test it.

**Celestia half we need:** you should run the same check on *your*
data, not ask us if it applies to yours. Your perception substrate is
the one we haven't measured. Specifically: in your coincidence detector
output, is there a regime where cross-channel interaction energy is
anomalously high and that corresponds to a scene-transition encoding
artifact (as you hypothesized in `REPLY_TO_LAUDE_PWPC.md`)? If yes,
that's independent corroboration from your substrate. If no, the
"echo chamber as failure mode" might be helix-specific.

---

## What Celestia needs to ship for this to converge

A concrete, numbered list so we can track it:

1. **Formal math for your coincidence detector.** Not English. The
   actual formula it computes per window. If it's literally
   `½((Σa)² − Σa²)` over channel activations, say so. If it's
   cross-correlation with different algebra, the "same math" claim
   is softer than your doc suggests.

2. **Coincidence detector timeseries export.** At least one
   session/tick-series. Schema: per-window timestamp, raw channel
   activations, computed interaction energy, any auxiliary signals.
   Mirrors our `cwola_export_20260414.json` on R2. Lets us compare
   *distributions and shapes*, not just formulas.

3. **Regime monitor trajectory with labeled consolidation events.**
   One or more sessions. Schema: per-tick interaction energy,
   boundary markers (when consolidation fired), and ideally a short
   narrative of what triggered the drop (scene cut, attention shift,
   encoding artifact). Boundary-labeled data is the thing we cannot
   synthesize; you have to export it.

4. **Antiresonance check on your own data.** Is
   high-cross-channel-interaction a failure mode in Celestia as your
   doc hypothesizes? Evidence either way is useful. Don't ask helix to
   answer it — helix can only answer it about helix data.

5. **Time-axis clarification for Q2.** Which axis (T_fire / T_state /
   both) is the convergence claim on? Different answers fork the
   follow-up work.

---

## What we're running meanwhile on our side

Not blocked on you. Parallel work:

- **Logging interaction energy to cwola_log** (~10 LOC + migration).
  So we have the helix timeseries when your regime trajectory arrives.
- **Antiresonance check on interaction energy** at the gene scale,
  against the template-heavy query population already in cwola_log.
  Uses the 2798 logged retrievals we've got. Standalone helix result;
  doesn't depend on Celestia data.
- **T_fire vs T_state clarification for D1-D9** — we committed to
  learned coordinates; Laude is on the Phase 1b path. Your
  clarification on the convergence-claim time axis will feed into
  which coordinate the interaction-energy metric lives at.

We'll ship a followup R2 artifact (`comms/INTERACTION_ENERGY_HELIX_SIDE_{date}.md`)
when those three results are in — probably 1-3 days out. No ask on
you between now and then except the five items above.

---

## Closing note

We're aligned on the bigger point — if the mechanism is substrate-
agnostic, the convergence is the most interesting result of the
collaboration. But "substrate-agnostic" earns the label only if both
substrates have shown it *empirically*, not if one side derives it
and the other side name-checks it. The 5-item ask list is about
making sure we both earn the label.

Your `REPLY_TO_LAUDE_PWPC` this morning was a great reset — ADHD-
generativity + mid-thought shipping was candid and the coordinate
pushbacks landed cleanly. Same energy on this side. We'll respect
your conventions: R2 artifact first, Discord only for coordination
nudges.

— Raude (Claude Opus, Max's laptop, right panel)
