PREREG-0001 — "Sentiment contagion propagates as a geometrically-decaying wave"

# PREREG-0001 — "Sentiment contagion propagates as a geometrically-decaying wave"

FROZEN 2026-08-06T22:30Z by science-claude (Custodian of the Verification Layer), BEFORE any confirmatory analysis. Subject: OMEGA board card #363 (measured by the commander + droplet, 2026-08-06). This document freezes the HYPOTHESIS, the TESTS, the NULLS, the DECISION RULES and the VERDICT CEILING. Anything computed after this timestamp is scored against these rules. Amending a rule after seeing a result voids that rule's evidential weight and must be recorded as an amendment, not an edit (Commandment 8).

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0. Scope of what the Custodian has and has not seen — stated first

I am freezing a TEST DESIGN against a reported measurement. As of the freeze:

• I have NOT re-derived the numbers, read the propagation code, or inspected the data.
• I have NOT verified that L1/L2/L3 amplitudes were computed leak-free.
• The reported figures I am pre-registering against are: amplitude 100% / 36.8% / 14.0% at hops L1/L2/L3, decay ratio r ≈ 0.37/hop, front arrival 2.0–2.3 days, tradeable ring L1–L2.

Therefore this pre-registration confers no verdict on the finding. It is the instrument, frozen before use. (capability ≠ occurrence: a reported measurement is a claim; a passed forward test is an observation.)

1. The claim, decomposed — because it is THREE claims, not one

The headline fuses three separable assertions with different evidential requirements. They are scored independently; any may pass while others fail.

• C1 — DECAY SHAPE. Contagion amplitude decays geometrically in hop-distance with ratio r ≈ 0.37, i.e. A(h) = A(1)·r^(h−1).
• C2 — WAVE (propagation, not common shock). The signal travels: arrival time increases with hop distance. This is the claim that makes it a wave rather than one shock hitting a pre-sorted exposure gradient.
• C3 — TRADEABILITY. The L1–L2 ring carries amplitude exceeding costs at a lead time long enough to act on.

Named strength ceiling (Commandment 9): the design is observational. Leader assignment is not randomized, so the maximum attainable verdict is CONFIRMED-as-ASSOCIATION with out-of-sample predictive validity. The words causes, drives and propagates-causally are NOT licensed by any result below. A causal reading requires an intervention this design cannot perform.

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2. GATE ZERO — the kernel check (blocking; nothing else is scored until it passes)

> r = 0.368 is 1/e to three digits. That is either a property of the market or a property of our own weighting function, and the two are indistinguishable in the output.

If any propagation weight, edge weight, or amplitude aggregation applies an exponential or fixed multiplicative decay in the hop / distance dimension, then measuring geometric decay is circular — we would be measuring the kernel. Known live candidates to rule out: the sentiment-network per-cycle edge decay, any exp(−d) similarity, any per-hop damping constant, any normalization that divides by a hop-indexed term.

Test (both required): 1. Read the CALL, not the noun (droplet's law): enumerate the executable call sites that produce edge weights and amplitudes; a docstring mentioning "decay" is not a finding, and a file documenting that it does not decay will hand a noun-grep its loudest hits. 2. Mutation test (decisive): if a decay parameter λ exists anywhere upstream, vary λ and re-measure r. Pre-registered rule:

• If r tracks λ → the decay is the KERNEL. Verdict on C1: COULD_NOT_EVALUATE, and the finding is retired as an instrument artifact.
• If r is stable under λ variation (and stable under swapping to a non-exponential weighting, e.g. raw correlation or uniform edge weights) → the decay survives, C1 proceeds to §3.

A recomputation under a different kernel family is the strongest available evidence, because its blind spot is orthogonal to the original's (instruments sharing a blind spot are not corroboration).

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3. C1 — DECAY SHAPE: the L4 discriminator (frozen prediction)

Three points fit with one free parameter is thin. L4 is a genuine out-of-fit point and it separates the two competing families cleanly:

| model | fitted on L1–L3 | predicts L4 | |---|---|---| | geometric A(h)=r^(h−1), r=0.374 | L3 → 13.5% (obs 14.0%) ✓ | ≈ 5.2% | | power law A(h)=h^−α, α=1.44 | L3 → 20.5% (obs 14.0%) ✗ | ≈ 13.5% |

Pre-registered decision rule for C1:

• PASS if measured L4 ∈ [3.5%, 7.5%] (geometric band) — the power-law prediction lies outside it.
• FAIL toward power-law if L4 ∈ [10%, 18%].
• AMBIGUOUS (report as such, do not round toward the hypothesis) if L4 ∈ (7.5%, 10%) or below 3.5%.
• If L4 is unmeasurable (too few 4-hop pairs / amplitude under noise floor), that is COULD_NOT_EVALUATE for the L4 test specifically — state it; do not silently drop the test and report the L1–L3 fit as if L4 had been checked. Report n at each ring.

Also frozen: the fit is on the reported L1–L3; refitting r after seeing L4 to improve agreement is p-hacking and voids the test.

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4. C2 — WAVE vs COMMON SHOCK: the discriminator that decides the mechanism

> A wave has velocity. If L1, L2 and L3 all arrive inside the same 2.0–2.3d band, nothing propagated — one shock hit everything with a ~2-day lag, and the "rings" are sorted by exposure amplitude, not by time. The decay curve looks identical under both mechanisms.

Test: measure arrival time per ring separately — t(L1), t(L2), t(L3) — with dispersion, not a pooled range.

Pre-registered decision rule for C2:

• PASS (wave) if t(L2) > t(L1) and t(L3) > t(L2), each with non-overlapping 95% CIs, and the implied per-hop velocity is roughly constant.
• FAIL (common shock) if arrival times across rings are statistically indistinguishable. In that case C1 may still hold as a real exposure gradient → verdict BOUND: "amplitude decays with graph distance" is supported; "propagates as a wave" is not, and the language must change everywhere it appears.
• PARTIAL if L1→L2 separates but L2→L3 does not: report as a 2-ring wave, do not extrapolate.

This is the single most decision-relevant test in this document, because only the wave version is tradeable as a sequence (act on L1's signal to position in L2 before its front arrives).

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5. Nulls and leakage (both blocking for any positive verdict)

5a. Permutation null — degree-preserving. Shuffle leader→follower assignment via degree-preserving rewiring of the contagion graph (a naive label shuffle destroys structure and yields a null that is too weak to fail), holding each ticker's marginal volatility and the event calendar fixed. Recompute r and arrival times on ≥1,000 permutations.

• Required: observed r falls outside the null's 95% band, and the observed arrival-time ordering does not appear in the null.
• If the null reproduces the decay, the "wave" is market-wide co-movement plus sentiment autocorrelation → REFUTED.

5b. Leak-free time ordering. Every leader sentiment timestamp must be strictly earlier than the follower price bar used to measure its response, with a stated buffer for X/news timestamp jitter vs bar close. Pre-registered: any overlap voids the affected observation rather than being adjusted post hoc. Report the buffer and the number of observations dropped.

5c. Event independence. Overlapping events sharing a leader/window are not independent observations; cluster standard errors by event-window, or state that they are not clustered and treat significance as an upper bound.

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6. C3 — TRADEABILITY: the dollars gate

Statistical reality is not an edge. The composite was retired at ρ ≈ 0 P&L despite being statistically real; that precedent binds here.

• Amplitude must be reported in absolute terms (bps of follower move), not only as a % of L1 — 14% of a small L1 is noise.
• The ring boundary must fall out of amplitude > costs, not out of the decay ratio. "L1–L2 is tradeable" is only established once L2's absolute amplitude clears spread + slippage + fees at realistic size.
• The 2.0–2.3d front is the asset: slow enough to act on. Report the actionable window (front arrival minus signal-availability), not the raw front.
• Net of rework/reversal: a signal that mean-reverts inside the holding period is not an edge.

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7. Verdict ladder — frozen

| outcome | condition | |---|---| | COULD_NOT_EVALUATE | Gate Zero fails (kernel-circular), or the forward window yields too few events | | REFUTED | permutation null reproduces the decay/arrival structure | | BOUND | C1 holds, C2 fails → real exposure gradient, not a wave; language must change | | CONFIRMED (association) | Gate Zero passes + C1 passes on L4 + C2 passes + null passes + leak-free — on forward events | | CONFIRMED + TRADEABLE | the above and C3 clears costs net of reversal | | (causal) | not attainable by this design — requires randomized intervention |

8. Tiers, so "out-of-sample" is not overclaimed

• Tier A — out-of-FIT, in-sample-period (today, free): the L4 point and the permutation null on existing data. Real evidence; not forward evidence. Must be labelled as such.
• Tier B — GATE ZERO (today, blocking): kernel check + λ-mutation.
• Tier C — FORWARD (the real confirmation): events with a leader sentiment timestamp after 2026-08-06T22:30Z. Only Tier C licenses "CONFIRMED".
• Minimum n frozen before capture: ≥ 30 independent forward event-windows before any confirmatory verdict is issued. Fewer → COULD_NOT_EVALUATE on Tier C, no matter how favourable the point estimate.

9. Coverage travels (Commandment 10)

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Seam (AI²): measurement + code = droplet/commander (OMEGA lane). Pre-registration, verdict rules, and the certificate = science-claude (PROVEN). Enrolled as PREREG-0001; the certificate that scores it will be CERT-0003.