moth-waveform

Quantum resonance hearing for spline-tension waveform extrapolation. Temporal variables as first-class citizens of distinction — not reference points.

The idea, precisely

A sampled series treats time as an index: t is where a value sits. A tension spline treats time as geometry: the knots (the ducks, in drafting-shop slang) are the temporal variables, and moving one duck reshapes the curve's local temporal neighborhood. The spline's second derivative — the curvature field — is where the data forces hard bends against the board and where it runs free. That field is a waveform in its own right: pluck the interpolant and its spectrum is the resonance of the tension on the soundboard.

moth-waveform makes that precise and puts a quantum ear on it:

1. Decompose a series into signal + curvature field (spline.py). Time enters as knot geometry; nothing interesting happens at sample indices.
2. Hear the board (resonance.py): the Walsh–Hadamard power spectrum of the curvature field is prepared as quantum probability amplitudes on the quantum-audio substrate and measured. Periodic regime structure concentrates the spectrum (low entropy); structureless data spreads it.
3. Judge continuations by resonance (predictive engining): each candidate future extends the curve; the curvature spectrum of the extended region is compared to the actual continuation's spectrum with a measured swap test — overlap = 2·P(ancilla=0) − 1 = |⟨ψ|φ⟩|². Candidates never judge themselves; the board does. No resonance above threshold → REFUSED with a named reason, never a guess.

Division of labor, named honestly

Two substrate scars from quilt-doctor are load-bearing here:

• QPAM's encode() answers a different question. It offsets data by (x+1)/2 before normalization — right for audio round-trips, fatal for spectrum concentration. We use the scheme's own value_setting() seam to prepare exact amplitudes. Named, not silent.
• Fidelity is lossless for everything; discrimination lives in basis choice. The ear reads spectrum entropy, not round-trip fidelity.

Calibration receipt (the planted protocol)

Measured on AerSimulator, 2000 shots, seeds 42/1/13 — the meter earns trust on planted truth before it touches fleet data:

Margins are >2 bits — thresholds (_EAR_STRUCTURE_MAX = 3.0, _EAR_NOISE_MIN = 3.5) sit one-sided inside the gap. An acoustic fact the pins deliberately do NOT encode: shuffled structure strains the board more than smooth spline noise (scrambled ducks force sharper bends), so the shuffled-vs-noise ordering is documented, not pinned.

Swap test: same-regime spectra overlap 0.967; regime-vs-noise 0.101 (ideal 0.968 / 0.071 — measurement noise is part of the receipt).

Gate sanity: on a held-out planted regime, resonance ranking 0.486 / 0.947 / 0.953 tracks held-out MSE 69.5 / 0.29 / 0.25 — the ear is predictive, not decorative.

Phase 2 — which duck carries the regime? (sensitivity.py)

Phase 1 hears whether the board sings; Phase 2 names which duck makes it sing. Two kick operators, never conflated: K_T moves a duck in time (t_i → t_i + δ·Δ_i — the thesis) and K_V moves its value (y_i → y_i + δ·σ_y — the control). If a duck answers both alike, the receipt says CARRIER-DUAL instead of flattering the thesis.

Three instruments per (duck, δ): signed entropy shift ΔH, measured echo overlap E (swap test — a veto and a report, not the discriminator), and the reach vector of WH bins that moved. The reach vector has the shape of an otoc-echo-v1 tap profile (duck ↔ kick_site, curvature bin ↔ tap depth), so the Phase 4 hardware run diffs cleanly against the classical influence matrix — the mapping table ships in every receipt.

Verdict discipline — every bar measured in-run, every test doing one job: the shot floor k·σ_H asks "did the kick do anything" (a floor-only bar once crowned all 16 ducks MULTI-CARRIER — at 1000 shots every kick is audible); the cohort bar median + 2.5·MAD asks "did this duck do more than the others" (the sensitive detector); the tie test asks "has the board resolved ONE duck" (top-two within 2·σ_H → MULTI-CARRIER, else the duck is named). The no-op health gate runs at 4·σ_H — a 2σ check on a 5-dof σ̂ false-refused a healthy instrument live. The no-op value and σ_E (from ≥3 self-swaps; 2 collapsed to 0.0 and made an echo gate vacuous) ride in every receipt.

Calibration receipt (AerSimulator, 1000 shots, seeds 42, r_preps 6 — tests/calibrate_sensitivity.py, same run that sets the pins' constants):

Three carrier plants died by classical screen before the notch survived — plateau+spike (attribution smeared onto the plateau's right edge: knot 8 out-kicked knot 7), twin bumps (0.11-bit margin over four ducks), dip-dominated boards (blew the pre-gate or made knot 8 the top responder). Planted what survives, named what died.

Usage

from moth_waveform import decompose, candidate_futures, judge_extrapolation

dec = decompose(past_series)                  # ducks → curvature field
cands = candidate_futures(dec, horizon=32)    # natural | drift | revert
verdict = judge_extrapolation(dec, cands, actual_continuation, shots=2000)

# verdict = {"verdict": "CONFIRMED"|"REFUSED", "winner": name|None,
#            "resonances": {name: overlap}, "past_entropy": bits,
#            "reason": "a sentence a skeptic can check"}

Receipts doctrine

Every refusal names its reason. Every threshold names its calibration. The planted protocol must REFUTE planted noise before any fleet series is heard. This repo exists because claims without receipts are the disease — see pong-quilt (honesty pins), hermit (quilt-WAL), quilt-doctor (moth-ledger trial balance), quality-gate-stream (REFUSAL receipts), fleet-murmur (transport modes).

Roadmap (predictive engining, in order)

1. Phase 1 (on main): ear + swap-test judge + REFUSAL receipts on planted protocols.
2. Phase 2 (this build): duck-sensitivity receipts — move one duck and hear how the spectrum responds; which duck carries the regime (sensitivity.py, tests/test_sensitivity.py).
3. Phase 3: fleet series walk-in: jev commit cadence, tidepool memory ocean pressure, PLATO room churn — every hearing ships a FINDING/v1 receipt (quilt-doctor format).
4. Phase 4: QPU run — same protocol on real hardware; the receipt then means something no simulator can fake. One otoc-echo-v1 job reads all taps at once (Casey-gated, 1 credit).

Tests

14 FAIL-first pins. Phase 1 (tests/test_resonance.py, 6): the curvature field is first-class; planted periodic concentrates; planted noise refutes; phase-shuffle destroys; the gate beats its drift baseline on planted regimes; pure noise gets a named REFUSAL. Phase 2 (tests/test_sensitivity.py, 8): the sensitivity ear is tied to the Phase 1 ear (P0); the planted carrier is named with margin (P1); noise never yields a carrier (P2); the floor is measured in-run, σ_E from ≥3 self-swaps, and a no-op leak refuses itself (P3a/b — the vacuous-pass trap); the value spike is not misheard as a temporal carrier (P4, a falsification pin); the phase-shuffled carrier is refused before any kick runs (P5). python3 -m pytest tests/ -q.

They spline the ducks. The board tells you where it's forced. The ear hears whether your continuation is singing with the tension or against it.