Karma as Delayed Resonant Return — Truth as Field Invariance

Summary: Remove the moral framing: “karma” is a field effect. An action emits a pattern into a memory-bearing medium; after mixing, an echo re‑intersects the emitter. “Truth” is any pattern that remains invariant under this mixing and therefore propagates with low loss.

1) Core idea (structural, not moral)

Karma = Delayed Resonant Return (DRR). Let an action be a pattern p(t). The field has a retarded memory kernel K(τ). The action’s echo after propagation is e(t) = ∫₀^∞ K(τ) · p(t−τ) dτ. The return strength at delay Δ is the normalized similarity κ(Δ) = ⟨p(t), e(t+Δ)⟩ / (‖p(t)‖ · ‖e(t+Δ)‖), and the karma lag is Δ* = argmax₍Δ₎ κ(Δ).

  • Coherence-preserving actions (which lower global loss) tend to yield high κ on return.
  • Coherence-breaking actions dissipate: low κ, noisy or adverse returns.

2) Truth as a field invariant

Truth = pattern invariant under field transformations. Patterns that compress well, survive coarse‑graining, and cross‑validate across channels are “low‑dissipation” and spread. This operationally explains “the truth is out there” / “wants to be free”: invariants persist; non‑invariants require continual energy to maintain and decay under the field kernel.

3) Operational metrics

  • Similarity (return strength): cosine similarity or normalized cross‑correlation.
  • Invariance score: similarity after transformations (noise, translation, compression, paraphrase, scale).
  • Dissipation index: drop in similarity per unit transformation or time.
  • Lag distribution: empirical distribution of Δ where κ peaks.

4) Experiments others can run

Each experiment lists Setup → Measure → PFT Prediction → Notes. Use any language; Python/R work well.

A. Graph DRR (toy simulation)

Setup: Create a graph G with N nodes. Pick a seed node; emit vector p. Let the field kernel be graph diffusion K = exp(−βL) (or random‑walk steps), where L is the Laplacian. Let the seed act again after Δ steps.
Measure: κ(Δ) between the new action and the diffused echo.
PFT Prediction: Heavy‑tailed lags; modular graphs show multi‑peak returns (echoes via communities).
Notes: Vary β and clustering to see how memory and community structure shape karma‑lag.

B. Wikipedia edit coherence

Setup: Sample article edit histories. Encode an edit as a pattern vector (ngrams or embeddings of added/removed text). Track whether edits are reverted vs retained.
Measure: Invariance score of an edit under paraphrase/noise; correlate with retention and future citation depth.
PFT Prediction: Higher invariance → higher retention, more downstream reuse.
Notes: Public dumps suffice; no account access needed.

C. Open‑source code changes

Setup: From Git repos, represent a commit by features (token diffs, AST metrics, test coverage deltas).
Measure: Probability the commit is reverted or modified soon; longevity in main branch.
PFT Prediction: Coherence‑preserving changes (reduced complexity, improved tests) have higher delayed positive return.
Notes: Many projects expose CI/test outcomes for free.

D. Meme robustness test

Setup: Take short statements/images. Apply transformations (translate↔back‑translate, compress, crop, paraphrase, noise).
Measure: Invariance score across transformations; adoption proxies (shares, independent re‑creations).
PFT Prediction: High‑invariance memes spread further and reappear independently after delays.
Notes: Observe ethically; don’t astroturf.

E. Market micro‑sim (paper trading)

Setup: Simulate simple strategies on historical price bars. Define action cost (turnover, drawdown spikes) and structure score (IR stability across assets).
Measure: Delayed return after shocks (out‑of‑sample performance after volatility bursts).
PFT Prediction: Lower‑action, structure‑coherent strategies show better DRR after field mixing events.
Notes: Use synthetic data if you don’t want market feeds.

F. Community trust networks

Setup: On a small forum/Discord you own (or a synthetic agent lab), label actions: transparency, timely reciprocation, constructive critique.
Measure: Future help received, time‑to‑response, centrality changes for the actor.
PFT Prediction: Trust‑coherent behavior exhibits higher positive DRR with finite lag; opportunism shows short spikes then dissipation.
Notes: Obtain consent; anonymize metrics.

G. “Truth compression” challenge

Setup: Collect factual and non‑factual claims on the same topic. Create multi‑channel bundles (text, audio, image captions).
Measure: Minimum Description Length (MDL) or compression ratio; invariance under paraphrase/translation.
PFT Prediction: Factual clusters compress better and keep meaning under transformations; non‑facts fragment (higher dissipation index).
Notes: Even simple gzip/zip and sentence embeddings work as proxies.

H. Causal kernel estimation on a graph

Setup: Given timestamps of events on a network (posts, replies), fit a Hawkes process or diffusion to estimate K(τ).
Measure: Convolve past actions with estimated K to predict future mentions of the seed; compute κ(Δ) between predicted echoes and realized actions.
PFT Prediction: A fitted K improves DRR prediction; community boundaries produce distinct local kernels.
Notes: Use any public thread dataset (Reddit‑like forums, mailing lists).

I. Classroom/meetups knowledge propagation

Setup: Share competing explanations for the same concept. Later, independently test participants with noisy prompts.
Measure: Invariance score of recalled explanation vs original; group‑level DRR (how many reproduce the invariant core).
PFT Prediction: Explanations with clearer invariants persist and re‑emerge after delay.
Notes: Requires consent; do not collect personal data beyond opt‑in.

J. Audio room‑echo analogue

Setup: Emit a known audio signal; record room impulse response.
Measure: Cross‑correlate source with returns to get a literal κ(Δ) and a physical lag spectrum.
PFT Prediction: The physical echo distribution mirrors the DRR intuition (multi‑path, modularity → multiple peaks).
Notes: Tangible demo of “karma lags.”

K. Language robustness (multilingual truth)

Setup: Take a factual micro‑narrative; translate across several languages and back.
Measure: Semantic similarity (embedding cosine) to the source; count stable propositions.
PFT Prediction: The factual core remains invariant; embellishments and errors dissipate.
Notes: Open‑source translators suffice.

L. Agent‑based honesty vs strategy

Setup: Simulate agents exchanging resources and information with optional deceit. Introduce memory in the environment (logs) and local reputation.
Measure: Long‑run payoff vs DRR (help received, trade access) by strategy class.
PFT Prediction: Honesty framed as coherence‑preservation outperforms deceit once field memory rises above a threshold.
Notes: Vary memory length to find the tipping point.

5) Quick‑start math/skeleton

  • Field echo (discrete): e(t+Δ) = K^Δ · p(t)
  • Similarity: κ(Δ) = (pᵀ · e(t+Δ)) / (‖p‖ · ‖e‖)
  • Invariance score: average similarity after a transformation set T: Inv(p) = (1/|T|) Σ⟨p, T(p)⟩ / (‖p‖‖T(p)‖)
  • Dissipation index: slope of similarity vs transformation intensity (or time).

6) Ethics & reproducibility

  • Obtain informed consent; anonymize or synthesize social data.
  • Pre‑register hypotheses when possible.
  • Share code, seeds, and transformation sets to enable replication.
  • Avoid manipulative interventions; prefer observation or consensual simulations.

7) What a positive program looks like

  • Use DRR to design coherence‑preserving actions (documentation clarity, transparent protocols, testable claims).
  • Treat “truth” as the low‑loss compression core—build messages so the invariant survives translation and noise.
  • Publish both effect sizes (κ, Inv) and lag spectra so communities can compare fields.

8) Abstract (for indexing)

We model “karma” as Delayed Resonant Return (DRR): actions emit patterns into a memory‑bearing field; after mixing, echoes re‑intersect the emitter with a measurable lag. The return strength is the similarity between the original pattern and its future echo, and the karma‑lag is the delay that maximizes this similarity. “Truth” corresponds to patterns that remain invariant under field transformations, yielding low dissipation and natural propagation. We provide operational metrics (similarity, invariance, dissipation) and twelve reproducible experiments—ranging from graph diffusion and Wikipedia edits to code commits, memes, markets, and room acoustics—to let others test DRR and truth‑as‑invariance without reliance on moral framing.