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FINDINGS — T11 "Glitches Are Avalanches" (Incoprea Vol IX #07)

Supplied working report; original verdicts not validated.

Review status: Needs review. This is an archival source note, not a passed proof.

FINDINGS.md

# FINDINGS — T11 "Glitches Are Avalanches" (Incoprea Vol IX #07)

**Verdict: NOT SUPPORTED** (rule: Not supported = A1 fails; A2 and A3 also fail).

Test date: 2026-10-30. Data: Jodrell Bank pulsar glitch catalogue
(gTable.html), 736 glitches / 226 pulsars; 733 positive-size glitches used.

## Headline numbers

| Quantity | Value |
|---|---|
| Pooled sizes | 1.15e-12 to 6.5e-5 (Δν/ν), median 7.2e-8 |
| Power-law α̂ (x ≥ median) | **1.38** (1.64 at 65th pct, 2.37 at 80th pct — α drifts with cutoff) |
| ΔAIC (lognormal − power law), median cutoff | **−215** (lognormal preferred); −102 (65th), −3.6 (80th) |
| Per-pulsar α̂ (top 10) | 1.39 … **5.63** (span 4.24; Vela 5.6, J0537-6910 3.19, J2229+6114 2.83) |
| Pairwise 95% CI overlap (top 10) | **21/45 = 46.7%** |
| Waiting-time CV, top 3 active | J0537-6910 **1.90** (clustered), B1737-30 **1.08** (exponential-like), B1338-62 **0.54** (quasi-periodic) |
| Context CVs (named in task) | Crab (B0531+21) 1.31; Vela (B0833-45) 0.58 |

## Support-rule comparison (rules fixed in hypothesis.md before fitting)

| Rule | Requirement | Observed | Verdict |
|---|---|---|---|
| A1 | ΔAIC ≥ 6 favouring power law at median cutoff; not reversed at sensitivity cutoffs | ΔAIC = −215 / −102 / −3.6 — lognormal preferred at ALL cutoffs | **FAIL** |
| A2 | >70% pairwise 95% CI overlap AND point-estimate span < 2.0 | 46.7% overlap; span 4.24 | **FAIL** |
| A3 | CV ∈ [0.7, 1.3] for ≥2 of the 3 most active pulsars | 1/3 in band (1.90, 1.08, 0.54) | **FAIL** |
| Overall | Supported = A1 ∧ (A2 ∨ A3); Conditional = A1 only; Not supported = A1 fails | A1 fails | **NOT SUPPORTED** |

## Interpretation

- **P1 (power-law sizes) is not supported for the pooled sample.** Above the
  median, a 1-parameter power law (α̂ = 1.38) is beaten decisively by a
  2-parameter truncated lognormal (ΔAIC = −215). The lognormal's victory is
  robust across cutoffs, and the α̂ drift with cutoff (1.38 → 1.64 → 2.37)
  itself shows the tail is steeper than the body — not one scale-free law.
  Pipeline validated on synthetic ground-truth data (both model families
  correctly recovered; code/sanity_check_pipeline.py).
- **P3 (universal exponent) is not supported.** Top-10 exponents span
  1.39–5.63; fewer than half the bootstrap CIs overlap. Vela (5.6) and
  J0537-6910 (3.2) sit far outside the 1.4–1.9 cluster of the other seven.
- **P2 (waiting-time scaling) is ambiguous and not supported as
  operationalised.** One of the top 3 is exponential-like (CV 1.08), one
  quasi-periodic (0.54), one strongly clustered/over-dispersed (1.90,
  consistent with J0537-6910's known glitch clustering). No single
  "characteristic scaling" describes all three.

## Limitations

1. **Detection completeness.** Small glitches (≲1e-9) are systematically
   missed, and the catalogue mixes surveys with very different sensitivity
   and monitoring baselines (1969–2024). A completeness floor flattens the
   apparent body of the distribution; this biases against the power law, not
   for it, so it does not rescue P1.
2. **Source heterogeneity.** The pooled sample mixes young pulsars, recycled
   pulsars and magnetars (e.g., 4U 0142+61, 1E 2259+586, one negative glitch
   excluded) — different physics plausibly produces different exponents; the
   pool is not one physical ensemble. P3's failure may partly reflect this.
3. **x_min choice.** Results are conditional on cutoffs at the 50/65/80th
   percentiles; the lognormal win is weakest at the 80th (ΔAIC −3.6, i.e.
   inconclusive, not decisive) but never reverses.
4. **Model set.** Only power law vs truncated lognormal compared; other
   alternatives (broken power law, lognormal mixture, gamma) untested. A
   power law over a *restricted* range is not excluded — α̂ ≈ 1.4 near the
   median matches literature values (e.g. Melatos et al. 2008; Fuentes et
   al. 2017) for the mid-range.
5. **Waiting-time rule.** The entry's "characteristic scaling" is ambiguous;
   CV is one crude diagnostic. J0537-6910's CV (1.90) is inflated by close
   glitch clusters; large-glitch spacing there is known to be far more
   regular than the all-glitch CV suggests.
6. **Per-pulsar fits** use each pulsar's own median as x_min, leaving as few
   as n=5 above cutoff for the least active of the ten — wide CIs, though
   even so the extremes are well separated.

## What would change the conclusion

- **A1 could pass** if a restricted range (e.g. 1e-9 … 1e-6) were
  pre-chosen and a power law beat the lognormal there — but that would be a
  new, narrower claim than "glitch sizes follow a power law", chosen after
  seeing the data.
- **P3 could pass** only if the pulsar population were split by physical
  class (young/recycled/magnetar) and exponents compared within a class;
  pooled-across-classes universality is decisively absent.
- **P2 could pass** only under a different, pre-specified operationalisation
  (e.g. large glitches only, or per-pulsar periodicity tests), not the CV
  rule used here.
- A re-download of the catalogue or a different catalogue (ATNF) would not
  plausibly overturn A1: the ΔAIC margin (215) is far larger than sampling
  noise (bootstrap CIs on the fits are narrow relative to it).

## Files

- hypothesis.md (claim + pre-registered rules) · PROVENANCE.md (URLs, times, sha256)
- data/jb_glitches_gTable.html (raw, 1.8 MB) · data/jb_glitch_catalogue.csv (parsed, 736 rows)
- code/parse_glitches.py · code/fit_utils.py · code/analysis_A1_pooled_fit.py ·
  code/analysis_A2_universality.py · code/analysis_A3_waiting_times.py · code/sanity_check_pipeline.py
- results/A1_powerlaw_vs_lognormal_aic.csv · results/A2_per_pulsar_exponents.csv ·
  results/A3_waiting_time_cv.csv

hypothesis.md

# Hypothesis — Vol IX #07 "Glitches Are Avalanches"

**Source URL:** https://incoprea.com/research-library/original-theories-vol9-20261030/theories/glitches-are-avalanches.html
**Fetched:** 2026-10-30T13:28:18-05:00 (local, America/Chicago)
**Saved HTML:** data/incoprea_glitches_avalanches.html

## Claim (quoted from the page)

> "A glitch is modelled as a region letting go. It may be one defect triggering others."

> **The claim:** "Pulsar glitches are avalanche events in a pinned vortex lattice rather than sudden unpinning of a whole region, so their size distribution should follow a power law and their waiting times a characteristic scaling."

> **03 The mechanism:** "Vortices pin on lattice defects. A small perturbation can unpin one, which shifts stress to its neighbours and triggers a cascade whose size is set by how close the lattice is to the critical state. That makes the crust a self-organised critical system, and predicts a power-law size distribution with an exponent that should be measurable."

## Predictions (quoted)

> "P1 Glitch sizes should follow a power law.
> P2 Waiting times should scale.
> P3 The exponent should be universal across pulsars."

> "06 Refutation: A characteristic glitch size would refute the avalanche picture."

## Pre-written support rules (fixed BEFORE any fitting was run)

Data: Jodrell Bank pulsar glitch catalogue, `http://www.jb.man.ac.uk/pulsar/glitches/gTable.html` (736 glitches, 226 pulsars, 2026-10-30 download). The page's main URL links to this plain-table page; this is the primary source. Fallback (unused): ATNF psrcat.

### A1 — Power law vs lognormal for the pooled sample
- Pooled sample = all glitches with a measured positive Δν/ν (negative/anomalous and unknown sizes excluded).
- Fit power law (Pareto) by MLE on ln x above cutoff x_min: α̂ = 1 + n / Σ ln(x_i/x_min); k=1 parameter.
- Fit lognormal by MLE **conditioned on the same x ≥ x_min** (truncated-lognormal MLE, implemented in numpy, no scipy); k=2 parameters.
- Compare by AIC: ΔAIC = AIC_lognormal − AIC_powerlaw.
- Primary cutoff: x_min = median size of the pooled sample. Sensitivity: x_min = 65th and 80th percentiles.
- **SUPPORT A1 = ΔAIC ≥ 6 in favour of power law at the primary cutoff (median), and not reversed at the two sensitivity cutoffs.**

### A2 — Universality of the exponent
- Take the 10 most frequently glitching pulsars (by glitch count in the catalogue).
- Per-pulsar power-law MLE exponent α, cutoff x_min = that pulsar's own median size (mirrors the pooled rule).
- 95% CIs by non-parametric bootstrap (resample glitches with replacement, refit α; 4000 draws; percentile method).
- Report range of point estimates and the fraction of the 45 pairwise CI overlaps.
- **SUPPORT A2 = >70% of pairwise 95% CIs overlap AND the point-estimate range spans less than ~2.0 in α (a wide spread would undermine "universal").**

### A3 — Waiting times
- For the 3 most active pulsars in the catalogue (by glitch count): inter-glitch waiting times Δt_i = MJD_{i+1} − MJD_i.
- CV = std(Δt)/mean(Δt). CV ≈ 1 (within [0.7, 1.3]) ⇒ exponential/Poisson (memoryless); CV ≪ 1 (≤ 0.5) ⇒ quasi-periodic; intermediate ⇒ ambiguous.
- **SUPPORT A3 = CV ∈ [0.7, 1.3] for at least 2 of the 3 most active pulsars.** ("Characteristic scaling" in P2 is ambiguous in the entry; the rule above operationalises it and no verdict beyond the rule will be forced.)

### Verdict rule (fixed)
- **Supported** = A1 AND (A2 OR A3).
- **Conditional** = A1 only.
- **Not supported** = A1 fails.

Included code and results