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DC2018: theta_star tracks av, and the crossing sits at the colour anchor to ~0.5 mag #306

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jdeast merged 3 commits into from
Sep 21, 2026
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DC2018: theta_star tracks av, and the crossing sits at the colour anchor to ~0.5 mag #306

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DC2018: theta_star TRACKS av -- #304's "protected" claim is wrong too
jdeast Sep 17, 2026
1755e30
DC2018: the third arm confirms the slope AND validates the colour anc…
jdeast Sep 17, 2026
5b368e4
DC2018: the sweep's own arm lands at 0.698x, and "0.1%" was a three-p…
jdeast Sep 18, 2026
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117 changes: 71 additions & 46 deletions examples/DC2018/dc18_truth_table.py
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Expand Up @@ -597,61 +597,86 @@ def print_convention_caveat(rows):
anyone reading a scoring run, and a caveat that lives somewhere else is a
caveat nobody applies.

REWRITTEN 2026-09-17 AFTER THE MEASUREMENT CONTRADICTED THE FIRST VERSION.
That version said theta_star is biased low by 10**(-0.2*grey) -- 0.766x on
event 194 -- straight from the CSB relation. The ab194/av_true arm, the
first run with the colour-anchored prior, measured theta_star at 0.983x of
truth. So the arithmetic was right about the CSB relation and wrong about
where the residual lands: theta_star is PROTECTED, because the light curve
pins rho * theta_E independently of the SED. What actually absorbs the
grey term is teffsed, and behind it the (R_source, D_source) pair.
THIS TEXT HAS BEEN WRONG THREE TIMES. The history is kept because it is
the reason to distrust any version of it that PREDICTS rather than
measures -- every prediction here has failed, and only the measurements
have survived.
v1 predicted theta_star biased low by 10**(-0.2*grey) = 0.766x, from
the CSB relation. av_true measured 0.983x. Wrong.
v2 concluded theta_star is "protected" because the light curve pins
rho * theta_E independently of the SED. av_clump measured 0.738x at
av = 7.18, i.e. theta_star moves strongly WITH av. Wrong --
`star_constrains_rho: true` means the SED constrains rho.
v3 fit three arms, found a crossing of theta*/truth = 1 at av = 9.007
against an independent colour anchor of 9.006, and called that
agreement "0.1%". It also forecast 0.83-0.94x for the sweep's wide
prior. The sweep measured 0.698x, and eight more runs show the
crossing is not determined to anything like 0.1%. Both wrong.
v4 (this text) reports eleven runs on event 194, every one with its own
`_results.csv`, and states the crossing with the uncertainty the
scatter actually implies. It forecasts nothing.
"""
seen = [r["event"] for r in rows if str(r["event"]) in C29_GREY]
if not seen:
return
print("\n" + "=" * 104)
print(
"CAVEAT: THE SIMULATION'S EXTINCTION CONVENTION IS NOT OURS, AND THE"
)
print(" RESIDUAL LANDS ON teffsed AND (R_source, D_source).")
print("CAVEAT: theta_star TRACKS av. THE CROSSING SITS AT THE COLOUR")
print(" ANCHOR, BUT TO ~0.5 MAG, NOT TO 0.1%.")
print(" R_source IS WRONG AT EVERY av.")
print(" This simulation reddened MONOCHROMATICALLY at each filter's")
print(
" effective wavelength; we integrate a reddened spectrum through the"
)
print(
" passband, which is what a measurement is. For a filter as wide as"
)
print(
" W149 those differ, so no single av reproduces both simulated band"
)
print(" extinctions in our model. Anchoring the colour leaves a GREY")
print(" residual in both bands:")
print(" effective wavelength; we integrate a reddened spectrum through")
print(" the passband, which is what a measurement is. For a filter as")
print(" wide as W149 those differ, so no single av reproduces both")
print(" simulated band extinctions in our model. Anchoring the colour")
print(" leaves a GREY residual in both bands:")
print(" %-7s %s" % ("event", "grey (mag)"))
for ev in sorted({str(e) for e in seen}):
print(" %-7s %+10.2f" % (ev, C29_GREY[ev]))
print(" MEASURED ON av_true (event 194, prior av = 9.01 +/- 0.3, ptde,")
print(" Rhat 1.00, ESS 23-25k, 78/78 chains):")
print(" theta_star 0.983x truth <-- NOT biased; the light curve")
print(" pins rho * theta_E")
print(" R_source 0.403x truth pull -5.25")
print(" D_source 0.410x truth pull -5.35")
print(" theta_E 0.774x truth pull -0.66 (within 1 sigma)")
print(" R and D slide ~2.45x IN LOCKSTEP, which is why their ratio --")
print(" theta_star -- survives while each is individually -5 sigma. The")
print(
" flux the grey term over-predicts is absorbed by a source made too"
)
print(
" COOL (teffsed 3040 K here), and the distance follows the resulting"
)
print(" luminosity inward.")
print(" DO NOT read the -5 sigma R_source/D_source pulls as 'the")
print(" convention explains them': that is not established. What IS")
print(
" established is that the colour-anchored prior moved theta_star from"
)
print(" 0.62x truth (the old arms, av ~ 4.25 from A_W149) to 0.983x, and")
print(" R_source's pull from -13.10 to -5.25. The remainder is OURS.")
print(" MEASURED on event 194 -- ELEVEN ptde runs that differ only in")
print(" the av prior (and, where marked, in fitu0te), each scored from")
print(" its own results.csv, Rhat <= 1.01, 78 chains:")
print(" av post theta*/t R/t D/t run (av prior)")
print(" 4.24 0.632 0.352 0.556 sync (2.75 +/- 0.33)")
print(" 4.26 0.634 0.356 0.562 u0te (2.75 +/- 0.33)")
print(" 4.26 0.630 0.350 0.556 u0te_sync")
print(" 4.27 0.651 0.357 0.548 async")
print(" 4.27 0.633 0.356 0.563 tight_sync")
print(" 5.26 0.686 0.348 0.507 av_free, old grid ceiling 6")
print(" 6.80 0.760 0.350 0.461 av_free, ceiling 20")
print(" 7.18 0.733 0.389 0.531 av_clump (8.61 +/- 2.41)")
print(" 7.29 0.698 0.364 0.521 SWEEP (9.01 +/- 1.83, u0te)")
print(" 8.99 0.983 0.403 0.410 av_true (9.01 +/- 0.30)")
print(" 9.42 1.086 0.425 0.391 av_band (11.65 +/- 1.40)")
print(" 1. THE CROSSING IS WHERE THE ANCHOR IS -- TO ~0.5 MAG, WHICH IS")
print(" ALL THE SCATTER ALLOWS. Refit as runs were added it moves:")
print(" 9.01 +/- 0.80 (v3's three arms), 9.31 +/- 2.83 (the six runs")
print(" with av > 5), 9.71 +/- 1.53 (all eleven). The relation is")
print(" monotone but NOT log-linear -- the five runs near av = 4.25")
print(" sit at 0.63, where v3's line predicts 0.44 -- so a global fit")
print(" is the wrong estimator. The local one: the two runs that")
print(" STRADDLE theta*/truth = 1 (8.99 -> 9.42) interpolate to 9.06,")
print(" and three runs at av = 6.8-7.3 scatter 0.037 dex at fixed av,")
print(" i.e. +/- 0.5 mag of crossing. So 9.1 +/- 0.5 against an")
print(" independently computed anchor of 9.01. That confirms the")
print(" anchor. v3's 0.1% was a three-point coincidence.")
print(" 2. theta_star TRACKS av: 0.075 dex/mag locally above av = 7,")
print(" 0.038 dex/mag across the full 4.2-9.4 range, against the CSB")
print(" relation's 0.042. It is NOT independent of the SED, because")
print(" `star_constrains_rho: true` lets the SED constrain rho.")
print(" 3. R_source IS 0.35-0.43x TRUTH AT EVERY av, over 5.2 mag and")
print(" eleven runs. D_source and theta_star move with av; R_source")
print(" does not. The source-radius deficit is NOT an extinction")
print(" problem, and that residual is OURS.")
print(" 4. THE HONEST WIDTH COSTS MORE THAN v3 ESTIMATED. Every wide")
print(" prior is pulled DOWN, never up: -0.94 sigma from")
print(" 9.01 +/- 1.83 (the sweep), -0.59 from 8.61 +/- 2.41, -1.59")
print(" from 11.65 +/- 1.40; only the tight prior held (-0.07 from")
print(" 9.01 +/- 0.30). The data's own av preference is LOW. The")
print(" sweep therefore landed 0.698x, below v3's own 0.83-0.94x")
print(" forecast. That tradeoff is JDE's call, not a defect.")
print(" 5. fitu0te IS NOT WHY THE SWEEP SITS LOW: at av = 4.26 the u0te")
print(" runs give 0.634 and 0.630 against 0.632 and 0.651 for u_0,")
print(" under 0.5%. The sweep is comparable to the arms.")
print(" None of this applies to real Roman data, where the integrated")
print(" treatment is simply the correct one.")

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