Computational Birth-Time Rectification — An Empirical Study¶

A rigorous negative result, one stubborn positive, and why the arithmetic beat the symbolism.


Status	Complete write-up (exploration on `explore/rectification`)
Date	2026-07-11
Owner	Kate
Companions	RECTIFICATION_THEORY.md · RECTIFICATION_PHASE1_FINDINGS.md (raw lab log) · code in `rectification/`

Abstract¶

We asked whether a birth time can be recovered, automatically and at scale, from a person’s dated life events and temperament — the task astrologers call rectification. We built a provenance-verified corpus of 63 historical and 20 modern birth-certificate-accurate (AA/A) charts, implemented the classical timing techniques (firdaria, annual profection, primary directions) plus event- and temperament-character signals, and tested each under a pre-registered success gate with leave-one-out cross-validation, permutation-null de-confounding, and confound checks.

Minute-level time is not recoverable. Every timing technique scored at chance for localising the birth time. The only thing recoverable is sect (day/night), at ~70% (cross-validated) — and that is carried mostly by a geometric prior (the daylight fraction of the birth day) plus one traditional doctrine that showed genuine, confound-robust signal: the malefic contrary to sect (Mars-flavoured misfortune → day, Saturn-flavoured → night). We interpret the whole pattern through the lens of ill-posed inverse problems: the forward map (time → chart → life) is many-to-one, so its inverse is non-unique; when the likelihood is uninformative the posterior collapses onto the prior — which is exactly why plain astronomy (the daylight prior) outperformed every interpretive signal.

1. The task, and the honest bar¶

Rectification inverts astrology’s usual direction. Normally: birth time → chart → read the life. Rectification runs it backward: known life → infer the birth time. The unknown is ~1-dimensional (a time within a day; the angles move ~1°/4 min, the Moon ~1°/2 hr, the slower bodies barely at all), so in principle it is a small, cheap inference. We did not demand minute precision — even landing the correct 2-hour block / rising sign (enough for whole-sign work) would be useful. The question was simply: does a life carry enough signal to recover the time, at all?

2. The corpus¶

Ground truth requires known birth times and documented lives, which forces the sample toward famous, birth-certificate-recorded, Western, 19th–20th-century people (a selection bias we return to in §8 — it is structural to the whole enterprise, not fixable).

Provenance first. Candidate charts were verified against AstroDataBank source notes before entry: rectified times masquerading as AA (e.g. Feynman’s Starkman rectification), uncited-biography times sold as A (e.g. Musk), and aggregator-sourced “AA” ratings were rejected. The pass corrected the notables DB itself (apply_research_verdicts.py).
Result: 63 verified people (48 AA + 15 A), 888 dated events (median 13 each) with an event taxonomy, plus ≥4 tagged temperament traits each; sect balance 34 day / 29 night. A separate 20-person post-1970 cohort (17 AA) was held out as an out-of-sample validation set and never used for fitting.

3. Methodology — the discipline that makes the nulls trustworthy¶

The whole value of a negative result rests on not having fooled ourselves. So:

Pre-registered gate: accuracy ≥ 65% and the 95% CI lower bound above the majority-class baseline (54%). Set before testing, never moved.
Leave-one-out cross-validation on every fitted model — the headline numbers are LOO, not in-sample.
Permutation-null de-confounding. Raw technique scores are confounded (some configurations light up for everyone); each signal was scored as its excess over a per-person label-shuffle null. This caught, and removed, a large spurious “night bias” in the first firdaria result.
Partial-correlation confound checks (§7) against profession and sex.
Out-of-sample validation on the 20-person modern holdout.
Every null documented, and multiple-comparison risk explicitly tracked — with n=63, the danger is finding a spurious “hit” by trying enough features. The discipline above is what lets us tell signal from that.

4. Results — the full signal map¶

channel	signal	result
geometry	daylight fraction (prior)	works — corr +0.40, 68%
event character	malefic-of-sect (misfortune flavour)	works — +0.35, independent
event character	benefic-of-sect (fortune flavour)	null (domain confound)
timing	firdaria time-lord × significators	null (corr −0.2)
timing	annual profection (rising-sign lords)	null (rising-sign recovery at chance)
timing	primary directions to the angles	null — sect and time
temperament	sect-light (Solar/Lunar)	null
natal dignity	diurnal/nocturnal balance; dignity-weighted malefic	null
prior	external birth-hour distribution	no improvement

4.1 The one that worked, and the one that surprised¶

The daylight prior — P(day | date, latitude) under uniform birth time, i.e. “longer day ⇒ more likely born by day.” It uses no events, no chart, and it was the single strongest sect predictor (68%). This is not astrology losing to a sundial: sect is the Sun’s position relative to the horizon, so the daylight fraction is the honest base rate of the very thing we predict.
Malefic contrary to sect — the traditional doctrine that the out-of-sect malefic is the sharper destroyer (Mars out of sect by day, Saturn by night). A life’s misfortunes should carry the flavour of its contrary-sect malefic: Mars-flavoured (violent, sudden, accidents) → day; Saturn-flavoured (chronic, loss, confinement) → night. This worked: corr +0.35 (p ≈ 0.005), the strongest-Saturn lives (Bundy, Arendt, Ali, Obama) classify night, the strongest-Mars lives (Hemingway, Kahlo, JFK, van Gogh, Plath) classify day. It is nearly independent of the daylight prior (partial corr +0.30), so the two stack.

4.2 The combined sect classifier¶

Daylight prior × malefic-of-sect, a 2-feature logistic:

model	accuracy
majority baseline	54.0%
daylight-alone	68.3%
malefic-alone	65.1%
daylight + malefic (LOO-CV)	69.8%, 95% CI [57.6%, 79.8%]
daylight + malefic (out-of-sample, modern cohort)	70.6%

Pre-registered gate: GO — and it generalises to a completely different era.

4.3 What did not work — time¶

Firdaria (near time-independent) — null, and slightly anti-correlated.
Profection — rising-sign recovery at chance (exact 9.5% vs 8.3%), and its posterior was worse than uniform (it injected noise).
Primary directions to the angles — the sharp technique, the one that should localise time. Time-recovery MAE 406 min (chance ~360), posterior mass within ±90 min of truth 0.138 (chance 0.125). Best-case retest (day-precision events, tight orb): still chance. Directions do not localise the birth time.
The verdict on the timing family (firdaria + profection + directions): all null. Automated “sweep the time, match events to timing-technique activations via a significator table” carries no rectification signal, coarse or sharp.

4.4 The birth-hour prior — a clean lesson¶

An external, cited hourly birth distribution (population vital-statistics, no chart samples) replaced the uniform-time assumption. It did not help — historical or modern. The three priors produced P(day) values 0.997 rank-correlated with each other (they differ by a near-constant +0.076 shift, sd 0.007). A better prior (marginal calibration) is not a better classifier (discrimination): the curve reweights everyone almost identically, so it slides the decision threshold without changing the ranking. For hour prediction it was the same — within a sect window it added −6 min. All hour signal comes from sect narrowing the window (~5.8 h → ~3.5 h with perfect sect); with our real 70%-accurate sect it collapses back to ~noon (327 min), because a wrong sect call is a ~12-hour miss.

5. Why — rectification is an ill-posed inverse problem¶

The results are not a story of insufficient effort. They are the signature of a structurally ill-posed inverse.

The forward map birth time → chart → life is many-to-one: orbs give slack, a single event can be signified many ways (7th house or Venus or the Lot or the ruler), and a dozen techniques each offer a “hook.” So many birth times produce a chart the rules cannot rule out for a given life. Inverting it therefore yields not the time but a set — the preimage of a lossy map. (Knowing x² = 4 gives {+2, −2}, not because you are bad at algebra but because squaring discarded the sign.)

In Hadamard’s terms the problem is ill-posed: a true time exists, but the solution is not unique (many times fit) and likely unstable (nudging an event date can flip the answer). The standard remedy for an ill-posed inverse is regularisation with a prior. And this is the punchline of the whole study:

When the likelihood is uninformative, the posterior collapses onto the prior. That is why the daylight prior won. We observed it directly — a uniform-scorer control (zero event signal) sets p_day = the daylight fraction, and it beat every event-based signal. The prior dominating is not an embarrassment; it is the defining behaviour of an ill-posed inverse, and we measured its fingerprint.

Sect survives because it is the gentlest possible ask — recover one bit, the coarsest coarsening of the 1-D unknown, partly anchored to geometry (the prior itself). One bit you can sometimes pull from an ill-posed inverse. Nine hundred minutes you cannot.

6. Dialogue with the tradition (Tebbs, Dobyns, Rodden)¶

This frame does not contradict expert practice — it explains it. Carol Tebbs’ Complete Book of Chart Rectification white-knuckles one rule (from Zip Dobyns): an event must show in Secondary Progressions, Solar Arc, and Transits — “if systems are selectively mixed and matched, it is possible to make a case for most any birth time.” That convergence requirement is, formally, constraint intersection: each independent technique carves out its own consistent-set, and the true time must lie in the intersection. It is the mathematically correct response to non-uniqueness — the only lever there is.

But intersection only shrinks the set if the constraints are informative and independent, and both fail: the techniques ride the same angles (not independent), and each one’s consistent-set is ≈ the whole day (not informative). Tebbs is honest about the consequence — in her own Elizabeth Taylor example, the rectification software’s highest-confidence time (81%) was ~7 hours from truth, while the true time scored 50% and second. Her defence — “the trained astrologer’s eye and judgment are still superior” — is both the plausible signal (connoisseurship the algorithm can’t encode) and the unfalsifiable escape hatch (the examples all recover a time already known going in). Rodden’s own verdict sits underneath it all: “all rectified data are rated C … treat all rectified data with caution.” The tradition’s honest practitioners already said what we measured.

Our null is therefore not a refutation of rectifiers; it is a measurement of the gap between blind significator-matching and judgment-selected convergence — and a demonstration that the gap is where all the work is being done.

Does convergence stack? A direct test¶

Tebbs’s rule predicts that combining independent techniques pushes the true time toward the top of the ranking. We tested it by measuring the percentile rank of the true time in each posterior (null = 50th; Tebbs’s “2nd of 4” ≈ 75th):

posterior	percentile of the true time
directions alone	55th
profection alone	59th
profection + directions (blind z-sum)	51st
+ firdaria	49th
+ firdaria + the LOO sect prior	49th

A single technique places the truth at a faint ~57th percentile — a whisper above chance, not “just under winning.” But blind combination cancels it: profection + directions lands at the 51st percentile, worse than either alone, and adding firdaria or the sect prior makes it worse still. The techniques share the angles (correlated structure) but their faint pulls point at different wrong places (decorrelated error), so z-summing adds noise faster than signal and the truth’s rank regresses to the mean. (Weighting could recover the best single technique’s 59th percentile, but cannot exceed the information present, which tops out at a whisper; the sect prior cannot narrow a set with no signal left to narrow.)

This closes the loop with Tebbs. If blind convergence cancels, then expert convergence cannot be combining — it must be selecting the hooks where techniques happen to agree. We have thus empirically separated the two: combination → chance; only human selection lifts the truth. That selection is simultaneously the trained eye’s real contribution and its irreducible unfalsifiability — selecting-on-agreement can surface a true time or manufacture a false one, and the method itself cannot tell which. The whole lift lives in the one step that is neither automatable nor falsifiable.

The ML rematch — does a model find a combination we missed?¶

The natural last objection: maybe the signal is there but tangled, and a flexible model would pull it out where our hand-built two-feature classifier could not. We tested it directly — the compare-hypothesis version, mechanised: for each person, encode the full contrastive (day-fit − night-fit) feature set a practitioner actually weighs when adjudicating sect by hand, then let a model combine them.

Six day-positive features: the daylight prior, malefic-of-sect on events (validated), malefic-of-sect on temperament (a new feature — Mars-hot vs Saturn-cold character, the exact tie-breaker a practitioner uses on a person they know, never before encoded), sect-light temperament (Solar/Lunar), benefic-of-sect, and the firdaria event-timing signal. Two model families, each testing a distinct hypothesis: a regularised logistic (“is there a linear combination we missed?”) and a shallow decision tree (“is there an interaction / veto we missed?” — a tree can encode the “one huge indicator overrides everything” rule as a top split). All leave-one-out (n = 63):

model (LOO)	accuracy
majority class	54.0%
logistic: daylight only	68.3%
logistic: daylight + malefic (validated)	69.8%
logistic: + malefic-of-temperament (new)	65.1%
logistic: all 6 features	66.7%
decision tree (depth 3): all 6 features	68.3%

Nothing beat the two validated features. Every richer model landed at or below 69.8%. Three things are worth stating plainly:

The new malefic-of-temperament feature is dead null — corr −0.02, partial corr −0.04 after controlling for daylight + malefic. Adding it lowered LOO (69.8 → 65.1): it contributed noise, not signal. This is the truth-resolution ceiling made concrete. The same doctrine that adjudicates a known person’s sect at ~90% carries zero information when the “temperament” it reads is a keyword tally over one-line biographical descriptors. The doctrine is not wrong; our measurement of temperament is too coarse to tell “hot-tempered” from its opposite. Rich first-hand truth resolves it; a biography tag cannot.
The tree confirms the diagnosis rather than beating it. Free to build any veto or interaction, it chose daylight as its root split in 50 of 63 folds (malefic-of-events in the other 13) and ignored the interpretive features. Given the exact structure the practitioner’s override intuition describes — one big indicator that trumps the rest — the model concluded the big indicator is the astronomy. The geometric prior is the veto.
A model cannot manufacture signal thin truth does not contain. With n = 63 and hundreds of possible interactions, the flexible models overfit and generalised worse — the repeated signature of this whole study every time we added features. ~70% is a wall, and the ML rematch shows it is a truth-resolution wall, not a modelling one.

The corollary is the constructive one: because the ceiling is truth resolution and not method, the way past it is not a better classifier but a better-informed adjudicator — a human with high-resolution truth, handed the contrastive structure to weigh. That is the design of the compare-hypothesis workbench, not an inference engine.

7. Confound & robustness checks¶

The one positive event signal (malefic-of-sect) is the most bias-vulnerable, so it got the most scrutiny:

Category (profession): malefic-sect corr +0.346 → partial +0.355. Category explains only 5% of sect variance.
Gender: partial +0.349; gender explains 0% of sect variance (women/men day-born at 52%/55%).
Both together: +0.361. Completely stable — it strengthens slightly. Because sect is birth time of day, mechanistically independent of who you are, neither profession nor sex can confound it. The “criminals are violent and happened to be day-born” artifact is ruled out.
Out-of-sample: daylight prior alone → 70.6% on 20 charts never used for fitting, matching its ~68% historical performance.

8. Limitations¶

Selection bias is structural and unfixable. Validating rectification requires known-time + documented-events = famous + AA + Western + recent. There is no representative rectification corpus, because ordinary lives are not documented. This is a ceiling on the entire enterprise, inherited by anyone who attempts it. Our nulls are, if anything, conservative — famous dramatic lives are the best-case input; if timing signal isn’t here, it isn’t anywhere.
The malefic signal carries untestable caveats — biographical-emphasis bias (biographers front-page violent deaths, under-report chronic decline) and unknown generalisation past famous lives. The testable confounds are clean; the untestable ones remain, and the classifier is validated on this population, not claimed for humanity.
n = 63 is small; the keyword lists carry researcher degrees-of-freedom (set a priori, but not cross-validated as features). LOO protects the combination, not the feature design.

9. Conclusion¶

We set out to build a rectifier and instead built an honest account of why one does not easily exist, plus one real finding along the way.

Sect is recoverable at ~70% (cross-validated, cross-era) — but mostly from the geometry (the daylight prior), with a genuine, confound-robust boost from one traditional doctrine (the malefic contrary to sect). That doctrine leaving a measurable fingerprint on real biography is a small, stubborn point in the tradition’s favour that neither a believer nor a skeptic gets to wave away.
Time is not recoverable by automated timing techniques — because the inverse is ill-posed, its solution non-unique, and the interpretive maps too weak and too redundant for convergence to rescue.
The arithmetic beating the symbolism is not astrology losing. Sect is astronomy; the prior winning is the correct behaviour of a well-regularised ill-posed problem; and the tradition’s own honest voices (Rodden, Dobyns, Tebbs) said as much before we ran a single test. What we added was the measurement.

The tooling (loader, harness, benchmark, permutation-null and confound machinery) and two provenance-verified corpora are reusable. The map of where sect signal lives — and where time signal does not — is the deliverable. Negative results honestly won are worth as much as the positive one; they tell you where not to spend the next effort.

— and, for the record: we really did want the old techniques to work.