Rectification — Methodology & Theory Overview

Status

Exploration / draft

Created

2026-07-10

Owner

Kate

Type

Theory & methodology (companion to RECTIFICATION_SPEC.md)

This document explains how the rectifier works conceptually — the statistical model and its astrological grounding — independent of implementation. The build plan is in RECTIFICATION_SPEC.md.

1. The problem

Rectification = inferring an unknown or uncertain birth time from what is known about a life: dated events (marriage, career turns, relocations, bereavements, accidents, public recognition) and, more softly, temperament. Traditionally a laborious manual craft; we want a computational, honest, and explainable version.

2. The core insight

Birth time maps almost entirely onto the angles (Ascendant / Midheaven and the house cusps) and, weakly, onto the Moon (~0.5°/hr). Planetary longitudes barely move across a birth-day. Two consequences drive the entire design:

  1. The unknown is effectively 1-dimensional — a time within a day (latitude/ longitude are normally known). This is tiny.

  2. The forward model is known, exact, and cheap. Given a candidate time t, Stellium computes exactly what every timing technique says — there is nothing to learn about the map t → activations; it is astrology’s math.

A third, practical fact: over a birth-day the slow bodies are ~fixed, so a candidate sweep does not need a full ephemeris recompute per candidate — compute them once and re-cast only the angles (cheap trig from sidereal time

  • latitude). The Moon is the exception (~0.5°/hr ≈ 13°/day) and must be recomputed or interpolated per candidate; it feeds the Moon significators and the sect-dependent Lot of Fortune/Spirit. (Build detail: build spec §4.1.)

3. The model

A hierarchical Bayesian model with a simulation-based forward model: the astrology engine is the exact simulator, birth time is inferred by grid evaluation over the 1-D window, and the likelihood is empirically calibrated on a corpus of known-time charts.

3.1 Prior — P(t)

  • Naive: uniform over the candidate window (the whole day if fully unknown, or ±N hours around a stated time).

  • Informed (optional): a soft bump around any recorded/approximate time, and birth-hour base rates (births genuinely cluster by hour — early-morning peaks, weekday-morning C-section humps).

3.2 Likelihood — L(events | t)

Each (event_i × technique_j) pair contributes L_ij(t) = how strongly technique j lights event i’s significators around its date, for a chart cast at t. Conditional on t and treating contributions as (approximately) independent:

log P(t | events) = log P(t) + Σ_i Σ_j w_j · log L_ij(t) + const

The w_j are per-technique weights (§7). The shape of each L_ij matters: a technique that activates at a precise instant (a directed MC→Venus arc exact at one minute) contributes a narrow bump; a coarse technique (profection, which depends only on the rising sign) contributes a broad plateau. This multi-resolution behaviour is a feature — see §4.

3.3 Posterior — grid evaluation

Because t is 1-D and the forward model is cheap, evaluate the un-normalised log-posterior on a grid of candidate times and normalise. No MCMC, no variational inference, no sampling — grid evaluation is the correct and exact method at this dimensionality. The rigorous label for “known simulator, invert to a posterior, likelihood not written analytically” is simulation-based (likelihood-free) inference; in 1-D it collapses to exactly this grid.

3.4 Why not deep learning

The core is the wrong shape for DL, for concrete reasons:

  • It would try to learn a forward model we already know exactly — discarding perfect information and demanding data we don’t have.

  • Per-person data is tiny (a handful of events); DL needs volume.

  • The inference is 1-D; DL’s high-dimensional strength is irrelevant.

  • Interpretability is mandatory (the practitioner must see why).

Learning has exactly one legitimate home here: calibrating the likelihood (§7), a small tabular problem best handled by classical methods.

4. Coarse-to-fine, and sect as a marginal

Techniques constrain at different resolutions, and the model exploits this:

  • Coarse (broad likelihoods): firdaria sect (flips at the horizon → constrains AM/PM), profection (rising sign only → ~2-hour plateau).

  • Sharp (narrow likelihoods): directions/transits to the exact angle, progressed-Moon aspects — minute-level.

Multiplied together, coarse likelihoods carve the plausible band and sharp ones resolve within it — exactly how a human rectifier works (AM/PM and rising sign first, then fine-tune). Critically, sect requires no separate model: it is the marginal of the same posterior,

P(day) = Σ over the day-cells of the grid,   P(night) = Σ over the night-cells,

so one model yields both the robust binary answer and the fine posterior. Note P(night) sums all night-cells — sect is whether the Sun is above/below the horizon, computed per candidate, so at temperate latitudes the night-cells are two disjoint runs (pre-dawn + post-dusk) while the widths and even the region count are season/latitude dependent (one region under polar day/night); never a fixed midpoint split (build spec §4.2). Sect is still the safest thing to report because it is a coarsening of t (hard to overfit), which is why it is the natural first deliverable (§ spec).

5. Evidence: hard-data, soft-data, and the information budget

Two evidence streams:

  • Hard data — dated events. Each event → significators (§6) → activation under the timing techniques → a likelihood over t. These are the strong, time-sharp constraints.

  • Soft data — temperament/personality. Maps to sect-role assignments (sect light; benefic/malefic of the sect) and dignity emphasis. Broad, subjective; contributes mainly to the sect marginal, and is treated as the least-rigorous channel (optionally human-in-the-loop or LLM-elicited, always flagged and calibrated).

The information budget (a genuinely useful lens). Borrowing the actuarial frequency × severity decomposition — but applied to the evidence, not the parameter:

  • Frequency = how many usable events you have.

  • Severity = each event’s discriminating power — how sharply its likelihood constrains t (a precisely-dated angular direction is high-severity; “she’s rather Venusian” is low-severity).

Their aggregate ≈ the total constraining information ≈ how tight a posterior you can even hope for. This gives the tool a principled way to say “your facts can support roughly a ±90-minute answer” and to elicit the highest-severity evidence next.

6. The event → significator model (the conceptual crux)

The hardest, fuzziest part is turning “married 1998” into “the 7th house / Venus / the Lot of Marriage should be activated around 1998.” We define a small event taxonomy, each type mapping to significators (houses, planets, lots) and the techniques best suited to catch it:

Event type

Typical significators

Relationship / marriage

7th house, Venus, Lot of Marriage, ruler of 7th

Career / public recognition

10th house, MC, Sun, Lot of Spirit, ruler of 10th

Relocation / emigration

4th/9th houses, Moon, ruler of 4th

Bereavement (parent)

4th/10th (parents), 8th, Saturn

Childbirth

5th house, Jupiter, Lot of Children

Health crisis / accident

1st/6th/8th, the malefics, Lot of Fortune

Windfall / loss

2nd/8th, Lot of Fortune, Jupiter/Saturn

Legal / imprisonment

12th, Saturn, ruler of 12th

The mapping is uncertain, so significators are best treated as a (small) set with weights and, ideally, marginalised over rather than fixed. This taxonomy is also what the data-collection prompt must target.

7. Correlation, calibration, and honesty

The independence assumption in §3.2 is false: ZR, profections, and directions all ride the same angles, so naively multiplying their likelihoods double-counts and yields an overconfident, too-narrow posterior. This cannot be fixed from first principles — the correlation structure is messy. So we fix it empirically:

  • Introduce per-technique weights w_j and an overall temperature.

  • Calibrate on a known-time corpus (§8) so the posterior is properly calibrated — its 68% credible interval actually contains the true time ~68% of the time on held-out charts (temperature scaling / conformal calibration).

This calibration is what turns a score into an honest probability. Formally this is the hierarchical layer: global parameters (per-technique reliability/orb, temperature) shared across everyone and fit once on the corpus; a per-person parameter (t) inferred from that person’s events.

For the combiner itself, in ascending complexity (use the simplest that passes validation): (1) expert-prior weights + a light global calibration; (2) regularised logistic regression over per-technique activation features; (3) gradient-boosted trees only if 1–2 underperform. Deep nets: no.

8. Validation — the notables benchmark

Stellium ships hundreds of AA-rated (birth-certificate-accurate) charts, so we know the true time. That makes an honest benchmark almost free:

  • Blind test: blank the time, feed documented events (+traits), run the rectifier, compare to truth.

  • Sect first: a clean binary classification accuracy — the most interpretable early signal (does the approach beat chance, and by how much?).

  • Then time: median absolute error, and — crucially — calibration (are the credible intervals honest?).

The corpus is both the training set for the calibration layer and the test set (held-out). This self-validation is the spine that separates this from vibes.

9. Optional extensions

  • Prenatal epoch / Trutine of Hermes — the classical rule relating the birth Moon/Ascendant to the pre-natal lunation. Stellium’s bidirectional lunation finder makes it computable, and it can enter as one more likelihood contributor.

  • LLM as a soft-evidence elicitor — for the personality channel only: “these traits — more consistent with the day role-assignment or the night one?” → a soft P(day). Appropriate use of an LLM (structured judgment over fuzzy text); never the inference engine; calibrated like everything else.

10. Framing & ethics

  • A computed indicator, not an oracle. The output is a distribution with an explicit uncertainty, always human-in-the-loop for the final call.

  • Explainable by construction — the posterior is a sum of per-event, per- technique contributions, so the tool can always show why a window scores well (“your 1998 marriage pulls toward 14:20–14:50 via the ZR Spirit peak and a directed MC→Venus”).

  • Honest about uncertainty — report the full distribution (often multi-modal) and the information budget, never a false-precision timestamp.

11. One-sentence summary

A hierarchical Bayesian model with the astrology engine as an exact simulation-based forward model, birth time inferred by grid evaluation over the 1-D window, sect read off as a marginal, the likelihood empirically calibrated on the known-time notables corpus so its credible intervals are honest — classical (not deep) learning reserved for the calibration layer, an optional LLM only for the soft personality channel.