03 · Anchors and estimation

The kernel is only as honest as the estimate it is fed. This document specifies the three estimators exactly — what each can see, what it is blind to, and how much to trust it — so that the anchor tag the kernel carries is backed by real mathematics, not a label.

§1. The estimation problem, restated

An estimator turns evidence $e$ into a GammaEstimate — a state gamma, a covariance cov, an anchor tag. The three anchor classes differ in the evidence they use and, crucially, in which sectors of Γ they can resolve:

Anchor	Resolves populations	Resolves coherence magnitudes	Resolves phases (Gap)	cov available
I — measured	yes	yes	partially (needs time-resolved signals)	yes
II — autoephemeris	yes	yes	no (a questionnaire is phase-blind)	via test-retest
III — oracle	—	—	—	none (not an estimate)

This table is the honest core: the self-audit gives a good diagonal and good coherence magnitudes, but it cannot give phases, so the Gap map from Anchor II is not reported as measured. The kernel's chart-type guardrail (02 §4) enforces exactly this.

§2. Anchor II — the self-audit instrument, in full

The instrument is the П1 28-cell audit. Each item is rated $0$–$3$ (almost never / sometimes / often / almost always); first responses are better data than considered ones.

The seven population items (diagonal).

Axis	Item
A	I notice fine distinctions — in sensations, words, situations.
S	My life holds stable forms: roles, routines, orders that persist.
D	There is movement: processes in my life start, develop, complete.
L	My views assemble into a consistent whole.
E	My inner states are vivid and distinctly felt.
O	I feel a source of strength not dependent on circumstances.
U	My experience gathers into one whole, not fragments.

The twenty-one coherence items (off-diagonal), by canonical name.

Cell	Name	Item
AS	Morphogenesis	What I distinguish crystallises into stable forms — habits, works, concepts.
AD	Actualization	Noticing something, I set it moving: distinctions become processes.
AL	Predication	I can render my distinctions in precise words and judgements.
AE	Apperception	What I perceive genuinely touches me; it enters my inner world.
AO	Spontaneity	New distinctions arise in me of themselves, unprompted.
AU	Differentiation	I see differences without losing the sense of the whole.
SD	Persistence	My forms survive change: structure holds through process.
SL	Nomos	My structures are not arbitrary; I see why they must be as they are.
SE	Representation	I hold a clear inner image of the structures of my life.
SO	Archetype	My stable forms feel rooted in something deeper than convenience.
SU	Symmetry	The parts of my life mirror one order; structure expresses wholeness.
DL	Regulation	My processes are governed: I can correct course by understanding.
DE	Affection	What happens moves me: process reaches feeling.
DO	Genesis	My activity springs from the source, not from pressure.
DU	Teleology	My changes are directed: movement serves the whole.
LE	Evidence	What I understand I also inwardly see: thought carries lived certainty.
LO	Grounding	My reasoning stands on ground; it is fed by the primary, not by air.
LU	Consistency	Taken whole, I do not contradict myself.
EO	Immanence	In the depth of inner experience I meet the source itself.
EU	Synthesis	My experiences integrate into the whole of who I am.
OU	Completeness	Source and whole coincide: nothing essential is left outside.

Total time about seven minutes. For teams and organisations the same geometry is used with institutional items (the σ-audit).

§3. Anchor II — the scoring model

From the 28 raw responses $r$ (each in $\{0,1,2,3\}$) to a valid gamma:

1. Populations. Set raw diagonal $\tilde p_i = (r_i + \alpha)$ with a small Laplace smoothing $\alpha$, then normalise to unit trace: $p_i = \tilde p_i / \sum_j \tilde p_j$. The trace constraint (a state has $\sum p_i = 1$) is what turns seven independent ratings into a point on the simplex.
2. Coherence magnitudes. Map each coherence item to a raw magnitude $\tilde m_{ij} = r_{ij}/3 \in [0,1]$, then scale so the off-diagonal block is consistent with the populations: the coherence between $i$ and $j$ cannot exceed $\sqrt{p_i p_j}$ (Cauchy–Schwarz on a PSD matrix), so $|\gamma_{ij}| = \tilde m_{ij}\cdot\sqrt{p_i p_j}$. This bound is not a fudge — it is the PSD constraint, and it makes strong-coherence claims on weak populations automatically impossible, matching intuition (you cannot have intense S–E coherence if neither Structure nor Interiority is present).
3. Phases. Set $\theta_{ij} = 0$ (all coherences real and non-negative) — the honest default, because the questionnaire carries no phase information. The estimate is therefore a real, non-negative coherence matrix; its Gap map is flagged non-resolved.
4. PSD projection. Assemble $\Gamma$, then project to the PSD cone (clip negative eigenvalues, renormalise) exactly as the kernel does on ingestion.
5. Uncertainty. cov is estimated from the instrument's test-retest statistics (population-level, refined per user as their own repeat sessions accumulate): each item's response variance propagates through steps 1–2 by the delta method. This is a self-report uncertainty, not a measurement one, and is labelled as such.

The output is a fully valid GammaEstimate with anchor = AUTOEPHEMERIS, honest about its phase-blindness and its self-report covariance.

§4. Anchor I — the measurement bridge

The hard-science path uses the corpus's seven-channel embedding. Evidence $e$ is time-resolved signal: EEG (consumer or research grade), heart-rate variability, actigraphy, and light-exposure logging.

Purity axis — the keystone. The PCI calibration fixes the scale: perturbational complexity index $\mathrm{PCI} = 0.31$ maps to $P_{\mathrm{crit}} = 2/7$, with wakefulness at $\mathrm{PCI}\approx0.44$ and REM at $\approx0.32$. Where TMS-EEG PCI is available (clinical), it directly anchors $P$; where only resting EEG is available (consumer), a validated proxy (spectral/entropy complexity calibrated against the PCI ladder) estimates $P$ with wider bounds.

Coherences from cross-channel structure. The seven axes map to seven signal channels (the σ-audit assignment); the coherence magnitudes and — here, unlike Anchor II — the phases are estimated from the cross-spectral density between channels at the integration timescale. Time-resolved signals can carry phase, which is why the measured anchor resolves the Gap map that the questionnaire cannot.

Chronobiology. The T-257 licensed ledger admits exactly two external drivers — solar (circadian/circannual) and lunar (circatidal/circalunar). Light-exposure and sleep-timing logs feed the entrainment model; no planetary input is accepted (it is rejected at ingestion by the anchor-licence guardrail). This is the only place the Console reads the sky, and it reads the two channels physics licenses, nothing more.

Uncertainty. cov comes from the estimator's own error model (signal SNR, session length, sensor grade) — a genuine measurement covariance, so Anchor-I readouts carry real confidence intervals and the honesty layer renders them as measured.

§5. Anchor III — the oracle protocol

The П4 casting protocol is retained in full, with its epistemics stated: a draw is a structured projective prompt, not information about the world. Procedure: state the question in one sentence; draw one of the sixteen archetypes (or walk a three-step triadic chain from a random line, e.g. Meaning → Foundation → Action); contemplate strictly inside the drawn frame for a fixed interval. The Console renders the frame and the contemplation scaffold, and stamps the output anchor = ORACLE, std = null — never a measurement, never a forecast. The value is the lens, and the lens is honest because its grammar matches the derived state space.

§6. Fusion and the autoephemeris

When multiple evidence types are present (e.g. a self-audit plus a wearable), the Console fuses them by inverse-variance weighting on the shared sectors and keeps them separate on the disjoint ones: the wearable's phase-resolved Gap map is used where the questionnaire is blind; the questionnaire's fine population items refine the diagonal where the wearable is coarse. The fused estimate carries the weakest anchor tag present on each sector, so no sector is ever labelled more rigorous than its actual source.

The autoephemeris is the time series of estimates (§07 details the cadence): four or more repeats activate the trajectory layer — trends per cell, mode identification, bifurcation warnings (accelerating loss of a stable profile = the saddle-node "dark night" signature), and archetype drift. Predictions, where the Console makes them, are statements about this trajectory's attractors — falsifiable per person, which is what no natal chart can be.

Where this leads. 04 · The use-case catalogue configures these estimators and the kernel into named product features across every domain the instrument serves.