Reference

Every quantity, law, experiment, withdrawn claim and open problem in the programme. This page is generated from the files that define each of them — nothing here is typed twice, so it cannot drift from the theory the way a hand-kept index would.

Symbols19

From the symbol table in lexicon.md.

Symbol	Reads as	Defined in
π	a probe	§1.2
P	probe measure	§1.3
m	the message / artifact	§1.4
B\\|m	receiver after conditioning on `m`	§1.4
d(A,B\\|π)	per-probe divergence	§2.1
D(A,B\\|P)	divergence over `P`	§2.2
Â	observed agreement rate	§2.3
D_self	self-divergence	§3.1
D_floor	noise floor	§3.2
F*_R	transfer fidelity	§4.1
C(m)	message cost	§4.2
η	noophoric efficiency	§4.3
Ĉ	claimed agreement rate	§5
Φ	phantom agreement	§5
β	calibration slope	§5.1
K_R	channel capacity	§6.1
U	residual	§6.2
R	reference disposition	§4.1.1
V_λ	net value	§4.3

Terms29

Struck text is a withdrawn claim kept in place, never deleted.

noophorics: the quantitative science of transferring understanding across systems with non-identical priors. From νόος (mind) + φορά (carrying).
noophor: a single act of transfer: sender, artifact, receiver.
antinoophor: a noophor with F* < 0. A message that leaves the receiver further from the sender than before it was sent.
noophoric act: the triple (A, m, B). Synonym for noophor; used when the components matter.
criterion-bearing / criterion-free: the two regimes a probe measure can be in (v0.4). *Criterion-bearing*: an answer exists independently of the sender, so a key or an adjudicator panel is an admissible reference and the word *understanding* is licensed. *Criterion-free*: the sender is the criterion by construction — a preference, a house style, a judgment call whose owner defines the right answer — so R = sender is correct rather than tolerated, and there is no sender error available to be replicated. Key *absence* does not move a measure into the second regime: that is an epistemic fact about the experimenter, not an ontological one about the probe.
agent: any system that maps a probe to a distribution over answers. Defined entirely by its answer distributions; internals are irrelevant.
sender / receiver: the two roles in a noophor. Roles, not properties: the same system is routinely both.
probe: a decidable decision whose answer depends on the understanding being transferred. *Decidable* means the answer space is finite and discrete.
probe measure (P): a distribution over probes. The noophoric frame of reference. No quantity is defined without one.
admissible probe measure: one on which the parties actually disagree before transfer. Measuring fidelity where agreement already exists measures nothing.
divergence (D): expected Jensen–Shannon divergence between the agents' answer distributions over P, in bits. Bounded [0, 1].
agreement rate (Â): fraction of probes on which the agents' modal answers match. Coarser than D, but the quantity parties can actually estimate about themselves.
self-divergence (D_self): an agent's divergence from itself under independent resampling. Agents are stochastic; this is the measure of it.
noise floor (D_floor): ~~mean self-divergence of the two agents; the irreducible divergence between perfectly aligned parties~~. Retracted in v0.3 (retraction 2): two perfectly aligned stochastic agents have identical true distributions, so their true divergence is exactly zero and there is nothing irreducible. D_floor is finite-sample estimator bias at a stated n, obtained by a permutation null over the pooled draws. It is a property of the measurement, not of the agents, and it belongs in the estimator rather than in the definition. Not correcting for it is still the most common error.
transfer fidelity (F*_R): the fraction of the closable gap toward a declared reference R that the message closed, floor-corrected. 1 = fully closed, 0 = no effect, < 0 = antinoophor. Never reportable without its R (v0.4). F*_{R=A} is identically the pre-v0.4 quantity.
cost (C): the price of the artifact, in the receiver's tokens unless stated otherwise. The receiver pays to read it.
noophoric efficiency (η): F*/C, understanding per unit cost, and valid only where F* ≥ 0. ~~The quantity engineering should optimize.~~ A ratio with a signed numerator is not an ordering (retraction 3): at F* = −1 a 100-token antinoophor scores −10.00 and an 800-token one −1.25, ranking the costlier failure higher. Use V_λ when the sign is unknown.
net value (V_λ): F*_R − λ·C. Monotone in both arguments at every sign, so it orders messages the way the field means to. λ is the declared exchange rate between fidelity and a token; sweeping it traces the frontier, which makes V_λ and K_R(C) the same object seen twice.
channel capacity between minds (K_R): sup_m F*_R(m). The best fidelity any message could achieve at unbounded cost, toward a declared reference. Estimated as a lower bound K̂ over a stated search budget, by sample-splitting — a max-over-search estimate is a winner's curse and overstates.
residual (U): 1 − K_R. The untransferable remainder toward a declared reference. Axiom A3 asserts it is nonzero. ~~Written R before 2026-07-31~~ — renamed because v0.4 gave R to the reference disposition without checking the symbol was free, and for a day this glossary listed R as the residual directly above a section defining R as the reference.
phantom agreement (Φ): claimed agreement rate minus observed agreement rate. Φ > 0 is a shared illusion of successful transfer: both parties believe it landed, probes say otherwise. The field's central pathology.
calibration slope (β): d(claimed)/d(observed): how far a party's claim moves when the outcome moves. 1 is calibrated in the responsive sense, 0 is inert, below 0 is anti-calibrated. Independent of [[phantom agreement]]: a party claiming the long-run mean every time scores Φ = 0 and β = 0, and is maximally uninformative. Reporting Φ without β is the same error as reporting bias without resolution. Report it per party and report the attenuation-corrected value beside the raw one, never instead of it. Pre-registered and measured in E-002c: sender −0.02, receiver +0.28.
invariant core: the part of an understanding that survives arbitrarily many chained transfers without loss. Conjectured (L4) to be constraints and prohibitions rather than descriptions.
contrastive encoding: a message specifying where the parties would diverge: boundaries, exclusions, edge cases, what *not* to do.
declarative encoding: a message describing what the sender understands. The default form of nearly every handoff written today.
pre-registration: committing an experiment's hypothesis and analysis plan before any data exists. The git history is the record.
probe test: running a probe measure after a transfer to measure what landed. The noophoric analogue of replication.
ablation ladder: truncating a message to successive cost levels and measuring the resulting F*(C) curve.
reconstructive test: asking whether the receiver can generate a message that achieves comparable fidelity with a *third* party. Tests whether understanding transferred deeply enough to be re-transmitted.

Conjectural laws6

A law enters the record only with a refutation condition attached, and leaves it never. From theory/laws.md.

	Law	Status	Refuted if
L1	Law of diminishing noophoric return	`conjectured`	`F*(C)` is linear over a substantial range, or reaches 1.0 (floor-corrected) for arbitrary sender/receiver pairs.
L2	Law of asymmetry	`conjectured` · headline form withdrawn as tautological	across pairs where domain prior and general capability point in opposite directions, the sign of the asymmetry follows capability, or follows neither at better than chance.
L3	Law of prior overlap	`conjectured` · operationalization incomplete	a non-circular overlap measure exists and fails to predict `K`.
L4	The curse of the summary	`conjectured` · restated after the original was found ill-typed	chain fidelity is not monotone (L4a); `log F*` is not approximately linear over the positive range (L4b); or constraint-form and description-form content show decay slopes that are statistically indistinguishable (L4c).
L5	Fluency inflates phantom agreement	`conjectured`	at equal cost, narrative and contrastive encodings produce statistically indistinguishable `Φ`, or narrative produces lower `Φ`.
L6	Optimal encoding is contrastive, not declarative	`conjectured`	contrastive encodings show `η ≤` declarative encodings at equal cost, across domains.

Experiments7

Status is read from which files exist in each directory — a VOID.md, a FINDINGS.md, a PREREGISTRATION.md — not from a label anybody maintains.

Id	Status	Results	Notes
E-001-fluency-cost	findings	1	—
E-001b-fluency-factorial	void	—	defect recorded
E-001c-fluency-length-controlled	registered, not run	—	—
E-002-phantom-agreement	void	1	—
E-002b-phantom-agreement-ladder	findings	1	—
E-002c-calibration-slope	findings	3	—
E-004-disagreement-detector	void	3	interrupted, resumed, an arm was blocked

Withdrawn claims11

Ours, with what killed each one. Full index at retractions.

#	Claim	Killed by
1	~~A3 — no bounded message closes an arbitrary prior gap~~	A 113-token lookup table reaching `F* = 1`. Restated for held-out probes under bounded cost.
2	~~`D_floor` is "the irreducible divergence caused by the parties' own stochasticity", and belongs inside the definition of `F*`~~	Two perfectly aligned stochastic agents have identical true distributions, so their true JSD is exactly zero. The floor is estimator bias, and a fidelity that changes when you sample more is not well-posed.
3	~~`η = F*/C` is "the quantity engineering should optimize"~~	A ratio with a signed numerator is not an ordering. At `F* = −1`, a 100-token antinoophor scores −10.00 and an 800-token one −1.25, so the message that spends eight times as much to do the same damage ranks higher. Replaced by `V_λ = F* − λC`.
4	~~Falsification criterion 2 — "`Φ ≈ 0` means the pathology does not exist"~~	Bias and resolution are independent. A party predicting 0.70 on every probe and averaging 0.70 has `Φ = 0` and no ability to say which probes it got wrong; it is maximally pathological and the criterion scored it as our refutation.
5	~~L2 headline form~~	Tautological as stated.
6	~~L4 — fidelity is multiplicative along a chain~~	Ill-typed: it multiplied fractions of different prior gaps, and two antinoophors composed to a positive product. Measured: hops of −0.629 and −1.000 multiply to +0.629. Restated as L4a/L4b/L4c.
7	~~L6 is "the field's first engineering prescription"~~	I-PASS, deployed and outcome-measured since 2014 across nine programmes and 10 740 admissions.
8	~~L5 is "our sharpest conjecture"~~	The human half is Carpenter et al. (2013) and Deslauriers et al. (2019). Status stays `conjectured` — a prior is not a test — but the framing was ours to lose.
9	~~`Φ` is "the part we have not found elsewhere", and is what "everyone had felt, nobody had weighed"~~	Keysar & Henly (2002), Newton (1990), Chang et al. (2010), Endsley (2020). It was weighed in 1990, and their instruments are in places better than ours.
10	~~Knowledge distillation "measures success as task accuracy"~~	Stanton et al. (2021) define fidelity separately from generalization and show accuracy does not imply it — E-001's construct failure, from a NeurIPS abstract, five years early.
11	~~"Fidelity-versus-correctness was separated in ML first"~~	Cronbach (1955) separated an accuracy score from an assumed-similarity score, each with its own decomposition; Edwards et al. (2006) measured team mental-model similarity and accuracy as two quantities and compared them as predictors. Both predate the ML work. The content survives; the primacy word does not.

Open problems14

#	Problem
1	The residual characterization problem
2	Non-circular prior overlap
3	The capacity theorem
4	Optimal encoding search
5	The asymmetry law
6	Probe measure generalization
7	Phantom agreement mechanics
8	The invariant core
9	Self-transfer
10	The multi-party problem
11	Post-transfer admissibility
12	The vanishing denominator
13	A hypothesis's reported statistic and its tested statistic are not checked against each other
14	When is a modal answer over `n` draws a stable observable?

Noophorics · Lab journal · Repository