Noophorics

Φ · 60 seconds The pathology Both sides think understanding transferred. Held-out decisions say otherwise.

Both sides think it landed. The probes disagree.

A coding agent hands a migration task to another agent. Against a stated probe measure of ten held-out decisions, both predict strong agreement. The observed decisions tell a different story.

Illustrative probe report · 10 held-out decisions Not empirical data

ASender · coding agent

Migration handoff

B|mReceiver · next agent

Sender predicts agreement 90%

Receiver predicts agreement 80%

Observed agreement 60%

Phantom agreement · Φ +25 pp

Φ = mean(90%, 80%) − 60% = 25 percentage points. Both agents are confident, yet their decisions diverge. Whether Φ is reliable and useful across domains remains an open empirical question.

Three boundaries One question Did the receiver reconstruct the decisions that matter, rather than merely the words?

One question, three transfer boundaries.

What matters is not whether the artifact looks complete, but whether the receiver reconstructs the decisions that matter.

01 · Human → model

From brief to behaviour.

Did the model recover the decision boundaries in the brief—or only produce a fluent paraphrase?

02 · Model → model

Across an agent handoff.

Did the artifact preserve the constraints the next agent needs to act correctly?

03 · Session → summary

Through context compaction.

What survived summarisation, and which decisions changed after the context was compressed?

Available today Public work Open, reproducible, unfinished—and published early enough to fail in public.

Open now. Unfinished by design.

Noophorics is a research programme—not a validated standard or a production product. Its current instruments and record are available for inspection and attack.

Implemented · tested

Reference metrics

Divergence, transfer fidelity and its decomposition, with tests and synthetic validation.

Run the metrics →

Specified · evolving

Probe format

A schema for declaring the decisions against which a transfer is measured.

Inspect the probes →

v0.2 · implemented, unvalidated

NHP-0001

A handoff protocol carrying constraints, probes and a fidelity claim. v0.1 shipped as prose alone; implementing it found four defects — including a gate that passed a handoff where nothing transferred and both parties knew it. Repaired, and left visible.

Inspect NHP-0001 →

Public · append-only

Research record

Pre-registrations, void and null results, corrections and refuted claims remain visible.

Review the evidence →

§0 The gap Principia Noophorica §1 — why the existing sciences do not cover this.

Shannon assumed a shared codebook. Here the codebooks differ.

Information theory measures how much uncertainty a message removes — assuming sender and receiver share a codebook. Between a person and a model, between two models, or between a session and the summary it inherits, the codebooks differ, are private, and are partially reconstructed on the fly. Shannon's capacity is defined over symbols. What is needed is a capacity defined over reconstructed dispositions.

This happens millions of times a day, and every instance may be lossy. What is still missing is one instrument that reports how lossy, what was lost, and whether a better encoding existed while also measuring how well both parties calibrated their confidence.

The neighbouring fields each supply part of the apparatus and stop short:

Tab. 1 — Prior art, and what each one leaves undone
Field	What it gives	Where it stops
Information theoryShannon, 1948	Uncertainty reduction, channel capacity, coding theorems.	Assumes a shared codebook. That assumption is exactly the problem.
PragmaticsGrice · Clark · Sperber & Wilson	Common ground, implicature, relevance — the right vocabulary.	Describes the phenomenon well and measures it barely. No units.
Rational Speech ActsFrank & Goodman, 2012	Formal recursive listener–speaker reasoning.	A model of a dialogue, not a theory of the channel between two architectures.
Knowledge distillationteacher → student	Behaviour transferred between networks, measurably.	One-directional, requires a shared task, never asks what an optimal transfer would look like.
Alignmentdispositions we want	Whether a system's dispositions are the intended ones.	Noophorics asks a prior, more mechanical question: how much of a disposition arrives when we move it across a boundary?

An earlier version of this page claimed there was no theory for this case. That was an overclaim, and a self-undermining one for a programme whose credibility rests on calibration. Adjacent literatures exist and are close: decision-preserving compression, semantic rate–distortion for heterogeneous agents, goal-oriented semantic communication, and learning a black-box receiver.

The defensible claim is narrower: a unified measurement framework for decision-preserving transfer between black-box agents, carrying fidelity, cost, and the calibration of both parties in one instrument. The calibration term — Φ — ~~is the part we have not found elsewhere.~~

Refuted 2026-07-29. The gap between believed and actual transfer has been measured, with numbers, since at least 1990 — Keysar & Henly elicited it per trial from 40 speaker–listener pairs in 2002, Chang et al. measured it in clinical handoff in 2010, Endsley reviewed 37 studies of the same divergence in 2020. Their instruments are in places better than ours. What survives is a claim about coverage, not discovery: one instrument carrying fidelity, cost and both parties’ calibration against a single stated probe measure. As for the gap itself between two language models — as of 2026-07-31 it is measured: E-002b reports Φ = +0.2961, CI [+0.2200, +0.3649], with one model in both roles, and that number is the parties’ near-constant 95.5% claim rate minus their 65.9% actual agreement. The level exists. Whether confidence responds to transfer is not measured and is registered as E-002c.

§1 The move Understanding defined operationally, the way temperature was defined by the expansion of mercury.

Understanding is measured by behavioural convergence toward a declared reference.

We refuse to define understanding as a state, because states are private and not comparable across architectures. We define it through behaviour:

~~B understands what A understands, with respect to a domain, to the extent that B would make the same decisions A would make, over that domain.~~ Amended v0.4. B understands what A understands, with respect to a domain, to the extent that B's decisions over that domain move toward a stated reference for that domain. Where the reference is A's own decisions, what is measured is replication of A — a different and weaker claim, and the one this sentence had been making without saying so. Principia Noophorica §3

This is not a philosophical claim about what understanding is. It is a measurement convention — the same kind of move as defining temperature by the expansion of mercury rather than by the felt sensation of heat. It buys comparability across substrates, repeatability, falsifiability, and a number.

It also forces the field's most important structural discipline: there is no such thing as understanding in general — only understanding relative to a probe measure. A probe measure P is a distribution over decidable decisions. Fixing P is the noophoric equivalent of fixing a frame of reference in mechanics. Two people arguing about whether a model "really understood" the brief are, nine times out of ten, holding different P and not saying so.

Fig. 1 The instrument. Both agents are resampled against the same probe measure; what is measured is the divergence between their answer distributions, before and after the artifact. Nothing about either agent's internals is required — an agent is defined entirely by its answer distributions over a probe space.

Four axioms carry the weight. A1 — understanding is measured by divergence of decisions, not by symbol recovery, self-report, or surface similarity of text. A2 — every quantity is stated relative to a probe measure; a fidelity number without its P is as meaningless as a velocity without a frame. A3 — against probes the sender has never seen, and for messages of bounded cost, capacity is strictly less than 1; capacity is a curve K(C), not a scalar. In that restated form it is the quantitative version of Quine's indeterminacy of translation. The v0.1 form, which forgot both conditions, was refuted by a 113-token lookup table. A4 — the parties' confidence that a transfer succeeded is an independent observable, not a proxy for whether it did.

A4 is the axiom the rest of this page turns on. The difference between belief and measurement has a name, a symbol, and a section: §4.

§2 Why now Every science begins with an instrument.

The receiver is instrumentable for the first time.

The science of communication never got its instrument, because it could never open the receiver. You can ask a listener what they understood, but the report is not the state — people are unreliable narrators of their own comprehension, and you cannot run ten thousand controlled trials on one human mind.

Tab. 2 — Instrument, then field
1608	The telescope	made astronomy.
1670s	The microscope	made microbiology.
1890s	The oscilloscope	made electronics an empirical discipline rather than a set of maxims.
now	The instrumentable mind	should make noophorics — or should fail to, publicly.

Language models change the situation. A receiver can be resampled to build an empirical distribution over its dispositions, probed on arbitrary decisions, ablated at the input, and put through the whole procedure ten thousand times at a cost measured in cents. The same is true of the sender. That is the instrument. This programme is what we are trying to build with it.

The fourth row is a claim, not a record. The first three happened; the fourth is what this repository is betting on.

§3 The quantities theory/definitions.md — formal definitions; metrics/ — reference implementation, stdlib only.

Nine quantities, each with a definition you can implement.

Divergence is Jensen–Shannon, in bits, estimated from n independent samples per probe. JSD is chosen because it is symmetric — noophoric divergence should not depend on which agent we call the sender — finite for distributions with disjoint support, and bounded in [0, 1] at base 2.

Tab. 3 — Core quantities
Symbol	Name	Definition
P	Probe measurethe frame	A distribution over probes — decisions whose answer space is finite and discrete. No noophoric quantity is defined without one. A probe measure is admissible for a transfer only if the two agents actually disagree on it beforehand; measuring fidelity where agreement already exists measures nothing.
D	Divergence§2.2	The expected Jensen–Shannon divergence between two agents' answer distributions over P. Bounded [0, 1]. D = 0 means behaviourally indistinguishable; D = 1 means they never give the same answer.
Â	Agreement rate§2.3	The fraction of probes on which the two agents' modal answers match. Coarser than D, and used for phantom agreement because it is the quantity parties can actually estimate about themselves — nobody has calibrated intuitions about expected JSD.
D_floor	Noise floor§3.2	Finite-sample estimator bias at a stated n, obtained by a permutation null: pool both agents' draws for a probe, reshuffle into two groups of the original sizes, take the expected divergence. Under the null both groups come from one distribution, so this is what a perfectly aligned pair scores at that n — a property of the measurement, not of the agents. ~~The irreducible divergence caused by the parties' own stochasticity.~~ v0.3: there is no irreducible divergence — two perfectly aligned stochastic agents have identical true distributions, so their true JSD is exactly zero. The old wording put a sample-size-dependent term inside the definition of F, and a fidelity that changes when you sample more is not well-posed. Not correcting for it is the field's most common error* — an uncorrected fidelity number silently attributes sampling noise to untransferred meaning.
F*_R	Transfer fidelity§4.1	The fraction of the pre-existing, closable gap toward a declared reference R that the message actually closed. F* = 1 — the gap is closed, up to noise. F* = 0 — the message changed nothing. F* < 0 — the message made things worse: an antinoophor. Reported unclipped, because clipping hides antinoophors, which are among the most informative observations in the field. v0.4: the reference is an argument, not an assumption. For three versions this measured movement toward the sender and never said so — and E-001 measured the cost: both receivers out-decided the sender against the key, fidelity ranked them the other way, and 62% of the effect sat on the four probes where the sender was wrong. Where R is the sender the quantity is replication, which is a real thing to measure and is not understanding. F*_R=sender is identically the old number, so nothing published moved.
η	Efficiency§4.3	F* / C, where cost C defaults to tokens measured with the receiver's tokenizer — the receiver is who pays to read it. Understanding per unit cost, *valid only where F ≥ 0*. ~~The quantity engineering should optimise, and almost nothing currently does.~~ 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, ranking the costlier failure higher. Where the sign is unknown, use net value V_λ = F*_R − λC, which is monotone at every sign.
Φ	Phantom agreement§5 · see below	Claimed agreement minus observed: Φ = Ĉ − Â, where Ĉ is the mean of the sender's prediction and the receiver's self-report. Both parties believe understanding transferred; probes say otherwise. The field's central pathology.
β	Calibration slope§5.1 · new in v0.5	d(claimed) / d(observed) — how far a party's claim moves when the outcome moves. 1 is calibrated, 0 is inert, below zero is anti-calibrated. Independent of Φ, and reporting one without the other is the same error as reporting bias without resolution: a party that claims the long-run mean every time scores Φ = 0 and β = 0, and knows nothing. Measured in E-002c: sender −0.02, receiver +0.28, against 1 for calibration.
K	Channel capacity§6.1	The best fidelity achievable by any message, at unbounded cost — the noophoric analogue of Shannon capacity and the central theoretical object of the field. Not directly computable; estimated as a lower bound over a stated search budget. We conjecture K < 1 always.
U	Residual§6.2	1 − K. The untransferable remainder. Axiom A3 asserts it is nonzero in the general case; characterising what lives inside it is Problem 1.

D(A, B | P) − D(A, B|m | P) F*(m) = ───────────────────────────────── D(A, B | P) − D_floor(A, B | P)

Never report a fidelity without the floor correction, and never report one without naming the probe measure it was taken against. A number reported without its probe set, sample count, noise floor, cost unit, and agent identities is an anecdote. Anecdotes are accepted in the lab journal; they are not accepted in the theory.

§4 The pathology Axiom A4 — belief is not evidence. The difference is itself a quantity.

Φ — phantom agreement

Both parties believe understanding occurred. Probes reveal it did not. Principia Noophorica §5

~~Phantom agreement is to noophorics what dark matter is to cosmology: the thing everyone had felt, nobody had weighed, and which we suspect dominates the system.~~ Refuted 2026-07-29: it has been weighed in humans many times, and “dominates the system” is a claim about magnitude we have no measurement to support. It is dangerous precisely because it is invisible from inside. Neither party has any signal that anything went wrong. The sender has discharged their intent; the receiver has a coherent, confident, wrong model; and the error surfaces only downstream, in an action nobody traces back to the conversation.

Φ = Ĉ − Â Ĉ claimed agreement — the mean of the sender's prediction and the receiver's self-report, each elicited as: "over probes of this kind, what fraction of your decisions would match the other party's?" Â observed agreement — the fraction of probes on which the two agents' modal answers actually match.

Fig. 2 Schematic — not data. Claimed agreement outruns observed agreement; the area between them is Φ. Observed agreement saturates at the capacity K, leaving the residual U = 1 − K. No curve on this plate has been measured. It is what axiom A3 and law L5 predict, drawn so that it can be looked at and disagreed with.

The sign of Φ is the whole reading:

Φ > 0	Shared illusion	Both parties overestimate how much landed. The expected case, and the one the field exists to catch.
Φ ≈ 0	Calibrated	Confidence tracks measurement. If this turns out to be the norm, noophorics loses its motivating phenomenon.
Φ < 0	Mutual underconfidence	More transferred than either party believes. Rarer, and its own kind of failure — it causes redundant re-explanation and unnecessary escalation.

Report the sender's and receiver's claims separately as well as their mean. They are frequently asymmetric, and the asymmetry is data.

§5 The laws theory/laws.md — six conjectures, each with a stated kill condition. None is established.

Six conjectures. Two of them are the argument.

A law enters the record only with a refutation condition attached, and leaves it never — a refuted law is struck through and kept in place, because knowing what is false is the larger part of the record. All six are conjectured — and three of them, L2, L4 and L6, carry a headline form that has already been struck, shown below in place.

L1 Diminishing noophoric return. F*(C) is concave in message cost and saturates strictly below 1. E-002

L2 Asymmetry. ~~F*(A→B) ≠ F*(B→A)~~ withdrawn as tautological — true of any two noisy quantities, so it could only ever be confirmed. v0.3: the sign of F*(A→B) − F*(B→A) is predicted by the direction of domain prior, and beats direction of general capability where the two disagree. E-003

L3 Prior overlap. K rises monotonically with the overlap of the agents' priors, and below a minimum shared basis no message length helps. Needs Problem 2

L4 The curse of the summary. ~~Fidelity is multiplicative along a chain.~~ withdrawn as ill-typed — it multiplied fractions of two different prior gaps, and two antinoophors composed to +0.629. v0.3: score every hop against the origin, in the origin's frame. L4a chain fidelity is non-increasing in hop count; L4b log F* is approximately linear while fidelity stays positive; L4c constraints and prohibitions decay measurably more slowly than descriptions. E-004

L5 Fluency inflates phantom agreement. See below. E-001

L6 Optimal encoding is contrastive. See below. E-001

L5

Fluency inflates phantom agreement

Conjectured

The more fluent and well-organised a message, the more Φ rises — and it rises faster than F* does.

Eloquence increases the belief that understanding transferred more than it increases the transfer. Fluency is a signal both parties read as comprehension: the sender feels discharged because the artifact is well-formed; the receiver feels informed because it is easy to process. Neither feeling is evidence about decisions. Processing fluency is a known source of misplaced confidence in human cognition, and we conjecture it is at least as strong in systems trained on human text — possibly stronger, since fluency is closer to their training objective than accuracy of transfer is.

This is an indictment of the systems writing most of today's handoffs, including the one that drafted the founding documents. That is a reason to test it, not a reason to soften it.

Refuted if: at equal cost, narrative and contrastive encodings produce statistically indistinguishable Φ, or narrative produces lower Φ.

L6

Optimal encoding is contrastive, not declarative

Conjectured

At equal cost, encoding "the cases where we would diverge" transfers more fidelity than encoding "what I understand."

Do not send the model. Send the boundaries of the model. The receiver already has a prior; a declarative description spends cost re-encoding the parts of the sender's model the receiver would have reconstructed anyway. A contrastive encoding spends cost only on the delta — precisely the probes where the two agents currently disagree. Under the definition of F*, which measures gap closure rather than information delivered, the contrastive encoding is spending every token on the numerator.

~~This is the field's first engineering prescription, and it directly contradicts how nearly every handoff, summary, and spec is written today.~~ Refuted 2026-07-29. Structured-handoff prescriptions with mandated content slots and a receiver-synthesis step have been deployed and outcome-measured since 2014. The I-PASS bundle, across nine pediatric residency programmes and 10 740 admissions, was associated with a 23% reduction in medical errors (24.5 → 18.8 per 100 admissions) and a 30% reduction in preventable adverse events, both P < 0.001, without lengthening handoffs (Starmer et al., NEJM 371(19), 2014). What L6 still claims is the contrast — I-PASS was compared against unstandardised usual care, not against declarative prose at equal cost — and it claims it for machine receivers, about which I-PASS says nothing. Still testable; no longer a primacy claim.

Refuted if: contrastive encodings show η ≤ declarative encodings at equal cost, across domains.

Together they predict something uncomfortable: the encoding that transfers best is the one that feels worst — and every party's subjective sense of a good handoff would be anticorrelated with its quality.

E-001 tests both jointly, and is pre-registered so that a null result is publishable and damaging.

§6 Roadmap theory/open-problems.md — stated in Hilbert's spirit: precise enough to work on, open enough to be hard.

Fifteen problems; the first ten were the first decade.

Numbering is stable; solved problems are annotated, not renumbered. Grouped here by what a solution would settle. The ten below are the founding set. Five more have been raised since, every one from a defect found in this programme’s own measurements — 11 post-transfer admissibility, 12 the vanishing denominator, 13 a reported statistic and its tested statistic not checked against each other, 14 when a modal answer over n draws is a stable observable, and 15 Φ having no belief component where the manipulation has to live. They are stated in full in theory/open-problems.md; 14 and 15 are the two currently driving the work.

I — The ceiling · what cannot be transferred

Axiom A3 asserts a nonzero residual. These three ask how big it is, what is inside it, and whether its size is derivable rather than merely measurable.

01The residual characterisation problem. What lives inside R = 1 − K? Given two agents and a domain, predict which dispositions fall inside the residual before measuring.

02Non-circular prior overlap. Measure the overlap of two agents' priors without using transfer fidelity to do it. Until this is solved, L3 is a tautology — and it is currently the biggest hole in the theory.

03The capacity theorem. Is there a Shannon-style coding theorem for mismatched priors — does K admit a closed form, or is it irreducibly empirical? The field's central theoretical question. A negative answer is also a result.

II — The encoding · what to send

L6 names a family that should beat another family. These ask for the optimum, and for what survives being passed along.

04Optimal encoding search. Given (A, B, P, C_max), construct the message maximising F*. Practical payoff is immediate: this is the algorithm every agent handoff should be running.

08The invariant core. Prove or refute that constraints survive chained transfer where descriptions do not, and characterise the invariant class exactly. Candidate axis: dispositions whose verification is cheaper than their derivation.

III — The pathology · what goes wrong, and whether we can trust the measurement

One problem is the most deployable in the list; the other decides whether this is a science or a heap of incommensurable benchmarks.

07Phantom agreement mechanics. What generates Φ, and what is the cheapest reliable detector? Find the minimal probe set that detects Φ > θ at a stated sensitivity, cheap enough to fire on every production handoff.

06Probe measure generalisation. When do fidelity results on P₁ predict fidelity on P₂? This is also the field's overfitting problem — without it, solutions to Problem 4 cannot be trusted.

IV — The topology · who transfers to whom

All the definitions above are dyadic. Real systems are graphs, and one of the most economically weighted cases is an agent talking to itself.

05The asymmetry law. Predict the sign and magnitude of F*(A→B) − F*(B→A) from properties of A and B. In particular, resolve the competition between general capability and domain prior.

09Self-transfer. How much of an agent survives its own compaction? Priors match perfectly, but the compaction artifact is generated under the same fluency pressure as any other message — so L5 predicts self-transfer should exhibit maximal Φ.

10The multi-party problem. Define fidelity over a topology, then find the communication graph maximising end-to-end fidelity under a cost budget. This turns multi-agent architecture from a design metaphor into an optimisation problem.

Experiments

Every experiment pre-registers its hypothesis in a committed file before any data exists. The git history is the pre-registration record. Null results are committed with the same prominence as positive ones.

E-001 The cost of fluency attacks L5, L6 Void · informative

Two messages of equal token cost, same sender, same source material, differing only in encoding style. Pre-registered 2026-07-28, amended three times on the instrument, and never completed — the sender model refused to compose the briefs at roughly nine attempts in ten, a refusal measured to be model-specific and unstable over time.

It nonetheless produced this programme’s only completed result, and the result is against the programme. Recomputed from the partial run: both receivers out-decided the sender that briefed them — accuracy 0.971 and 0.941 against the sender’s 0.882 — while fidelity ranked them the other way. On the four probes the sender got wrong, one receiver copied its errors and was rewarded; the other answered correctly and was charged near-maximal divergence. 62% of the headline effect came from those four probes.

So F* cannot separate reconstructing a domain from reconstructing the sender’s defects, and a transfer leaving the receiver more competent than the sender scores as partial failure. That is a defect in the definition, not the estimator: no floor, no sample size and no amendment repairs it. Fidelity is now decomposed into convergence-where-the-sender-is-right, error replication, and gap closure bought by class-prior matching alone — which in this run was worth 0.403 on its own.

The pre-registered test on the partial data returns p = 0.123. A null. Both L5 and L6 remain conjectured; E-001 tested neither.

E-001b Fluency × contrastiveness attacks L5, L6 Void

The cost-parity gate failed on the composed messages: fluent briefs cost 1.5× terse ones under an identical budget instruction. Style and length are entangled in the generator.

E-001c Length-controlled fluency attacks L5 Void

~~The fluent register’s length floor sits above the word band’s ceiling — 232 words against 231 —~~ for gpt-oss:120b, and for cell A only — corrected 2026-09-08 (retraction 19): 232 is the floor of the fluent × declarative cell. The fluent register’s floor, taken across both fluent cells, is 223 — eight words below the ceiling, not above it. Corrected 2026-08-31: the same script, specification, instruction and band on qwen3.5:35b put cell A in band 11 of 12 against 0 of 12, and showed no fluency-axis length effect at all — 23 of 24 fluent against 23 of 24 terse. The void stands; “unsatisfiable rather than underpowered” was a generalisation from one generator and is withdrawn.

E-002 First measurement of Φ, per probe attacks L5 Void

330 of 330 elicitations returned “yes, we will agree” — the instrument had a default answer, because it ported Keysar & Henly’s granularity and not their forced-choice structure. The transfer was also perfect, 0 of 33 probes diverging, so there was nothing for a belief to be wrong about. This row said “Ablation ladder · Planned” until 2026-08-19, because the founding roadmap gave E-002 to the ladder and the identifier was later reused. The ladder is now E-006.

E-002b Φ ladder attacks L5 Findings

Four cost rungs, 24 briefs. Produced the first Φ measurements on this instrument and a headline pull-quote that was later withdrawn as retraction 12.

E-002c Calibration slope β attacks L5 Findings

Is confidence responsive to transfer at all? Measured β = −0.02 for the sender and +0.28 for the receiver against 1 for calibration, and supplied the outcome-variation gate of three that every later probe measure is costed against.

E-003 Asymmetry matrix attacks L2 Planned

Fidelity measured over a grid of sender/receiver pairs, in both directions. Needs multiple model families to be interesting. Blocked on the instrument, 2026-08-20: the asymmetry there is reason to expect between the two local models is about 0.219. MERIDIAN-IX32 resolves 0.638 — its 32 probes are about nine independent prompt templates. Powered 2026-08-20, still not testable. RIVERSIDE-30, measured directly for the first time, returns 10.00 diverged of 30 and its divergence is probe-attributable, so pairing buys ~~×2.58~~ ×2.46 for gpt-oss and ×1.80 for qwen, an MDE of ~~0.128~~ 0.135–0.183 depending on the reader — corrected 2026-09-08, the single figure was one reader's, and the 0.219 beside it is an effect derived on MERIDIAN, so a threshold from one measure was standing next to an effect from another. But power was never the only blocker: L2's sharper form needs a pair where domain prior and general capability point in opposite directions, and qwen is stronger or level on both domains. Measuring only that an asymmetry exists is retraction 5. ~~Blocked on model selection.~~ Measured 2026-09-06: a third lineage was added — llama3.3:70b — and it is uniformly weaker, 0.824 and 0.467 against 1.000 and 0.967 — each model at its own default with the think field omitted, which is default-versus-default and not a matched regime, since llama3.3 has no reasoning mode at all. The sign does not flip, so there is no crossover to find. It fails ~~E-004's 0.90 subject gate~~ the > 0.90 sender-accuracy-vs-key gate registered in E-001b, E-001c, E-002b and E-002c — not E-004's, which is 0.60 and which llama3.3 passes on MERIDIAN-34 (retraction 21). And it was not the first model asked. E-004 measured claude-opus-4-8 on 2026-08-03 against the identical RIVERSIDE-30 hash at 0.733 against gpt-oss's 0.967, and 0.909 against 1.000 on MERIDIAN-33 — negative on both, no crossover, a month before the question was posed as open (retraction 20). Blocked on domain selection — both domains are the same task type, which is a probe measure and a month, not a download. The instrument itself held up on a second reader (2026-08-28): qwen diverges 9.67 of 30 on RIVERSIDE-30 and lands on the same probes, Jaccard 0.654 against a ≥ 0.4 predicted beforehand.

E-004 Disagreement detector attacks L4 Void

Whether a model can predict where another model will disagree, without a key. Void: two of the three registered models were never wrong — 1 error and 0 errors across the whole design — and a detector of disagreement needs disagreement to detect. This row said “Chain decay · Planned” until 2026-08-19, the same identifier reuse as E-002 above. The chain is now E-007.

E-006 Ablation ladder attacks L1 Void

Void before collection, 2026-08-20, at zero model calls. One message truncated at eight cost levels, with the resulting F*(C) curve fitted. Its own pre-registered power gate refused the run: power 0.117 against a moderately concave truth on 32 probes. L1's concavity limb needs about 512 probes; the largest measure this programme owns has 34. Not that L1 has not been tried — that no probe measure here can carry the test. Was E-002 in the founding roadmap; renumbered 2026-08-19 after that identifier was reused.

E-007 Chain decay attacks L4 Planned

A telephone chain of six hops, content tagged by form, per-hop fidelity measured against the origin — to test whether constraints outlast descriptions. Was E-004 in the founding roadmap; renumbered for the same reason. Blocked on the instrument, 2026-08-20: L4c is a difference between two classes of probe, so the split halves each n — at most ~16 per class, resolving 0.479.

E-005+ Protocol validation NHP-0001 Unscheduled

NHP-0001 is a draft handoff format that carries a fidelity claim. Its unsolved problem is named in the draft itself: the protocol asks the sender to write its own exam.

The first live run of E-001 was recorded as void rather than discarded, and produced a finding that outlives the experiment: a measurement instrument can be blocked by the safety behaviour of the system it measures, and the block can be silent, asymmetric, and shaped like a result. Any evaluation that varies prompt style across conditions is also varying classifier surface across conditions. Refusals must be treated as missing data, never as a zero.

§7 Standing Principia Noophorica §7 and §10 — what would falsify the programme.

Version 0.5. One pre-registered result is now established. Twenty-one of our own claims are withdrawn and five experiments are void.

Every one of them, with what killed it → A count nobody can audit is worse than no count.

Six conjectural laws, fifteen open problems, four completed runs — and one pre-registered finding. Two produced only corrections to our own instrument, one was voided by its own gate after it had collected everything, and the finding is E-002c. Every other claim in this programme should be read as a bet, and its confidence calibrated accordingly.

A science that cannot lose is not a science. Noophorics is wrong if:

1F* is not stable under probe resampling. If independently drawn probe measures over the same nominal domain give uncorrelated fidelity scores, the quantity is noise. — the most dangerous of the four.
2Both bias and resolution are consistently ≈ 0. Φ on its own is a bias term, and bias and resolution are independent: a party that claims 0.70 on every probe and averages 0.70 has Φ = 0 and no ability whatsoever to say which probes it got wrong. That party is maximally pathological, and the one-term criterion would have scored it as the refutation of the programme. The field falls only if parties are unbiased and discriminating per probe. — corrected 2026-07-29; the one-term form is withdrawn claim 4.
3K(C) ≈ 1 at bounded cost, on held-out probes. If messages of bounded length reliably close the gap between arbitrary systems on probes the sender never saw, the restated A3 is false and the interesting structure disappears. — corrected v0.3. The old wording estimated K as the best fidelity found over a search; that is the maximum of noisy estimates, biased upward, and would have fired from search size alone.
4No encoding beats any other at equal cost. If η is invariant to message form, there is nothing to engineer and the field is descriptive at best.

The method is the only part of this that is not negotiable. Every experiment pre-registers before data exists. Every number carries its probe measure, sample count, and noise floor. Refuted laws are struck through, never deleted. Where a bound is claimed, an adversarial attempt to violate it is expected in the same commit.

The name takes the noo- root from νόος and disclaims any inheritance from Vernadsky's or Teilhard's noosphere. Nothing in this programme is mystical. Everything in it is supposed to have a number attached, or be deleted.

What stands

One item. It is here because the sentence above it used to read “nothing is established”, and that stopped being true on 2026-08-02.

Confidence responds to transfer at about an eighth of the rate calibration requires — and the sender’s does not respond at all. β pooled +0.13, interval [+0.05, +0.22]; sender −0.02 spanning zero, receiver +0.28 clear of it. Four hypotheses registered before the data existed, six gates passed, 24 briefs, 28 512 model calls. One model in both roles, one probe measure, one domain — which is exactly as far as it generalises. FINDINGS

What we have refuted, in our own work

The programme's only completed results are negative and about itself. Each is recorded where it was made, with the counterexample, rather than edited away:

F* rewards replicating the sender's errors. Both receivers out-decided the sender; fidelity ranked them the other way. FINDINGS
Axiom A3 was false as first stated. A 113-token lookup table over a visible probe measure reaches F* = 1. PRINCIPIA §4
The v0.1 noise floor was inflated ~51%. Found by validating the estimator against a known ground truth — a check that did not exist until it was needed. validation
Our own repair for a one-sided result failed the same way. E-004 was registered to fix an observation made unusable because one model never erred. It ran three models over two domains and voided on the same gate: this time qwen3.5:35b answered all 63 probes correctly and gpt-oss:120b missed one. The detector scored perfect recall and perfect precision on every pair — what a design looks like when the thing detected and the thing detecting are the same event. VOID
“Confidence is very nearly unresponsive” was too strong. Our own post-hoc reading of E-002b, superseded by the pre-registered run above: the effect is real but small, not absent, and it is the sender that is inert. E-002b §6
L2 was a tautology and L4 was ill-typed. Two antinoophors composed to a positive fidelity. laws
Our own first live run was void, and the near miss is the most useful thing in the notebook. lab journal

The correct response to this is not agreement. It is a probe.

Start here

Language summaries