Observer Bit Model · Surface vs effective bits

What observers can measure

Observers can fill notebooks with recordable symbols and still learn nothing usable about the secret. Surface bits are not effective bits.

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~7 min overview · ~6 min formalContinue: Unicity distance

Two meanings of “bits”

People casually call both quantities “bits.” Notebook bits are what you can write down from the screen or the network tap. Surface bits are that recordable entropy. Knowledge bits are how much the secret actually shrinks: effective bits, mutual information with the secret. Capture is not compromise when the second stays empty.

Surface bits versus effective bits with observer independence — Observer sees bits, not knowledge
Compare surface bits the observer can record with effective bits about the secret. Independence of the observer from the hidden map keeps I_effective empty even when the notebook is full. Takeaway: seeing the transcript is not learning the secret.

Observer bit budget: H_surface filled versus I_effective at zero — Surface ≠ effective · recordable ≠ informative
Compare the filled surface-entropy meter with the zeroed effective-information meter. Recording can grow H_surface while I_effective about the secret stays empty under the model. Takeaway: recordable bits are not informative bits about the secret.

The Observer Bit Model (Rosario–Wang) formalizes the budget: given challenge C, surface entropy $H_{\mathrm{surface}}$ can be positive while I(secret; observation | C) : the effective quantity: is designed to be zero (notation).

Surface bits are what an observer can record; effective bits are mutual information with the secret, and those are different quantities.ValidatedH_surface ≈ log₂(6) ≈ 2.585 bits per bearing; I_effective is designed to be zero under the Rosario–Wang observer model.

A full recording of the ceremony yields zero effective bits about the secret.ValidatedUniform synonym marginals and one-shot burn keep I(secret ; observation | challenge) = 0; capture is not compromise.Holds under the reference architecture

Parameter table (reference)

Reference architecture parameters used on the public site. They are reference numbers, not sacred constants for every deployment.

Reference observer bit budget parameters
Parameter	Value	Note
$H_{\mathrm{surface}}$ / bearing	$\log_2 \lvert B\rvert = \log_2 6 \approx 2.585$ bits	Observable bearing entropy only (reference model).
$I_{\mathrm{effective}}$	$0$ bits	Mutual information with the secret under the axioms.
Ring sizes (reference)	26 + 26 + 10 = 62 symbols	Disjoint uppercase, lowercase, digit rings.
Zone / bearing cardinality	$\lvert B\rvert = 6$	Six zones, six bearings: reference architecture parameters.

Why surface entropy can be nonzero

Uniform surprise on the channel is not secret leakage. Six equiprobable bearings still produce about 2.585 bits of recordable entropy per character: the notebook fills. That entropy is about which public symbol appeared, not about which secret produced it. Flat marginals are the structural reason; see A flat, unreadable channel.

Computational brute force assumes a searchable residue of the secret in the transcript. Effective-zero means the transcript is not such a residue under the model, even for unbounded search of “what the bits mean.”

Observer Bit Model (Rosario–Wang)

An observer can record a full ceremony (camera, screen capture, network tap) and still learn nothing usable about the secret when uniformity, independence, and empty effective mutual information hold. The public channel carries surface symbols; the private map and hidden state stay off-channel. This page stays information-theoretic: no patent manufacturing steps.

Observer captures transcript bits while hidden knowledge remains zero — Capture is not knowledge
Follow the observer path: a full transcript fills the notebook while the vault for the secret stays closed. Surface bits are recordable; effective mutual information with the secret stays empty under the model. Takeaway: capture of the channel is not knowledge of the secret.

See also (ledger metaphor): Recording without learning. Empty-channel framing: When the channel reveals nothing. Why more archive length still fails to uniquely determine the secret: Why more data doesn't help.

Falsifiability

Absolute $I=0$ holds only under the axioms. What would violate the budget: skewed zones, leaked private map, nonce reuse, correlated sessions that reintroduce redundancy. Those are model-scope failures, not “wait for a bigger computer.”

Formal mathematics and notation

Formal surface vs effective bits

Reference model often quotes surface entropy per bearing near $\log_2 6 \approx 2.585$ bits when |B|=6, while effective mutual information with the secret is designed to be zero:

Surface bits versus effective bits

H_{\mathrm{surface}}(O)>0,\qquad I_{\mathrm{effective}}(X;O\mid C)=0

Read as: The observable surface can contain entropy while effective mutual information with the hidden state is zero.

Arguments

$O$: : observable transcript whose surface symbols can be counted
$X$: : hidden state the surface symbols must not reveal
$C$: : challenge context for the effective leakage measure

Operators

$H$: : surface entropy in the observable transcript
$I$: : effective mutual information with the hidden state
$= 0$: : no secret-relevant leakage despite measurable surface bits

Significance: It distinguishes measurable transcript entropy from information that actually reduces uncertainty about the secret.

Computational contrast: A computational system can leave surface artifacts and rely on recovery cost; this budget separates observable bits from secret-relevant bits.

References:Effective bits

See notation, axioms, and Claims.