Principle Weighting Notation

Large language models allocate attention roughly proportional to surface area. A 500-word explanation of a formatting preference gets more weight than a 12-word principle that governs the entire system. The model doesn’t know one is load-bearing and the other is decorative.

This creates a specific failure mode: the most important ideas in a context document are often the shortest, and therefore receive the least attention.

A governing principle like “publish methodology, sell execution” is four words. A section explaining table formatting rules might be three hundred. Without explicit weighting, the model treats the three-hundred-word section as seventy-five times more important than the principle that should constrain all decisions.

Decouple importance from word count using gravitational density notation— a compact markup system that tells the model how much mass a passage carries, regardless of its length.

The metaphor is physics: a black hole is tiny relative to the solar system, but everything bends around it. A governing principle should function the same way in a context document. Small. Dense. Everything else orbits it.

3.1Three Components

Every weighted principle has three markers.

[Symbol] G=[value] | [SCOPE] — [Domain]
[The principle itself]

3.2Symbol — Visual Density

3.3G-Value — Gravitational Weight

Explicit numerical rank from 0.1 to 1.0. Tells the model exactly how much this principle should influence surrounding decisions.

3.4Scope Label — Reach

How far the principle extends.

4.1The Problem

Some principles have real mass, but only under specific conditions. A principle that should only activate during the decision stage of a sales conversation, or only when the audience is technical, had to be written as a full standalone principle or left implicit in the Domain label. Both paths leak.

4.2The Notation

[Symbol] G=[value] [WHEN: condition] | [SCOPE] — [Domain]
[The principle itself]

The [WHEN:] marker sits between the G-value and the scope label. It reads as a gate: gravity only activates when the condition is true.

4.3Examples

◼ G=0.9 [WHEN: Stage=Decision] | GOVERNING — Framing
Loss frame only. Experience and potential frames are off the table.

◼ G=1.0 [WHEN: Phase=Handoff] | BEDROCK — Access
Root Admin transfers to client. No exceptions. No retained access.

◆ G=0.7 [WHEN: Audience=Technical] | CONSTRAINING — Explanation
Skip Layer 1 analogies. State architecture directly.

◆ G=0.7 [WHEN: User=Hostile] | CONSTRAINING — Tone
No validation-forward language. No softening. Direct clarification only.

4.4Valid Conditions

Any condition the model can evaluate from the task context:

• [WHEN: Stage=Decision] — buyer journey stage
• [WHEN: Phase=Handoff] — engagement phase
• [WHEN: Audience=Technical] — reader profile
• [WHEN: Task=Drafting] — agent mode
• [WHEN: Channel=Email] — output medium
• [WHEN: User=Hostile] — interaction state

Keep conditions binary or small-enum where possible. [WHEN: Complexity>0.7] is valid but weaker than [WHEN: Task=Analysis], because the model has to infer the threshold.

5.1The Problem

A governing principle should be restated at enforcement points. But restating the full principle mid-document violates Density Inversion — you end up with a G=0.9 principle appearing twice, each time in compact form, followed by a long section that dilutes the echo. What we actually want is a lightweight pointer that re-spikes attention on the already-stated principle without reintroducing mass.

5.2The Notation

[ECHO: ◼ G=[value] Domain]

Placed inline, right before the section where the principle most often gets violated.

## Proposal Generation

[ECHO: ◼ G=0.9 Sales Philosophy — Hormozi transparency]

Generate the proposal now…

5.3Why This Works

The ECHO tag reactivates the already-loaded principle by name, not by restatement. The model has the full principle in context from its original declaration; the ECHO just points at it and says “this principle is live for what comes next.” This is the lowest-cost way to re-spike attention in a long document without double-declaring.

5.4Placement Rule

ECHO immediately before the section where enforcement matters most. Not at the top of the document. Not scattered throughout. Rough cap: no more than one ECHO per 2,000 words of surrounding content, and no more than one ECHO per referenced principle per document. If you’re ECHO-ing the same principle three times, the principle probably needs to be weighted higher or the document needs to be shorter.

6.1The Problem

The hierarchy handles different-G conflicts cleanly: higher G overrides lower. But when two principles at the same weight class give contradictory guidance, the spec is silent. In practice the model averages them out, which tends to produce mediocre hybrid output rather than strong adherence to either.

Example: ◆ G=0.7 | CONSTRAINING — Voice says plain declarative sentences, no hedging. ◆ G=0.7 | CONSTRAINING — Format says use comparison tables when evaluating three or more options. The task is evaluating four vendors. Voice wants prose. Format wants a table. Both are G=0.7.

6.2The Resolution Rule

“

Narrowest scope wins.

When two principles at the same G-value collide, the one whose scope most directly governs the immediate task takes precedence. Specificity beats generality.

In the vendor-evaluation example, Format governs “evaluating three or more options” — the exact task at hand. Voice governs all outputs. Format is narrower, so Format wins: the output is a table. Voice constrains everything inside the table cells (plain declarative, no hedging) but doesn’t override the table itself.

6.3Declaring Scope Narrowness

Scope narrowness is inferred from the Domain label and the activation condition. Two heuristics for the model and for the engineer reviewing the principle:

• Principles with [WHEN:] conditions are narrower than unconditional principles at the same weight, because they only apply in specific states.
• Principles whose Domain matches the immediate task name are narrower than principles whose Domain is categorical. Voice, Framing, Tone, Format apply broadly; Proposal-Generation, Vendor-Comparison, Cold-Email apply narrowly.

If scope narrowness is genuinely ambiguous, the collision is a design smell. Raise one principle to G=0.8 or drop one to G=0.5 — don’t leave two truly equivalent constraints in conflict.

7.1Bedrock Principles

◼ G=1.0 | BEDROCK — Identity
The Ownership Flip: capability AND autonomy. Build it, hand over the keys, leave.
The system gets better because it's theirs.

◼ G=1.0 | BEDROCK — Platform
Google-native only. No hybrid Microsoft environments. No exceptions.

◼ G=1.0 | BEDROCK — Role
You are the Architect. You are not the General Contractor.

7.2Governing Principles

◼ G=0.9 | GOVERNING — Sales Philosophy
Hormozi transparency model: publish the methodology, sell the execution.
Alchemease delta: Layer 1 is free. Layer 3 is the moat.

◼ G=0.9 | GOVERNING — Content
Editorial filter: Clear, Useful, Yours.
Every content piece passes all three or it doesn't ship.

◼ G=0.9 [WHEN: Stage=Decision] | GOVERNING — Framing
Loss frame only. Match frame to buyer stage in all other cases.

7.3Constraining Rules

◆ G=0.7 | CONSTRAINING — Voice
Flinch Test: if a 15-year veteran in this field would flinch reading this sentence, rewrite it.

◆ G=0.7 | CONSTRAINING — Language
AI is a system, not a tool. Never call it a "tool" in participant-facing content.

◆ G=0.7 [WHEN: Audience=Technical] | CONSTRAINING — Framing
Skip Layer 1 explanations. State architecture directly.

7.4ECHO in a Long Document

## Proposal Generation Section

[ECHO: ◼ G=0.9 Sales Philosophy]
[ECHO: ◼ G=0.9 Pricing — Bottom line is top line]

Generate the proposal for the three-vendor evaluation…

8.1The Physics Analogy

In gravitational systems, mass determines influence regardless of volume. A neutron star is smaller than Earth but bends spacetime around it. A gas cloud can be enormous but exerts almost no gravitational pull.

Context documents work the same way. A 12-word governing principle with G=1.0 should bend all surrounding decisions. A 400-word formatting guide with G=0.3 should influence style but yield to any higher-G constraint.

The notation makes this explicit. Without it, the model treats the document as flat — every word gets roughly equal attention. With it, the model has a density map.

8.2Concept Pointer Activation — The Load-Bearing Mechanism

The deeper reason this notation works: LLMs already have the concepts in their weights. When you write “Hormozi transparency model,” you’re not teaching the model what that means — you’re activating everything it already knows about it. The notation tells the model how much that activated concept should influence the current task.

This means the actual instruction content can be extremely compact. Name the concept. Specify the company-specific delta. Weight it. Done.

◼ G=0.9 | GOVERNING — Sales Philosophy
Hormozi transparency model.
Alchemease delta: Layer 1 free, Layer 3 is the moat.

Twenty-eight words total. The model fills in everything between the named concept and the specific delta from its own training. The G-value tells it this governs all downstream decisions.

8.3A Note on Mechanism Claims

It is tempting to describe this system in terms of attention matrices, softmax weights, and vector clusters. Those descriptions make the framework sound more mechanistic than it actually is. The honest mechanism is simpler and better-supported: named concepts activate trained priors, explicit ranking resolves ambiguity, and compact notation respects the tokens-per-instruction budget that bloated prose violates. Everything beyond that is metaphor.

9.1Where to Use This

9.2Placement Rules

• Highest G-values go first. The model sees them before anything else.
• Group by weight class. Bedrock together, governing together, preferences together.
• No more than 3–5 bedrock principles. If everything is G=1.0, nothing is.
• ECHO governing principles at enforcement points. Not full restatement.
• Lower-G items can be longer. Preferences and structural defaults can include examples and explanation. Bedrock should be terse. Density increases with importance.
• Conditional principles group with their weight class. The [WHEN:] gates activation, not weight.

9.3The Density Inversion Rule

“

The higher the G-value, the fewer words it should use.

This is counterintuitive but critical. Bedrock principles should be the shortest statements in the document. Preferences can be verbose. The notation handles the importance signaling — the words handle the content. Don’t let a G=1.0 principle bloat into a paragraph.

◼ G=1.0 | BEDROCK — Client owns Root Admin. No exceptions.

◼ G=1.0 | BEDROCK — We believe that at the end of every engagement,
the client should receive full Root Admin access to their infrastructure,
including all passwords, recovery keys, and administrative credentials,
because we believe in the principle of ownership transfer and do not
want to create dependency through access control…

The first version is dense. The second is a gas cloud with a G=1.0 label on it. The notation can’t fix bloat — it can only rank compact principles correctly.

Three expansions were proposed during review. All three are documented here so future reviewers (human or agent) don’t reintroduce them without new evidence.

11.1Rejected: Negative Gravity Notation

The proposal: Add a repulsor symbol and negative G-values to express prohibitions as mathematical “push-away” forces, on the logic that LLMs struggle with negative constraints.

Why rejected. The existing framework already handles prohibitions at bedrock weight through phrasing: ◼ G=1.0 | BEDROCK — Google-native only. No hybrid Microsoft environments. No exceptions. That reads as a prohibition without needing a separate notation. More importantly, the proposed use case (word-level blocklists like “never use ‘delve’”) risks backfire — injecting forbidden tokens into context with a “do not use these” flag reliably raises the probability of the model producing them. Positive reframing (“use precise Anglo-Saxon verbs”) outperforms negative lists in controlled tests. Adding mathematical weight to negation doesn’t fix this — it may amplify it.

Revisit if: Testing surfaces a specific prohibition that the current notation genuinely cannot express, and positive reframing of that prohibition fails in measurement. Both conditions required.

11.2Rejected: Total Mass Budget

The proposal: Cap total G-mass per context document at a fixed number (e.g., 15.0) to prevent “instruction collapse” from too many high-weight principles.

Why rejected. The existing bedrock cap of 3–5 principles addresses the real failure mode without requiring a total-mass calculation. The proposed number (15.0) is not derived from measurement of any model’s actual instruction-following degradation curve. Adding a made-up budget on top of a working rule is pseudo-rigor. And total mass calculation adds engineer overhead every time a new principle is introduced, which either gets performed mechanically (friction) or ignored (defeating the point).

Revisit if: Measurement establishes a specific instruction-count or total-weight threshold beyond which adherence degrades for a defined model class.

11.3Rejected: Meta-Primer Preamble

The proposal: Inject a ~40-word preamble at the top of every system prompt explicitly instructing the model to “activate GCD parsing behavior.”

Why rejected. Models don’t have a GCD switch; they interpret notation through concept-pointer activation and attention allocation regardless of whether the preamble is present. The Quick Reference Card already serves this function — when it is loaded with the weighted principles, the decoder travels with the symbols. And adding a preamble violates Density Inversion at the document level: 40 words of meta-instruction at the top cost attention budget that higher-G principles should be claiming.

Revisit if: Side-by-side testing shows the preamble produces measurable adherence gains on identical weighted-principle documents.

The whole notation is an answer to a single observation about how models read: they read by volume, and volume is not mass. A governing principle is small on purpose, because the work it does is done inside the reader, not on the page. Prose that bloats a principle to match its importance has already lost — the bloat trains the model to read it as typical content, and it responds accordingly.

The fix is not to write more. It is to mark what matters, so the reader can treat a neutron star as a neutron star and a gas cloud as a gas cloud. Four words, weighted, will outlast four hundred words that drift. That is the whole trick. Everything above is just the syntax.