An open format specification for structured LLM prompts, grounded in the Nyquist-Shannon sampling theorem.
A raw LLM prompt is a continuous signal on the specification axis. Like any bandlimited signal, it can be perfectly reconstructed from discrete samples taken at or above the Nyquist rate. The sinc-prompt format defines exactly 6 frequency bands that must be sampled. Omitting any band is undersampling — the prompt-space equivalent of aliasing, which manifests as hallucination, drift, and instruction loss.
| n | Band | Zone | Weight | Description |
|---|---|---|---|---|
| 0 | PERSONA |
Z1 | 7.0% | Who should answer. The expert identity. Gates the amplitude term via G(Z1): binary presence function, smoothly transitions 0→1 between 2-5 tokens. |
| 1 | CONTEXT |
Z2 | 6.3% | Situation, background, facts, dates. Feeds the Hill function H(Z2) which peaks at 94 tokens—too little starves the model, too much causes spectral leakage. |
| 2 | DATA |
Z2 | 3.8% | Specific inputs, metrics, data points. Combined with CONTEXT into zone Z2 for the Hill function. |
| 3 | CONSTRAINTS |
Z3 | 42.7% | Rules, MUST/NEVER directives, boundaries. The dominant band. Drives the ramp function R(Z3): zero below 37 tokens, linear growth at 3% per token above threshold, saturating at 1.0. Must be the longest fragment. |
| 4 | FORMAT |
Z4 | 26.3% | Output structure specification. Gates the amplitude term via G(Z4): binary presence function identical to Z1. |
| 5 | TASK |
Z3 | 2.8% | The objective. Clear imperative. Combined with CONSTRAINTS into zone Z3 for the ramp function. |
The Signal-to-Noise Ratio quantifies prompt reconstruction quality:
| Function | Zone | Definition | Behavior |
|---|---|---|---|
G(x) |
Z1, Z4 | clamp((x, 2) / 3, 0, 1) |
Binary gate. Absent below 2 tokens, fully present above 5. |
H(z) |
Z2 | (z/94)^4.56 / (1+(z/94)^4.56) * exp(-1.36e-5*(z-94)^2) |
Hill function. Peaks at 94 tokens, sigmoidal rise, Gaussian decay. |
R(z) |
Z3 | clamp(0.03 * max(0, z, 37), 0, 1) |
Ramp. Zero below 37 tokens, +3% per token, saturates at 1.0. |
SNR range: 0.588 (floor, raw unstructured prompt) to 0.855 (ceiling, all zones optimally filled). Grades: EXCELLENT (≥0.80), GOOD (≥0.70), ADEQUATE (≥0.65), ALIASED (≥0.60), CRITICAL (<0.60).
The Nyquist-Shannon sampling theorem states that a bandlimited signal can be perfectly reconstructed from samples taken at twice the highest frequency component. An LLM prompt carries information across 6 identifiable frequency bands on the specification axis — from the low-frequency persona identity to the high-frequency task directive. A raw, unstructured prompt is a single sample of this 6-band signal: a 6:1 undersampling ratio that guarantees aliasing. In prompt space, aliasing manifests as hallucination (the model fabricates missing band content), instruction drift (constraints leak into other bands), and format collapse (output structure is unspecified). The sinc-prompt format eliminates aliasing by requiring exactly one sample per band — the minimum sampling rate for faithful reconstruction. The multiplicative SNR model confirms this: zeroing any gate function (G or R) collapses the amplitude term to zero, reducing the prompt to its 0.588 noise floor regardless of how well-specified the other bands are.
{
"formula": "x(t) = Sigma x(nT) * sinc((t - nT) / T)",
"T": "specification-axis",
"fragments": [
{"n": 0, "t": "PERSONA", "x": "..."},
{"n": 1, "t": "CONTEXT", "x": "..."},
{"n": 2, "t": "DATA", "x": "..."},
{"n": 3, "t": "CONSTRAINTS", "x": "... (longest fragment)"},
{"n": 4, "t": "FORMAT", "x": "..."},
{"n": 5, "t": "TASK", "x": "..."}
]
}
| Field | Type | Description |
|---|---|---|
formula | string | The sinc reconstruction formula. |
T | string | Sampling axis identifier. |
fragments | array | Array of 6 fragment objects (7 with optional TASK_ARCHIVED). |
fragments[].n | integer 0-5 | Band index. |
fragments[].t | string enum | Band name: PERSONA, CONTEXT, DATA, CONSTRAINTS, FORMAT, or TASK. |
fragments[].x | string (non-empty) | Band content. |
{
"formula": "x(t) = Sigma x(nT) * sinc((t - nT) / T)",
"T": "specification-axis",
"fragments": [
{
"n": 0,
"t": "PERSONA",
"x": "You are a senior fintech compliance analyst with 10 years of experience in payment processing regulations across EU and US jurisdictions."
},
{
"n": 1,
"t": "CONTEXT",
"x": "PSD2 Strong Customer Authentication enforcement began September 2019 in the EU. The US has no equivalent federal mandate but NACHA updated ACH rules in March 2024. Our platform processes 2.3M transactions/month across both regions."
},
{
"n": 2,
"t": "DATA",
"x": "Current SCA exemption rate: 34%. Transaction decline rate post-SCA: 12.7%. Average transaction value: EUR 47.20. TRA threshold: EUR 500. Low-value threshold: EUR 30."
},
{
"n": 3,
"t": "CONSTRAINTS",
"x": "State facts directly -- never hedge with 'I think', 'probably', 'might'. Use exact regulatory article numbers for every claim (e.g., PSD2 Article 97(1)(c)). Never conflate EU and US requirements in the same paragraph. Always specify which jurisdiction a rule applies to. Must include effective dates for every regulation cited. Never recommend a compliance approach without citing the specific exemption clause. Always quantify financial impact using the provided transaction data. Do not speculate on future regulatory changes -- state only enacted rules."
},
{
"n": 4,
"t": "FORMAT",
"x": "Lead with a 3-row summary table: Requirement | EU (PSD2) | US (NACHA). Then structured sections with H2 headers per topic. Numbered lists for action items. Code blocks for any API payload examples. No parenthetical asides. No trailing summary."
},
{
"n": 5,
"t": "TASK",
"x": "Produce a compliance gap analysis comparing our current SCA implementation against PSD2 RTS requirements and NACHA 2024 ACH rules. Identify the top 5 gaps ranked by financial risk using our transaction data."
}
]
}