# Acoustic Incident Reconstruction Standard (AIRS)

**Physics-Bound Reconstruction from  
Unsynchronized Consumer Sensors**

---

## 0. Status and Intended Use

AIRS defines a repeatable and auditable method  
to reconstruct event timing and relative geometry  
from multiple independent recordings.

Recordings may include audio and optional video  
captured on unsynchronized consumer devices.

AIRS is designed for forensic and incident analysis  
where claims must be bounded by physics  
and supported by reproducible logs.

AIRS does **not** guarantee identification,  
intent, or causality.

All conclusions are conditional,  
include confidence bounds,  
and define explicit failure conditions.

---

## 1. Definitions

**Observer**  
A recording device  
(phone, camera, dashcam, recorder)  
providing audio and optional video.

**Incident**  
A bounded time interval  
containing one or more events of interest.

**Event**  
An acoustically observable transient  
(impulse, crack, thud, shout, gunshot, collision)  
or a defined acoustic pattern.

**Direct Arrival Candidate (DAC)**  
A segment believed to represent  
the first arrival path,  
not a reflection.

**Offset**  
A constant time shift  
between an observer clock  
and a reference.

**Drift**  
A time-varying clock error,  
typically linear over short windows.

**Phase Wrapping**  
Ambiguity introduced by integer cycles  
in phase-based measurements.

**Constraint Closure**  
The condition where all observers  
admit a single globally consistent solution.

---

## 2. Scope and Preconditions

### 2.1 Required

- Two or more independent observers  
  (three or more recommended for strong closure)
- Access to original files when possible  
  (avoid re-exports)
- Documented chain-of-custody metadata  
  for each file

### 2.2 Optional but Recommended

- Video for frame-anchored timing  
  and corroboration
- Estimated sensor locations or constraints  
  (e.g., “within 5 m of dugout”)

### 2.3 Exclusions

AIRS does not apply when recordings are known  
to be time-warped, heavily edited, or synthesized  
in ways that prevent reproducible measurement.

Such transformations may only be used  
if explicitly modeled and validated.

---

## 3. Evidence Handling and Chain of Custody

### 3.1 Acquisition

For each file, record:

- Source device and model (if known)
- Acquisition method  
  (direct export, messaging app, social download)
- File hash (SHA-256)
- Container and codec details
- Sample rate and bit depth
- Creation and modification timestamps  
  (not assumed reliable)

### 3.2 Preservation

- Store originals as read-only
- Perform analysis only on copies
- Maintain a run log mapping  
  derived artifacts back to source hashes

---

## 4. Data Preparation

### 4.1 Normalization (Non-Destructive)

- Decode to a standard analysis format  
  (e.g., WAV / PCM)  
  without resampling when feasible
- If resampling is required:
  - log the method and parameters
  - retain pre- and post-hashes

### 4.2 Quality Checks

Document the presence of:

- Clipping
- Automatic gain control artifacts
- Compression artifacts  
  (e.g., smeared transients)
- Dropouts and discontinuities
- Audio/video desynchronization (A/V offset)

---

## 5. Event Selection and Annotation

### 5.1 Event Candidate Identification

Identify potential event windows using:

- Transient detectors  
  (energy rise, spectral flux)
- Manual review for corroboration
- Video cues  
  (impact frame, muzzle flash, gesture)

### 5.2 Direct Arrival Candidate (DAC) Criteria

A segment qualifies as a DAC when:

- Onset is sharp relative to reverberation
- Timing is stable under small bandpass changes
- Cross-observer alignment is plausible  
  under speed-of-sound bounds

If a DAC cannot be established:

- Mark the event as **non-resolvable**, or
- Switch to a reflection-aware model  
  with increased uncertainty

---

## 6. Observer Clock Model

For each observer *i*:

Local time (tᵢ) relates to reference time (t) as:

```
local time = offset + (drift × reference time)

tᵢ = aᵢ + bᵢ · t
```

Where:

- aᵢ is the clock offset  
  (constant time shift)
- bᵢ is the clock drift factor  
  (approximately 1 over short windows)

AIRS requires estimating or bounding  
offset and drift values.

Timestamps must not be assumed correct.

---

## 7. Measurement Model

### 7.1 Timing Measurements

For each event *e* and observer *i*, measure:

- Estimated arrival time at observer *i*
- Associated timing uncertainty
- Measurement method used  
  (cross-correlation, onset detector,  
  matched filter)

### 7.2 Phase / Cycle Measurements (If Used)

Phase-based inference is permitted only when:

- The analysis frequency band is specified
- Phase is computed consistently  
  across observers
- Integer cycle ambiguity is explicitly modeled:

```
measured phase
= true phase
+ (2π × integer number of cycles)

φᵢ,ₑ = φ*ᵢ,ₑ + 2π · kᵢ,ₑ
kᵢ,ₑ is an integer
```

Phase may improve precision,  
but may not establish absolute distance  
without constraint closure.

---

## 8. Physical Constraints

### 8.1 Propagation Constraint

For an event occurring at location xₑ  
and an observer located at xᵢ:

```
arrival time at observer
= event time
+ (distance from event to observer ÷ speed of sound)

tᵢ,ₑ = tₑ + |xₑ − xᵢ| / c
```

Where:

- c is the speed of sound

AIRS requires bounding the speed of sound  
based on environmental assumptions  
(e.g., temperature and humidity),  
which must be logged.

### 8.2 Cross-Observer Consistency

For any pair of observers *(i, j)*:

```
difference in arrival times
= arrival time at observer i
− arrival time at observer j

Δtᵢⱼ,ₑ = tᵢ,ₑ − tⱼ,ₑ
```

The time difference must be compatible  
with physical geometry  
and the bounded speed of sound.

### 8.3 Closure Requirement

Acceptance requires a solution set including:

- event time
- event location
- observer offsets
- observer drift factors
- integer cycle assignments (if used)

This solution must:

- Minimize residual error
- Satisfy all physical constraints
- Hold across all included observers
- Remain within declared uncertainty bounds

---

## 9. Solver and Hypothesis Testing

### 9.1 Candidate Generation

Generate hypotheses over:

- Event time ordering
- Offset and drift parameters
- Integer cycle assignments (if applicable)
- Feasible geometry regions

### 9.2 Rejection and Falsification

Rejected hypotheses must be logged  
with explicit reasons, such as:

- Violation of speed-of-sound bounds
- Implausible drift requirements
- Incompatible integer cycle assignments
- Residual errors exceeding thresholds

### 9.3 Acceptance Criteria

A solution is admissible only if:

- Residual RMS is below a predefined threshold
- No competing solution with similar residual  
  exists within uncertainty bounds
- Constraint closure holds across:
  - Three or more observers when available
  - Two observers only with elevated uncertainty  
    and explicit limitation

---

## 10. Uncertainty and Reporting

### 10.1 Required Outputs per Event

- Estimated event time  
  with a confidence interval
- Relative arrival ordering with bounds
- Geometry estimates expressed as regions  
  unless point estimates are justified
- Residual distributions per observer
- Sensitivity analysis  
  (effects of speed of sound,  
  drift bounds, and event window selection)

### 10.2 Prohibited Output Styles

- Single-point claims without intervals
- “Exact distance” claims without closure proof
- Conclusory statements about identity or intent

---

## 11. Failure Modes and Non-Convergence

Analysts must report **non-resolvable** when:

- A DAC cannot be established
- Observers are too few or correlated
- Recordings show time-warping or editing  
  not modeled
- Multiple competing solutions remain  
  within tolerance

Non-convergence is a valid outcome  
and must be documented.

---

## 12. Validation Protocol

### 12.1 Reproducibility

An independent analyst must be able to reproduce:

- Decoded analysis files
- Event windows
- Parameter bounds
- Solver outputs

Using only the logged configuration  
and evidence hashes.

### 12.2 Benchmarking

AIRS recommends validation against:

- Synthetic known-geometry impulse sets
- Controlled recordings with measured placements
- Adversarial cases  
  (echoes, AGC, compression, partial edits)

---

## 13. AIRS Conformance Checklist

Minimum conformance requires:

1. Source hashes recorded (SHA-256)
2. Device and acquisition pathway documented
3. Event windows and DAC rationale logged
4. Offset and drift modeled or bounded
5. Speed-of-sound bounds stated
6. Rejected hypotheses logged with reasons
7. Residuals and uncertainty reported
8. Non-resolvable outcomes documented
9. Outputs reproducible from configuration

---

## 14. Standard Deliverables

An AIRS-compliant case package includes:

- Case Summary (1–2 pages)
- Evidence Manifest  
  (hashes, devices, provenance)
- Event Table  
  (times, intervals, uncertainty)
- Method Section  
  (model and parameters)
- Residual and Closure Report  
  (plots and thresholds)
- Rejection Log  
  (failed hypotheses)
- Repro Pack  
  (configs, scripts, deterministic seeds)

---

## 15. Standard Language for Testimony

> “AIRS constrains interpretations of multiple  
> recordings to those consistent with physics  
> and measured uncertainty.  
> Where the recordings do not support  
> a unique reconstruction,  
> AIRS reports non-convergence  
> rather than selecting a preferred narrative.”
