When Computation Succeeds but Reliance Quietly Breaks
Post-Hoc Diagnostics for Stability Erosion
Deterministic • Observation-Only • Exact Classical Preservation • Canonical Evidence
For decades, computation has been trusted the moment it produces an answer.
If a solver converges,
if an ODE integrates,
if a linear system returns a solution —
we assume the execution is safe to rely on.
But real systems reveal a sharper truth:
Many computations “work” while structural stability is already eroding.
They succeed numerically, yet become fragile, non-repeatable, or dangerously sensitive to small shifts in inputs, ordering, precision, or runtime conditions.
Classical mathematics does not label that erosion.
SSD exists to reveal it.
🔍 What Is Shunyaya Structural Diagnosis (SSD)?
SSD is a deterministic, trace-based framework for post-hoc structural diagnosis of real executions.
It answers a question classical computation never asks:
Not: “Did the computation return a value?”
But: “How safely did it return that value — and what stability debt accumulated along the way?”
SSD does not replace solvers.
SSD does not tune parameters.
SSD does not reroute computation.
SSD does not change numerical outcomes.
SSD observes traces — then explains reliance risk.
🧱 Core Principle — Diagnose Without Touching the Result
SSD treats an execution as a sequence of structural states derived from recorded traces.
It enforces the non-negotiable collapse invariant:
phi((m, a, s)) = m
Where:
m— classical magnitude (exact, unchanged)a— alignment posture observed from trace behaviors— accumulated structural pressure and reliance strain
No matter what SSD detects, the classical result remains untouched.
Truth is preserved.
Reliance becomes visible.
🧭 What SSD Reveals (That Classical Output Cannot)
SSD makes hidden stability conditions explicit:
- Drift corridors — safe, boundary, unstable, undefined regimes
- Regime mixing — alternating safe/unsafe behavior while still “working”
- Structural pressure — accumulation that predicts fragility before failure
- Early warning — how soon erosion becomes measurable
- Explainable attribution — which trace behaviors drive instability
In short:
Same answer.
Different safety.
SSD separates:
“It works.”
from
“It works safely and repeatably.”
🧪 Proof by Execution — Completed, Reproducible Case Series
SSD is validated through executable, deterministic proof cases:
🧩 Case 1 — Nonlinear Solver (MGH17)
- Detects mixed vs stable regimes
- Attributes drift without solver failure
📐 Case 2 — Calculus Corridor Diagnostics
- Identifies safe, boundary, undefined corridors
- Distinguishes denial vs abstention without intervention
🧮 Case 3 — Linear System Conditioning
- Reveals pressure accumulation before numerical breakdown
- Abstains under singular regimes with clear attribution
⏱ Case 4 — ODE Time-Evolution Erosion
- Diagnoses time-accumulated structural fatigue
- Flags denial during continued computation
All cases are:
- deterministic
- offline
- audit-ready
- reproducible under identical traces
📄 Canonical Evidence Model (Citation-Ready)
SSD is built to be reviewable, not just runnable.
It produces authoritative artifacts:
- Diagnostic ground truth:
ssd_report.json/.txt - Canonical evidence: SVG snapshots under
ssd_out_*(stable, citation-ready)
Optional visuals (for example, Matplotlib PNGs) are explicitly treated as non-evidence reference outputs.
Evidence hierarchy is explicit.
Claims are inspectable.
🔒 Guarantees (Non-Negotiable)
SSD is strict by construction:
- Deterministic
- Post-hoc only
- Non-invasive
- Observation-only
- Collapse-safe (
phi((m, a, s)) = m) - Explainable drift attribution
- Audit-ready and citation-ready
No learning.
No heuristics.
No approximation.
No guesswork.
🧩 Where SSD Fits in the Shunyaya Framework
Shunyaya is a conservative extension stack — each layer answers a different question while preserving exact classical meaning.
🟦 SSOM — Origin Layer
Is this construction structurally fit to exist at origin?
🟩 SSM — Posture Layer
Is the value centered or drifting, without changing it?
🟨 SSUM — Runtime Structure Layer
How does structure evolve during motion or iteration?
🟥 SSD — Diagnostic Layer
Where is stability eroding, and how early can we see it?
🟪 SSE — Trust Governance Layer
Should this mathematically correct result be relied upon here at all?
All layers preserve classical truth under collapse.
🌍 Why SSD Matters
Most failures do not arrive as explosions.
They arrive as:
- silent fragility
- loss of repeatability
- reliance drift
- corridor edge behavior
- unstable regimes that still return answers
SSD makes these visible early — without interfering.
That is the shift:
From output-only truth
to reliance-aware truth.
🔗 Repository & Source
Shunyaya Structural Diagnosis (SSD)
https://github.com/OMPSHUNYAYA/Structural-Diagnosis
Master Index — Shunyaya Framework
https://github.com/OMPSHUNYAYA/Shunyaya-Symbolic-Mathematics-Master-Docs
📜 License
Creative Commons Attribution 4.0 (CC BY 4.0)
Attribution:
Shunyaya Structural Diagnosis (SSD)
Provided “as is”, without warranty of any kind.
🏁 Closing Thought
Classical computation tells you what answer you got.
SSD tells you what that answer cost in stability — and whether reliance is quietly breaking.
Deterministic.
Explainable.
Audit-ready.
Classically exact.
SSD does not challenge computation.
It completes the story of reliability.
OMP
SHUNYAYA 