Turn day-1 logs into CFO-ready ledgers and deterministic vendor choices.
Purpose. Provide copy-paste tables, formulas, and tiny reducers so finance/ops can quantify impact without touching product logic. Classical magnitudes remain pristine (phi((m,a)) = m). Alignment stays bounded (|a| < 1), and roll-ups are order-invariant via U += w*atanh(a), W += w, a_pool := tanh( U / max(W, eps_w) ). Defaults: eps_a = 1e-6, eps_w = 1e-12, w := |m|^gamma with gamma = 1, bands unchanged, gate modes "mul" and "u_scale".
N1) KPI lane picks (choose 3–5 per service)
Recommended defaults (dimensionless; bounded after mapping with tanh). Paste any/all into your worksheet.
# Tokens per success (lower is better)
e_tokens := (target_tokens_per_success - observed_tokens_per_success) / max(target_tokens_per_success, eps)
a_tokens := tanh( c * e_tokens )
# Latency p95 (lower is better)
e_latency := (target_p95_ms - observed_p95_ms) / max(target_p95_ms, eps)
a_latency := tanh( c * e_latency )
# Retry rate (lower is better)
e_retry := (target_retry - observed_retry) / max(target_retry, eps)
a_retry := tanh( c * e_retry )
# Acceptance / pass rate (higher is better)
e_pass := (observed_pass - target_pass) / max(target_pass, eps)
a_pass := tanh( c * e_pass )
# Vendor unit cost (lower is better)
e_cost := (target_cost_per_1k - observed_cost_per_1k) / max(target_cost_per_1k, eps)
a_cost := tanh( c * e_cost )
# u-space pool across chosen KPI lanes (choose w_k; often w_k := 1)
U_pool := sum_k w_k * atanh(a_k)
W_pool := sum_k w_k
RSI_pool := tanh( U_pool / max(W_pool, eps_w) )
Notes. Keep Unit and c per KPI as calibrated in Appendix I. Publish chosen KPIs and weights for audit.
N2) ROI formulas (calculator-fast; copy-paste)
# Token reduction (%)
tokens_saved_pct := (baseline_tokens - ssm_tokens) / max(baseline_tokens, eps)
# Latency reduction (%)
lat_saved_pct := (baseline_p95_ms - ssm_p95_ms) / max(baseline_p95_ms, eps)
# Retry reduction (abs and %)
retry_drop := baseline_retry - ssm_retry
retry_drop_pct := retry_drop / max(baseline_retry, eps)
# Unit cost reduction (%)
unit_cost_saved_pct := (baseline_cost_per_1k - ssm_cost_per_1k) / max(baseline_cost_per_1k, eps)
# Net savings (period)
savings_usd := tokens_saved * price_per_token + retry_saves_usd + latency_value_usd
# Publish valuation assumptions; keep them outside SSM-AI math.
# Bounded health index (weekly)
RSI_pool_env := g_week * RSI_pool # or tanh( g_week * atanh(RSI_pool) ) per manifest
# Bands via defaults A++/A+/A0/A-/A--
Guardrails. Do not modify classical KPIs; phi((m,a)) = m holds at all steps. Use RSI_pool_env only for routing and policy.
N3) CFO weekly ledger (tab-separated; paste → Word “Convert Text to Table”, separator = Tabs)
Block A – Vendor A (illustrative)
WEEK: 2025-10-13
SERVICE: search
VENDOR: Vendor A
RSI_pool_env (band): 0.552100 (A+)
Bands A++/A+/A0/A-/A--: 0/3/7/0/0
Tokens total: 812000000
Tokens per success: 320
p95 latency (ms): 310
Retry rate: 0.070000
Cost per 1k: $0.90
Estimated net savings (USD): $182400
knobs_hash: sha256:...
Block B – Vendor B (illustrative)
WEEK: 2025-10-13
SERVICE: search
VENDOR: Vendor B
RSI_pool_env (band): 0.401200 (A0)
Bands A++/A+/A0/A-/A--: 0/2/8/0/0
Tokens total: 890000000
Tokens per success: 355
p95 latency (ms): 345
Retry rate: 0.100000
Cost per 1k: $1.00
Estimated net savings (USD): $0
knobs_hash: sha256:...
Block C – Tools / Vendor A (illustrative)
WEEK: 2025-10-13
SERVICE: tools
VENDOR: Vendor A
RSI_pool_env (band): 0.612500 (A+)
Bands A++/A+/A0/A-/A--: 1/4/5/0/0
Tokens total: 341000000
Tokens per success: 190
p95 latency (ms): 280
Retry rate: 0.060000
Cost per 1k: $0.90
Estimated net savings (USD): $96300
knobs_hash: sha256:...
Block D – Tools / Vendor B (illustrative)
WEEK: 2025-10-13
SERVICE: tools
VENDOR: Vendor B
RSI_pool_env (band): 0.455000 (A0)
Bands A++/A+/A0/A-/A--: 0/3/7/0/0
Tokens total: 377000000
Tokens per success: 215
p95 latency (ms): 312
Retry rate: 0.090000
Cost per 1k: $1.00
Estimated net savings (USD): $0
knobs_hash: sha256:...
Notes. RSI_pool_env is a u-space pool across the chosen KPI lanes, then gated; bands from the manifest. knobs_hash ties rows to the manifest in force that week.
Navigation
Previous: SSM-AI – Appendix M — Interop & Wire Protocol (M7–M10)
Next: SSM-AI – Appendix N — Economics & Rollout Worksheets (N4–N5)
Directory of Pages
SSM-AI — Table of Contents
SHUNYAYA 