Audited witnesses
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Maniflood
Unified category-theoretic audit of the trading pipeline (branches A · B · C)
Categorical Audit
Unified audit · branches A · B · C
The trading pipeline, audited as category theory.
Three independent structural audits run over the same engine: the
tesseract sign-series as a confluent rewrite graph (A), the
adaptive-meta stage as an indexed natural transformation
ηd (B), and the trade ledger as a category with
an associative composition and a monotone sizing functor (C). Each emits falsifiable
witnesses, all reproducible from scripts/categorical_audit_all.py.
Flipped to hold
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Mean score penalty
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Max |Δscore|
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Branch A · Tesseract sign-series
The curvature sign-state series as a rewrite graph, checked for confluence.
Each curvature sample lands on a sign-pattern vertex (e.g. +-+-); consecutive
samples induce directed edges. The audit checks two-path redundancy
(a Church–Rosser / confluence condition): any two rewrite routes between the same
endpoints must agree, so the series has a well-defined terminal state.
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Two-path redundancy: ok — max intermediate count 0, no ambiguous
pairs. The dominant edge +-+- → +-+- fires 95×, i.e. the regime is a
stable fixed point over this window.
Branch B · the categorical model
What objects, morphisms, and indices the audit assigns to the adaptive-meta stage.
The audit changes no trading semantics. It centralizes the adaptive-meta math and exposes falsifiable witnesses for the structural laws below.
Naturality square
For a pipeline morphism f, applying ηd should commute with f.
eta_d( f(s) ) ≈ f( eta_d(s) )
The residual is the commutation error measured on the scalar projections (score, alpha, confidence) plus an action-match flag. Identity morphisms commute exactly; nonlinear pipeline morphisms leave a measured residual, which is exactly what the audit surfaces.
Audited witnesses
Synthetic signal battery checked at drawdown d = 0.25 (from the CLI audit).
| Signal | Fibration monotone | η & identity | η & score-scale | action @ d=0.25 | section flips→hold |
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"commutes" means residual within tolerance (1e-6); "residual" means the morphism is nonlinear enough to leave a measured commutation gap. Hover a cell for its score residual.
Drawdown explorer
Move along the fibration base B and watch ηd re-weight a signal live.
F0(s) · base object
Fd(s) · ηd applied
| d | score penalty ↑ | alpha scale ↓ | score | alpha | action |
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Fibration consistency requires score penalty to be non-decreasing and alpha scale non-increasing along d. A ▲ marks any violation; the math is computed in your browser from the same coefficients as the live engine.
Branch B · pipeline naturality
ηd commuted against the live pipeline morphisms on the curvature base.
| Morphism f | Verdict | |Δscore| | |Δalpha| | |Δconfidence| | action match |
|---|---|---|---|---|---|
| flow-hybrid | residual | 0.0872 | 0.0143 | 0.0403 | yes |
| de Rham | residual | 0.0572 | 0.0109 | 0.0218 | no |
| full pipeline | residual | 0.1129 | 0.0192 | 0.0532 | yes |
These morphisms act on the curvature-realized base, so they are audited once for the pipeline rather than per instrument. The de Rham square breaks action match: at d = 0.25 the adaptive-meta order vs. de Rham order disagree on the discrete action, which is exactly the kind of ordering defect the audit is built to expose.
Branch C · ledger category
Closed trades as composable morphisms on equity, with a sizing functor.
Objects are equity states; each closed trade is a morphism between them, and composing the whole chain must be associative — the realized equity path may not depend on how trades are bracketed. The position-sizing rule is audited as a functor whose multiplier must not jump up after a drawdown.
Prefix multipliers stay flat at 1.0 across all 7 trades and the full-window multiplier is
1.0 (reason: insufficient_closed_trades to scale up), so the sizing functor is
trivially monotone here — conservative by construction on a short ledger.
Why this matters
Structural guarantees that a pile of if-statements cannot give you.
- Confluence (A) proves the regime series has a well-defined terminal state, not a path-dependent mess.
- Monotonicity (B) proves risk-off behavior strengthens with drawdown, never reverses.
- Naturality residuals (B) quantify exactly where adaptive meta and a pipeline stage disagree.
- Associativity and a monotone sizing functor (C) keep the realized equity path bracket-independent.
- Every claim here is reproducible from
scripts/categorical_audit_all.py --branch all --synthetic.