From 72d77d0239b0a5e3c8db1f2e6c899d06a4bceb91 Mon Sep 17 00:00:00 2001 From: Erin Spencer Date: Sat, 1 Aug 2026 22:11:55 -0700 Subject: [PATCH 1/2] Add complete EDCM mathematical reference --- CANON.md | 16 +- MANIFEST.in | 1 + README.md | 7 + docs/EDCM_MATHEMATICS.md | 982 +++++++++++++++++++++++++++++++++++++++ 4 files changed, 1005 insertions(+), 1 deletion(-) create mode 100644 MANIFEST.in create mode 100644 docs/EDCM_MATHEMATICS.md diff --git a/CANON.md b/CANON.md index bbfd037..802b703 100644 --- a/CANON.md +++ b/CANON.md @@ -88,6 +88,20 @@ standing: historical maintained baseline, not joint canon Its marker canon, parser, eleven-component round vector, and circuit recurrence remain available for comparison. Existing integrity gates preserve its identity; they do not confer empirical validity. +## Compiled mathematical reference + +[`docs/EDCM_MATHEMATICS.md`](docs/EDCM_MATHEMATICS.md) is the complete +human-readable index of the mathematics currently declared or implemented in +this repository. It records the maintained baseline equations, auxiliary risks, +agent-facing projections, signed-ternary construction, experiment candidates, +identity functions, and explicit mathematical absences. + +The reference is a synchronized copy, not a separate authority and not a canon +selection. The owning source modules and frozen data remain implementation +authority; this file governs their epistemic status. The Interdependent Way +textbook or website may reproduce a commit-pinned copy but may not silently +redefine the equations or promote candidates. + ## Experiment rules Every joint experiment must record: @@ -168,4 +182,4 @@ Every report is research evidence. No report is a canon file, and no report may ## hmmm -External holdout custody, independently authored graph annotations, human outcome labels, multilingual evidence, separate implementation replication, and the authority procedure for the first joint canon selection remain open. \ No newline at end of file +External holdout custody, independently authored graph annotations, human outcome labels, multilingual evidence, separate implementation replication, and the authority procedure for the first joint canon selection remain open. diff --git a/MANIFEST.in b/MANIFEST.in new file mode 100644 index 0000000..67e2c1f --- /dev/null +++ b/MANIFEST.in @@ -0,0 +1 @@ +include docs/EDCM_MATHEMATICS.md diff --git a/README.md b/README.md index 02ee55c..7cb2ab3 100644 --- a/README.md +++ b/README.md @@ -34,6 +34,13 @@ NA -> 0: false See [`CANON.md`](CANON.md) and [`docs/UCNS_EDCM_EXPERIMENT_PROGRAM.md`](docs/UCNS_EDCM_EXPERIMENT_PROGRAM.md). +The complete compiled mathematics currently declared or implemented by EDCM +is indexed in [`docs/EDCM_MATHEMATICS.md`](docs/EDCM_MATHEMATICS.md). The +reference separates the frozen baseline candidate, signed-axis construction, +joint experiment candidates, controlled goal-vector candidate, and unresolved +formal boundaries. A textbook or website may carry a source-pinned copy but is +not the mathematical authority. + ## First joint experiment The initial fixed corpus pressures four load-bearing distinctions: diff --git a/docs/EDCM_MATHEMATICS.md b/docs/EDCM_MATHEMATICS.md new file mode 100644 index 0000000..50c61f3 --- /dev/null +++ b/docs/EDCM_MATHEMATICS.md @@ -0,0 +1,982 @@ +# EDCM mathematical reference + +Version: 0.1.0 + +Date: 2026-08-02 + +Status: complete compiled reference for the mathematics currently declared or +implemented in this repository; not a joint UCNS–EDCM canon selection + +## Authority and scope + +This document is the human-readable copy of the current Energy–Dissonance +Circuit Model mathematics. Its scope is exact: + +- `edcm/measurement/` is the maintained implementation authority for the + frozen baseline candidate `edcm-measurement-v1`; +- `edcm/ucns_objects.py` is the implemented EDCM signed-axis construction + layer, not formal UCNS geometry; +- `edcm/ucns_edcm_experiments*.py` contains noncanonical joint experiment + candidates; +- `edcm/goal_vector_experiment.py` contains the controlled goal-vector + candidate; +- `edcm/measurement/canon/data/*_v1.json` supplies frozen marker data, not + empirically validated universal language laws; +- `CANON.md` governs epistemic status and the proof/measurement firewall. + +The Interdependent Way textbook is a normative and explanatory artifact. It +may publish a source-pinned copy of this reference, but it does not redefine +EDCM mathematics. If a copied equation disagrees with the exact EDCM source +identified above, the copy has drifted. + +The repository and source distribution include this file. The runtime wheel +remains code-focused; installed-wheel behavior is defined by the owning source +modules and packaged frozen data. + +“Complete” here means that every mathematical surface presently declared or +implemented by EDCM is indexed below, including its unresolved boundaries. It +does not mean the model is empirically validated, mathematically final, or +joint canon. + +## Status vocabulary + +| Status | Meaning | +|---|---| +| implemented baseline candidate | Executed by `edcm/measurement/` and preserved by integrity gates | +| implemented EDCM construction | Executed by EDCM, but not formal UCNS geometry | +| experiment candidate | Versioned, executable, and falsifiable; no canon selection | +| represented evidence | Exact source or structural observation retained without an EDCM measurement claim | +| `NA` | Required evidence, context, geometry, or authority is unavailable; never numeric zero | +| hmmm | An unresolved constraint carried forward rather than guessed | + +The baseline's numeric functions may return `0` for a measured zero or no +marker hit inside their declared domain. Missing adapters, absent evidence, +disabled axes, and unavailable geometry are represented outside that numeric +domain as typed `NA`. + +## 1. Transcript and round domain + +Let a transcript be an ordered sequence of turns + +$$ +T=(u_1,u_2,\ldots,u_m),\qquad +u_i=(a_i,x_i), +$$ + +where $a_i$ is the speaker identifier and $x_i$ is the exact turn text. +Turn order and multiplicity are load-bearing. + +The maintained parser supports two round partitions: + +- `cycle`: the first observed speaker is the anchor; a new round begins when + that speaker regains the floor after at least one other speaker has spoken; +- `pairs`: consecutive pairs of turns form rounds, with a final singleton + permitted. + +For round $t$, let $y_t$ be the single space-joined text of its turns and let +$B_t=(b_{t,1},\ldots,b_{t,n_t})$ be the lowercase token sequence produced by +the baseline tokenizer. Let $A_t=B_{t-1}$ when a previous round exists and the +empty sequence otherwise. + +The rule-based parser separately classifies frozen-canon “bone” tokens and +unmatched “flesh” tokens. Bone counts are audit continuity data; the current +behavioral metric vector is computed from round text, token statistics, +markers, and prior-round context rather than from a bones-only operator. + +## 2. Common operators and text statistics + +### Clamp + +$$ +\operatorname{clamp}(z)=\min(1,\max(0,z)). +$$ + +### Type–token ratio and repetition + +For token sequence $B$ with $n=|B|$ and vocabulary $V(B)$: + +$$ +\operatorname{TTR}(B)= +\begin{cases} +0,&n=0,\\ +\dfrac{|V(B)|}{n},&n>0, +\end{cases} +$$ + +$$ +\operatorname{Rep}(B)=1-\operatorname{TTR}(B). +$$ + +Consequently, the historical baseline returns `1` for repetition on an empty +token sequence through `1 - TTR`; normal round computation does not emit an +empty parsed round. + +### Shannon entropy + +For empirical token probabilities $p_v$: + +$$ +H(B)=-\sum_{v\in V(B)}p_v\log_2 p_v, +$$ + +with $H(\varnothing)=0$. + +### Repeated n-gram density + +Let $G_n(B)$ be the ordered list of all length-$n$ n-grams, and $f(g)$ the +frequency of $g$ in that list: + +$$ +\operatorname{RepN}_n(B)= +\begin{cases} +0,&|G_n(B)|=0,\\ +\dfrac{\sum_{g:f(g)>1}(f(g)-1)}{|G_n(B)|},&\text{otherwise}. +\end{cases} +$$ + +The maintained baseline uses $n=3$. + +### Pattern density + +For a regular-expression marker pattern $r$ and raw text $x$: + +$$ +\rho_r(x)= +\begin{cases} +0,&|x|=0,\\ +1000\dfrac{\#\operatorname{matches}(r,x)}{|x|},&|x|>0. +\end{cases} +$$ + +Matches follow Python `re.findall` behavior; despite an older docstring, the +implementation does not add lookahead to make arbitrary patterns overlap. + +### Novelty + +$$ +\operatorname{Nov}(B\mid A)= +\begin{cases} +0,&|B|=0,\\ +\dfrac{\sum_{b\in B}\mathbf 1[b\notin V(A)]}{|B|},&|B|>0. +\end{cases} +$$ + +Token occurrences, not only unique types, contribute to the numerator. + +### Bag-of-words cosine similarity + +Let $c_A$ and $c_B$ be aligned count vectors over $V(A)\cup V(B)$: + +$$ +\operatorname{cos}(A,B)= +\begin{cases} +0,&A=\varnothing\ \text{or}\ B=\varnothing,\\ +\dfrac{c_A\cdot c_B}{\|c_A\|_2\|c_B\|_2},&\text{otherwise}. +\end{cases} +$$ + +### Jaccard similarity + +$$ +J(X,Y)= +\begin{cases} +0,&X\cup Y=\varnothing,\\ +\dfrac{|X\cap Y|}{|X\cup Y|},&\text{otherwise}. +\end{cases} +$$ + +### Correction fidelity + +For original response $A$, new response $B$, and correction/target $C$: + +$$ +\operatorname{CF}(A,B,C) +=0.5J(V(C),V(B))+0.5\left(1-\operatorname{cos}(A,B)\right). +$$ + +### Per-100 normalization + +$$ +\operatorname{per100}(z,B)= +\begin{cases} +0,&|B|=0,\\ +100z/|B|,&|B|>0. +\end{cases} +$$ + +## 3. Maintained baseline vector + +For each round, the baseline emits + +$$ +M_t=(C_t,R_t,F_t,E_t,D_t,N_t,I_t,O_t,L_t,P_t,\kappa_t). +$$ + +Except for $O_t\in[-1,1]$, the metric components and state are clamped to +$[0,1]$. + +Let $h_X(y_t)$ be the number of matches from the first frozen marker category +for metric $X\in\{C,R,I\}$. With $n_t=|B_t|$: + +$$ +C_t=\operatorname{clamp}\left( +\frac{h_C(y_t)}{\max(1,n_t/10)}\right), +$$ + +$$ +R_t=\operatorname{clamp}\left( +\frac{h_R(y_t)}{\max(1,n_t/10)}\right), +$$ + +$$ +I_t=\operatorname{clamp}\left( +\frac{h_I(y_t)}{\max(1,n_t/10)}\right). +$$ + +### Fixation + +$$ +F_t=\operatorname{clamp}\left( +0.30\operatorname{Rep}(B_t) ++0.30\operatorname{RepN}_3(B_t) ++0.40(1-\operatorname{Nov}(B_t\mid A_t)) +\right). +$$ + +### Loop risk used by escalation + +$$ +R_{\mathrm{loop},t}=\operatorname{clamp}\left( +0.50\operatorname{Rep}(B_t) ++0.30\operatorname{RepN}_3(B_t) ++0.20\operatorname{cos}(A_t,B_t) +\right). +$$ + +### Escalation + +For the first round, the loop term is explicitly set to zero. Otherwise: + +$$ +E_t=\operatorname{clamp}(0.60R_t+0.40R_{\mathrm{loop},t}). +$$ + +### Deflection + +$$ +D_t= +\begin{cases} +0,&t=1,\\ +\operatorname{clamp}(1-\operatorname{cos}(B_t,A_t)),&t>1. +\end{cases} +$$ + +This is a lexical proxy, not full semantic deflection. + +### Noise + +Let $\widehat H_t=\operatorname{clamp}(H(B_t)/10)$: + +$$ +N_t=\operatorname{clamp}\left( +0.60\operatorname{Rep}(B_t)+0.40(1-\widehat H_t) +\right). +$$ + +### Confidence polarity + +Let $o_t$ and $u_t$ be overconfidence and under-confidence marker hits: + +$$ +O_t= +\begin{cases} +0,&o_t+u_t=0,\\ +2\dfrac{o_t}{o_t+u_t}-1,&o_t+u_t>0. +\end{cases} +$$ + +Positive is overconfident, negative is under-confident. This baseline zero is +a within-domain no-hit value; it must not be reused as typed absence. + +### Coherence loss + +The implementation supplies a first-round novelty default of $0.5$: + +$$ +L_t=\operatorname{clamp}\left( +0.50\operatorname{Rep}(B_t)+0.50(1-\nu_t) +\right), +$$ + +where + +$$ +\nu_t= +\begin{cases} +0.5,&t=1,\\ +\operatorname{Nov}(B_t\mid A_t),&t>1. +\end{cases} +$$ + +### Progress proxy + +Let + +$$ +g_t= +\begin{cases} +0.5,&H(B_{t-1})=0,\\ +\operatorname{clamp}\left( +\dfrac{H(B_t)-H(B_{t-1})}{\max(H(B_{t-1}),10^{-9})} +\right),&H(B_{t-1})>0. +\end{cases} +$$ + +Then + +$$ +P_t=\operatorname{clamp}(0.60\nu_t+0.40g_t). +$$ + +$P$ is the baseline's health-oriented component. It is a lexical proxy, not +an externally validated measure of beneficial progress. + +## 4. Dissonance and circuit recurrence + +The baseline's round dissonance energy is the unweighted mean + +$$ +\mathcal E_t +=\operatorname{clamp}\left( +\frac{C_t+R_t+F_t+E_t+N_t+I_t+L_t}{7} +\right). +$$ + +$D_t$, $O_t$, $P_t$, and $\kappa_t$ do not enter this mean. The term “energy” +denotes a dimensionless model quantity; it is not measured in joules and does +not establish a physical-energy claim. + +With persistence $\alpha=0.85$ and maximum resolution rate +$\delta_{\max}=0.30$ by default: + +$$ +g_t=\delta_{\max}\max(0,1-\mathcal E_t), +$$ + +$$ +\delta_t=\min(\delta_{\max},g_t), +$$ + +$$ +\kappa_t=\operatorname{clamp}\left( +\alpha\kappa_{t-1}+\mathcal E_t-\delta_t +\right),\qquad \kappa_0=0. +$$ + +Because $\mathcal E_t\in[0,1]$, the current implementation has +$\delta_t=g_t$. The public `energy_step` returns $(\mathcal E_t,\kappa_t)$; +the accepted legacy `prev_energy` argument is ignored. + +## 5. Auxiliary risk proxies + +These are implemented functions but are not all invoked by the default +round-vector path. + +### Broken return + +$$ +R_{\mathrm{broken}}(A,B,C)=\operatorname{clamp}\left( +0.55\operatorname{cos}(A,B)+0.45(1-J(V(C),V(B))) +\right). +$$ + +### Escalation or shutdown risk + +For refusal density $\rho_R$ and hedge density $\rho_H$, both measured per +1,000 characters: + +$$ +R_{\mathrm{esc}}=\operatorname{clamp}\left( +0.45R_{\mathrm{broken}}+0.35\frac{\rho_R}{5} ++0.20\frac{\rho_H}{5} +\right). +$$ + +### Stagnation + +For caller-supplied gain $G\in[0,1]$: + +$$ +R_{\mathrm{stag}}=\operatorname{clamp}\left( +0.45\frac{\rho_R}{5} ++0.35(1-\operatorname{Nov}(B\mid A)) ++0.20(1-G) +\right). +$$ + +### Fixation and loop + +$R_{\mathrm{fix}}$ is exactly the $F_t$ equation in section 3. +$R_{\mathrm{loop}}$ is the loop equation used by $E_t$. + +These values are bounded behavioral proxies. Their names do not establish +diagnosis, intention, morality, consciousness, or external truth. + +## 6. Agent-facing projections + +The implemented Layer-3 vector is + +$$ +A_t=(CM_t,DA_t,DRIFT_t,DVG_t,INT_t,TBF_t)\in[0,1]^6. +$$ + +The exact linear projections are + +$$ +CM_t=\operatorname{clamp}(0.50C_t+0.50I_t), +$$ + +$$ +DA_t=\operatorname{clamp}(0.40\kappa_t+0.40E_t+0.20R_t), +$$ + +$$ +DRIFT_t=\operatorname{clamp}(0.50L_t+0.50(1-P_t)), +$$ + +$$ +DVG_t=\operatorname{clamp}(0.50D_t+0.50N_t), +$$ + +$$ +INT_t=\operatorname{clamp}(0.50E_t+0.50F_t). +$$ + +### Turn-balance Gini + +Let $x_1\le\cdots\le x_n$ be total token counts by speaker in the round and +$S=\sum_i x_i$. For $n\le1$ or $S=0$, $TBF_t=0$. Otherwise: + +$$ +G=\frac{2\sum_{i=1}^{n}ix_i}{nS}-\frac{n+1}{n}, +$$ + +$$ +TBF_t=\operatorname{clamp}\left(\frac{G}{(n-1)/n}\right). +$$ + +Higher $TBF$ means greater token-share imbalance. “Fairness” here names this +specific distributional proxy; it does not measure social or substantive +fairness. + +## 7. Alerts and risk crosswalk + +Alerts fire only when the metric is strictly greater than its threshold: + +| Alert | Metric | Threshold | +|---|---:|---:| +| `ALERT_CM_HIGH` | $CM$ | 0.70 | +| `ALERT_DA_RISING` | $DA$ | 0.60 | +| `ALERT_DRIFT` | $DRIFT$ | 0.50 | +| `ALERT_DVG_HIGH` | $DVG$ | 0.60 | +| `ALERT_INT_HIGH` | $INT$ | 0.70 | +| `ALERT_TBF_SKEW` | $TBF$ | 0.40 | + +The implemented nonnumeric crosswalk is: + +| Risk | Associated alerts | +|---|---| +| $R_{\mathrm{fix}}$ | `ALERT_INT_HIGH`, `ALERT_DRIFT` | +| $R_{\mathrm{esc}}$ | `ALERT_DA_RISING`, `ALERT_CM_HIGH` | +| $R_{\mathrm{stag}}$ | `ALERT_DRIFT`, `ALERT_DA_RISING` | +| $R_{\mathrm{loop}}$ | `ALERT_INT_HIGH` | + +Thresholds and crosswalks are version-1 candidate policy, not empirically +selected universal constants. + +## 8. Matrix identity and present duplication + +`edcm/measurement/metrics/matrix.py` declares `MATRIX_VERSION = "1.0"`, the +Layer-0-to-Layer-1 weight dictionary, projections, thresholds, and crosswalk. +The runtime formulas for the Layer-1 metrics remain hardcoded in +`compute.py`; the matrix itself states that it is documentation-shaped rather +than the runtime source of those calculations. This document therefore records +the executed `compute.py` equations above and treats the matrix as a +versioned intended mirror. + +For any matrix dictionary $Q$, `freeze(Q)` computes + +$$ +\operatorname{id}(Q)= +\operatorname{SHA256}(\operatorname{canonicalJSON}(Q))[0:16], +$$ + +then attaches that hexadecimal prefix as `_sha256`. `diff` reports every +changed `(metric, primitive)` coefficient pair. + +hmmm: the declared matrix and the executed Layer-1 equations still have two +maintenance locations. Making the matrix the runtime source requires a +separate versioned migration and equivalence tests. + +## 9. Signed-ternary EDCM construction + +An enabled metric axis is + +$$ +X=(s,m),\qquad s\in\{-1,0,+1\},\quad m\in[0,1]. +$$ + +Typed absence is + +$$ +X=NA\iff enabled=false\land s=null\land m=null. +$$ + +Therefore + +$$ +NA\ne(0,0). +$$ + +The implemented grains are token, turn, round, session, and archive. + +### Constraint field + +Let a `ConstraintField` contain raised-field count $r\ge0$, contact direction +$c$, contact magnitude $m_c$, resolution state $z$, and resolution magnitude +$m_z$. Presence is + +$$ +present\iff r>0. +$$ + +If $r=0$, contact, resolution, $R$, $D$, $I$, and resistance-$L$ readouts are +all `NA`. + +Contact direction is mapped as + +$$ +toward\mapsto+1,\qquad against\mapsto-1,\qquad away\mapsto0. +$$ + +Resolution is mapped as + +$$ +closed\mapsto+1,\qquad open\mapsto-1,\qquad unresolved\mapsto0. +$$ + +For a present field, the behavioral readout signs are: + +| Contact | $R$ refusal/resistance | $D$ deflection/return | $L_{resistance}$ | +|---|---:|---:|---:| +| `against` | +1 | 0 | +1 | +| `toward` | -1 | -1 | -1 | +| `away` | 0 | +1 | 0 | +| omitted | 0 | 0 | 0 | + +Each receives magnitude $\operatorname{clamp}(m_c)$. The $I$ readout uses the +resolution sign and magnitude $\operatorname{clamp}(m_z)$. + +### Field motion + +For axis reads $q_1,\ldots,q_n$, let + +$$ +\bar q=\frac1n\sum_i q_i. +$$ + +A present `FieldMotion` emits + +$$ +s=\operatorname{sign}(\bar q),\qquad +m=\min(1,|\bar q|). +$$ + +An empty read list on a present motion emits $(0,0)$; an absent motion emits +`NA`. The three right-angle readouts are: + +- recurrence reads $\rightarrow F$ fixation/release; +- intensity reads $\rightarrow E$ escalation/de-escalation; +- scope reads $\rightarrow O_{scope}$ expansion/contraction. + +All three share the same ordered transition parent +`previous_field_hash->current_field_hash` while preserving distinct metric +identities. The field and transition hashes are deterministic content +identifiers, not formal UCNS objects or signed authentication. + +The axis registry also names $C,R,D,I,F,E,O_{scope},O_{confidence},L_{load}, +L_{loss},L_{resistance},N,P,\kappa$ and the six projections. Registration does +not make an axis canonical. + +## 10. Controlled goal-vector candidate + +For a declared goal with $d$ components, each available component state is +`toward` $(+1,1)$ or `away` $(-1,1)$. An unavailable component is `NA`; a turn +that makes no claim about a component is `no-claim`. Both unavailable states +carry null sign and magnitude rather than numeric zero. + +Let $T_t$, $A_t$, and $U_t$ be the counts of toward, away, and `NA` component +states after turn $t$, so $T_t+A_t+U_t=d$. The declared-loss scalar projection +is + +$$ +q_t=\frac{T_t-A_t}{d},\qquad q_0=0. +$$ + +The complete component state remains authority-bearing evidence. $q_t$ is not +sufficient to reconstruct which components produced the value. + +Motion is + +$$ +\Delta q_t=q_t-q_{t-1}. +$$ + +For a sequence $z_1,\ldots,z_n$, the candidate uses population variance + +$$ +\operatorname{Var}(z)=\frac1n\sum_{i=1}^{n}(z_i-\bar z)^2, +\qquad +\bar z=\frac1n\sum_{i=1}^{n}z_i. +$$ + +Thus + +$$ +V_{motion}=\operatorname{Var}(\Delta q_1,\ldots,\Delta q_n), +$$ + +$$ +V_{trajectory}=\operatorname{Var}(q_1,\ldots,q_n). +$$ + +A terminal state is `candidate-complete` exactly when all $d$ components are +toward and the contradiction ledger has no active entry. Formal completion +remains `NA`. + +Contradiction status is procedural over declared fixture claims: + +- a claim opposing the prior component sign creates a contradiction; +- it is `resolved` only when that opposing claim is explicitly declared a + revision; +- otherwise it remains `active`; +- no claim about dishonesty, intention, diagnosis, morality, consciousness, + or external truth follows. + +The sealed v0.1.0 fixture produced: + +| Case | $q_n$ | $V_{motion}$ | $V_{trajectory}$ | Active contradictions | +|---|---:|---:|---:|---:| +| contradiction resolved | $1$ | $1/8$ | $5/32$ | 0 | +| contradiction active after reordering | $1/2$ | $9/64$ | $11/256$ | 1 | + +This is controlled candidate-measured evidence: eight supported findings, zero +falsified findings, and no canon selection. + +## 11. Initial joint experiment candidate + +The historical v0.1 experiment also retains a transparent, noncanonical +sequence candidate. For each turn $i$, phrase-hit signals +$c_i,r_i,z_i\in[0,1]$ represent constraint, refusal, and resolution; $p_i=1$ +when the normalized turn has appeared earlier in the same case and $0$ +otherwise. + +$$ +pressure_i=0.35c_i+0.35r_i+0.20p_i, +$$ + +$$ +release_i=0.55z_i, +$$ + +$$ +\tau_i=\operatorname{clamp}(0.72\tau_{i-1}+pressure_i-release_i), +\qquad \tau_0=0. +$$ + +The reported constraint, refusal, resolution, and repetition pressures are +their arithmetic means over turns. Final tension is $\tau_n$. + +Three support assignments were tested: + +$$ +\mu_{unit}=1, +$$ + +$$ +\mu_{token}=\max(1,\operatorname{tokenCount}), +$$ + +$$ +\mu_{pressure}=1+c_i+r_i+z_i+p_i. +$$ + +The experiment exposes all three UCNS product-character candidates +(`cell-support-geometric-mean`, `cell-support-maximum`, +`cell-support-minimum`) and all three faithful-breadth candidates +(`cell-log-support`, `cell-detail`, `retained-presence`) under each support +assignment. Their definitions and authority belong to the experiment-pinned +UCNS producer; EDCM records their readouts and comparisons without adopting a +winner. + +Ordered-sequence, unordered-multiset, and set projections are compared. A +projection is incompatible for a named EDCM readout only when it declares two +cases equivalent while that readout materially differs under the declared +comparison policy. This is scoped falsification, not universal rejection. + +### v0.2 occurrence, coverage, and latency candidate + +Unlike v0.1, v0.2 does not clamp phrase occurrences to one. For turn $i$, let +$c_i$ be total constraint-phrase occurrences, $f_i$ the number of distinct +constraint phrase families hit, $r_i$ refusal occurrences, $z_i$ resolution +occurrences, and $p_i$ the repeated-turn indicator. + +$$ +pressure_i=0.30c_i+0.55r_i+0.20p_i, +$$ + +$$ +release_i=0.65z_i, +$$ + +$$ +\tau_i=\max(0,0.78\tau_{i-1}+pressure_i-release_i), +\qquad \tau_0=0. +$$ + +The candidate records occurrence totals, family-hit totals, refusal rate, +terminal tension, peak tension, and tension area + +$$ +Area=\sum_{i=1}^{n}\tau_i. +$$ + +If first pressure occurs at zero-based event index $j$ and the first resolution +observed once pressure has occurred is at $k$, resolution latency is $k-j$. +It is `-1` when either event +is absent. If pressure occurs but resolution does not, the comparison horizon +is $n+1$ rather than `-1`. + +Its support assignments are + +$$ +\mu_{unit}=1, +\qquad +\mu_{token}=\max(1,\operatorname{tokenCount}), +$$ + +$$ +\mu_{occurrence}=1+c_i+r_i+z_i+p_i, +$$ + +$$ +\mu_{dissonance}=1+c_i+r_i+p_i. +$$ + +### v0.3 assertion and local-scope candidate + +v0.3 emits an ordered event sequence from nonoverlapping phrase spans. +Each event retains kind, family, speaker, source position, polarity, quotation, +hypothetical, conditional, attribution, retraction, ownership, and active +flags. The implemented active predicate for a mention is + +$$ +active=\neg negated\land\neg quoted\land\neg hypothetical\land\neg retracted. +$$ + +Attribution and conditionality remain separately counted; they do not by +themselves make the event inactive. An owned refusal additionally requires a +refusal event, first-person `I` evidence, and neither quotation nor attribution. + +Let $a_i$ be active pressure after event $i$. An active constraint or refusal +increments pressure by one; a repair event resets it to zero: + +$$ +a_i= +\begin{cases} +0,&event_i=repair,\\ +a_{i-1}+1,&event_i\text{ is an active constraint or refusal},\\ +a_{i-1},&\text{otherwise}. +\end{cases} +$$ + +The candidate reports $a_n$, $\max_i a_i$, $\sum_i a_i$, exact event counts, +and the index distance from first active pressure to first later repair, or +`-1` if either is absent. + +For event complexity + +$$ +k_i=\mathbf1[negated]+\mathbf1[quoted]+\mathbf1[hypothetical] ++\mathbf1[conditional]+\mathbf1[attributed]+\mathbf1[retracted], +$$ + +the support policies are + +$$ +\mu_{mention}=1, +$$ + +$$ +\mu_{scope}=1+k_i, +$$ + +$$ +\mu_{active}=1+2\mathbf1[event_i\text{ is an active constraint or refusal}]. +$$ + +These are deterministic synthetic-scope rules, not a general semantic parser. + +### v0.4 discourse-graph candidate + +v0.4 is a finite, bounded graph-state experiment. A case contains ordered +discourse nodes, positive reference expressions, and declared relations. +Candidate resolvers select targets by explicit label or ordinal, nearest +compatible prior node, nearest same-speaker prior node, all compatible family +nodes, or every ambiguity-preserving singleton alternative. Only nodes earlier +than the reference are eligible. Ambiguity expansion is capped at 32 generated +interpretations and then deduplicated by exact interpretation digest. + +The node-state transition is + +$$ +\operatorname{transition}(s,r)= +\begin{cases} +retracted,&r\in\{retracts,repairs\},\\ +suspended,&r=suspends,\\ +active,&r\in\{resumes,activates\},\\ +inactive\_condition,&r=deactivates,\\ +s,&\text{otherwise}. +\end{cases} +$$ + +A `contradicts` edge increments the target's contradiction count without +changing its state. A reference with no selected target remains positive +unresolved-reference evidence. + +Across admissible interpretations, the readout reports the number of +alternatives, number of distinct state signatures minus one, minima and maxima +of active/suspended/retracted/contradiction/unresolved/edge counts, declared +target hits and misses, per-node active/retracted bounds, and per-speaker active +bounds. Minima encode what holds across every retained interpretation; maxima +encode what occurs in at least one retained interpretation. + +Graph support is: + +$$ +\mu_{node-reference}=\mu_{node-edge}=1 +$$ + +for nodes, while `state-detail` uses + +$$ +\mu_{node,state}=1+\mathbf1[active]+\mathbf1[contradictions>0], +$$ + +$$ +\mu_{reference,state}=1+\mathbf1[unresolved]. +$$ + +Each retained graph or quote edge has support one under `node-edge` and +`state-detail`. Exact ordered labeled, labeled multigraph, unlabeled +multigraph, flat node multiset, and active-state summary views explicitly list +their information losses. + +The v0.2–v0.4 complete executable definitions and sealed results remain +versioned in `edcm/ucns_edcm_experiments_v2.py` through +`edcm/ucns_edcm_experiments_v4.py` and `experiments/results/`. None replaces +the maintained baseline equations or selects joint canon. + +## 12. Exact UCNS observation boundary + +The current profile supplies exact ordered word-gonol observations with one +unit of support per speaker turn. It retains exact Unicode source values, +carrier assignments, SPACE boundaries, multiplicity, and turn order. + +It does not currently supply an EDCM equation for: + +- formal Möbius coordinates; +- word-to-turn-to-dialogue higher-gonol composition; +- lawful scalar projection into EDCM axes; +- formal completion; +- measurement validity. + +Those quantities are `NA`, not zero. A UCNS observation digest establishes +deterministic content identity under its schema; it is not signed producer +authentication and transfers no theorem or proof status into EDCM. + +## 13. Identity and reproducibility mathematics + +EDCM evidence records use canonical JSON bytes + +$$ +J(x)=\operatorname{UTF8}(\operatorname{JSON}(x; +sort\_keys=true,separators=(\texttt{,},\texttt{:}),ensure\_ascii=false)). +$$ + +Content identity is + +$$ +d(x)=\operatorname{SHA256}(J(x)). +$$ + +For a self-digesting report, `report_digest` is removed before computing +$d(x)$ and then attached to the report. The immutable evidence file also has a +SHA-256 over its exact serialized bytes. These identities detect drift; they +do not prove truth, authorship, or empirical validity. + +## 14. What is not yet mathematics + +The following are deliberately not filled with convenient equations: + +- an empirically calibrated mapping from language to every EDCM axis; +- a validated threshold or coefficient selection procedure; +- a canonical global objective or optimization function; +- a numeric `hmmm` penalty or hidden uncertainty scalar; +- METAPAT semantic labels converted directly into measured values; +- formal UCNS geometry or completion inferred from observation identity; +- real-dialogue goal authority inferred by the model; +- physical-energy units or conservation claims; +- diagnosis, intention, morality, consciousness, or external truth. + +`hmmm` is a boundary object carrying unresolved constraints and provenance. It +is not silently mapped to zero, averaged away, or inserted as an unvalidated +term in an objective function. + +## Usage guidance + +For the maintained baseline: + +```bash +python -m edcm.integrity +python -m pytest -q +``` + +For the controlled goal-vector candidate: + +```bash +python -m edcm.goal_vector_experiment \ + --ucns-source-root /path/to/ucns-at-a98c9e6c69804a8a08d0786b1d8b450bb2c49a97 \ + --output /tmp/goal-vector.json +``` + +When changing any equation, coefficient, threshold, state domain, tokenizer, +marker source, round boundary, or projection: + +1. change the owning source and its tests; +2. update this reference in the same change; +3. version any changed candidate or evidence schema; +4. preserve old sealed reports unchanged; +5. rerun integrity, metadata, complete tests, build, and wheel checks; +6. record falsified and unresolved consequences rather than rewriting them. + +A textbook or website copy must cite the EDCM repository path and exact commit +from which it was copied and must label itself non-authoritative. + +## hmmm + +The maintained baseline now has one complete mathematical reference, but its +coefficients remain candidate policy and the Layer-1 matrix still duplicates +runtime equations. Independent semantic annotation, calibrated outcome data, +formal higher-gonol composition, signed producer records, external holdout +custody, and the first joint canon decision remain unresolved. From 2f09f9af10ef950ce68c765bcbed7dca83625c65 Mon Sep 17 00:00:00 2001 From: Erin Spencer Date: Sun, 2 Aug 2026 01:20:59 -0700 Subject: [PATCH 2/2] Complete v0.3.1 mathematics reference --- CANON.md | 5 +- README.md | 6 +- docs/EDCM_MATHEMATICS.md | 323 ++++++++++++++++++++++++++++++++++++++- 3 files changed, 324 insertions(+), 10 deletions(-) diff --git a/CANON.md b/CANON.md index 802b703..13aaa7c 100644 --- a/CANON.md +++ b/CANON.md @@ -93,8 +93,9 @@ Its marker canon, parser, eleven-component round vector, and circuit recurrence [`docs/EDCM_MATHEMATICS.md`](docs/EDCM_MATHEMATICS.md) is the complete human-readable index of the mathematics currently declared or implemented in this repository. It records the maintained baseline equations, auxiliary risks, -agent-facing projections, signed-ternary construction, experiment candidates, -identity functions, and explicit mathematical absences. +agent-facing projections, signed-ternary construction, the implemented v0.3.1 +architecture layer, experiment candidates, identity functions, and explicit +mathematical absences. The reference is a synchronized copy, not a separate authority and not a canon selection. The owning source modules and frozen data remain implementation diff --git a/README.md b/README.md index 7cb2ab3..596406f 100644 --- a/README.md +++ b/README.md @@ -37,9 +37,9 @@ See [`CANON.md`](CANON.md) and The complete compiled mathematics currently declared or implemented by EDCM is indexed in [`docs/EDCM_MATHEMATICS.md`](docs/EDCM_MATHEMATICS.md). The reference separates the frozen baseline candidate, signed-axis construction, -joint experiment candidates, controlled goal-vector candidate, and unresolved -formal boundaries. A textbook or website may carry a source-pinned copy but is -not the mathematical authority. +implemented v0.3.1 architecture layer, joint experiment candidates, controlled +goal-vector candidate, and unresolved formal boundaries. A textbook or website +may carry a source-pinned copy but is not the mathematical authority. ## First joint experiment diff --git a/docs/EDCM_MATHEMATICS.md b/docs/EDCM_MATHEMATICS.md index 50c61f3..c2e059d 100644 --- a/docs/EDCM_MATHEMATICS.md +++ b/docs/EDCM_MATHEMATICS.md @@ -16,6 +16,9 @@ Circuit Model mathematics. Its scope is exact: frozen baseline candidate `edcm-measurement-v1`; - `edcm/ucns_objects.py` is the implemented EDCM signed-axis construction layer, not formal UCNS geometry; +- `edcm/edcmucns/` is the implemented v0.3.1 EDCM architecture layer; its + historical “design canon” label does not override the current pre-canon + status in `CANON.md` or make its local carriers formal UCNS geometry; - `edcm/ucns_edcm_experiments*.py` contains noncanonical joint experiment candidates; - `edcm/goal_vector_experiment.py` contains the controlled goal-vector @@ -604,11 +607,313 @@ All three share the same ordered transition parent identities. The field and transition hashes are deterministic content identifiers, not formal UCNS objects or signed authentication. +The exact `ConstraintField` content identity is the first 16 hexadecimal +characters of SHA-256 over the UTF-8 pipe-joined sequence + +$$ +(schema\_id,grain,raised\_field\_count,contact,contact\_magnitude, +resolution,resolution\_magnitude,witness). +$$ + +The field reader retains `previous_field_hash->current_field_hash` and appends +`#` plus the first 16 hexadecimal characters of SHA-256 over Python `repr` of +the motion-presence flag and the three exact read tuples. This is a +runtime-language identity contract, not a portable canonical-JSON signature. + The axis registry also names $C,R,D,I,F,E,O_{scope},O_{confidence},L_{load}, L_{loss},L_{resistance},N,P,\kappa$ and the six projections. Registration does not make an axis canonical. -## 10. Controlled goal-vector candidate +## 10. Implemented v0.3.1 architecture layer + +`edcm/edcmucns/` implements the v0.3.1 identity and composition architecture. +Its source docstrings preserve the historical label “ratified as architecture +(frozen design canon).” Under the repository-wide status authority in +`CANON.md`, that label is scoped to this implemented architecture: it is not a +joint UCNS–EDCM canon selection, formal UCNS geometry, or empirical +measurement validation. + +The architecture declares the measurement dependency + +$$ +M_{EDCM}=\operatorname{readout} +\left(G_{carrier},\Pi_{provenance},payloads,field\_state,policy\_manifest\right). +$$ + +`G_carrier` here is the EDCM-local `Window` construction described below. The +implementation does not construct or validate the six-field formal UCNS +object reproduced by the earlier design handoff. + +### Manifest and family gauge + +The exact v0.3.1 family-to-prime gauge is + +$$ +P\mapsto3,\qquad K\mapsto5,\qquad Q\mapsto7,\qquad +T\mapsto13,\qquad S\mapsto29. +$$ + +`PolicyManifest` requires this exact gauge and the residue-rule identity +`non_origin_residue_v031`. Its canonical JSON contains the gauge and seven +policy-version fields. The manifest identity is + +$$ +h_{manifest}=\operatorname{SHA256}(\operatorname{UTF8}(J_{manifest})). +$$ + +The polarity, bone-emission, payload-governance, lens-readout, and +training-update version strings are architecture identifiers. The contact +predicate remains explicitly `v031-frontier-unimplemented`; the strings do +not establish that the named empirical policies are validated. + +The ordered readout-bearing witness fields are `family`, `ordinal_m_f`, +`residue_r_f`, `turn_id`, `speaker_or_source`, `surface_form`, `role`, +`constraint_governance`, and `payload_attachment`. A witness hash is SHA-256 +over their sorted-key compact JSON object; an ordered bundle hash is SHA-256 +over the compact JSON array of those objects. Decorative witness fields never +enter either identity. The bundle order is chronological and readout-bearing. + +### Non-origin residue and anchors + +For one-based ordinal $m\ge1$ and family prime $p\ge2$: + +$$ +r(m,p)=1+((m-1)\bmod(p-1)), +$$ + +$$ +\theta_{bone}(m,p)=\frac{r(m,p)}{p} +$$ + +as an exact fraction of a turn in $[0,1)$. Bone residues therefore cycle +through $1,\ldots,p-1$ and never land at the origin. An origin anchor has + +$$ +\theta=0,\qquad face=0,\qquad lattice\_n=1, +$$ + +and carries no family, ordinal, or residue metadata. Bone faces are exactly +$-1$ or $+1$. + +An explicitly caller-constructed cadence fixture uses + +$$ +\theta_{cadence}(m,n)=\frac{m\bmod n}{n}. +$$ + +Cadence admission from transcript text is not implemented. The source also +retains an exact `hmmm`: when $m\bmod n=0$, the cadence helper returns the +datum angle even though non-origin `Anchor` validation rejects that collision. + +### Mass, carriers, shares, and field load + +For a window $W$ with host anchors $A(W)$, bone anchors $B(W)$, cadence +anchors $C(W)$, and payloads $P(W)$: + +$$ +L_{geo}(W)=|A(W)|, +\qquad +L_{op}(W)=|B(W)|. +$$ + +The implemented carrier functions are least common multiples over their +declared scopes, with the empty least common multiple equal to one: + +$$ +n_{host}(W)=\operatorname{lcm}\{a.lattice\_n:a\in A(W)\}, +$$ + +$$ +n_{family}(W)=\operatorname{lcm}\{a.lattice\_n:a\in B(W)\}, +$$ + +$$ +n_{cadence}(W)=\operatorname{lcm}\{a.lattice\_n:a\in C(W)\}, +$$ + +$$ +n_{payload}(W)=\operatorname{lcm}\{p.reduced\_carrier:p\in P(W)\}. +$$ + +Only $n_{family}$ carries the architecture's active-family factor claim. +Payload carriers do not automatically enter $n_{host}$. + +For family $f$, the operator share is + +$$ +share_f(W)= +\begin{cases} +\text{absent from the returned map},&L_{op}(W)=0,\\ +\dfrac{|\{a\in B(W):a.family=f\}|}{L_{op}(W)},&L_{op}(W)>0. +\end{cases} +$$ + +Shares after chronological append are derived from summed counts, never by +averaging the two input share maps. + +Field load remains separate from both masses: + +$$ +\lambda_{field}(W)= +\begin{cases} +NA,&TOK(W)\le0,\\ +\dfrac{raised\_field\_count(W)}{TOK(W)},&TOK(W)>0. +\end{cases} +$$ + +The Python value for this typed absence is `None`, not numeric zero. + +### Turn and payload absence + +The implemented turn sum type is + +$$ +OperatorTurn=Present(Window)\mid AbsentOperatorGeometry(ContentLensEvent). +$$ + +A no-bone turn emits `AbsentOperatorGeometry`. Its operator-presence readout +is `NA`; a present turn emits $(+1,1)$. A no-bone turn is neither the geometric +unit nor numeric zero and remains available to the content layer. + +For payload $p$: + +$$ +p.reduced\_carrier= +\begin{cases} +1,&p.status=closed,\\ +p.carrier\_n,&p.status=open. +\end{cases} +$$ + +Its content identity is SHA-256 over the exact UTF-8 string + +$$ +payload\_id\;|\;carrier\_n\;|\;status\;|\;tension\;|\;content. +$$ + +This delimiter-based identity is the implemented contract; it is not silently +re-described as canonical JSON. + +The architecture-only kappa ledger is + +$$ +\kappa_{balance}(W)= +\sum_{p\in P(W):p.status\ne closed}p.tension. +$$ + +A nonzero balance emits a `kappa_leak` diagnostic. This placeholder is not the +maintained baseline circuit recurrence in section 4 and makes no empirical +stored-tension claim. + +### Chronological append and reserved interaction product + +For windows sealed under the same manifest, `SeqAppend` is exact tuple +concatenation of anchors, witnesses, payloads, and field-chain entries, with +token and raised-field counts added: + +$$ +L(A\boxplus B)=L(A)+L(B), +\qquad +F(A\boxplus B)=F(A)\mathbin{\|}F(B). +$$ + +Appending windows with different manifest hashes raises `EpochBreakError`. +The reserved interaction product returns a non-window signature with + +$$ +L(A\boxtimes B)=L(A)L(B). +$$ + +The current implementation does not implement the earlier handoff's payload +product, XOR face product, mirror construction, or external zero/unit algebra. +Those equations therefore must not be reconstructed by a publication +consumer as current EDCM implementation. + +### Exact implemented equivalence + +The local carrier-equivalence predicate is + +$$ +A\equiv_{carrier}B +\iff +n_{host}(A)=n_{host}(B) +\land +sort\{(\theta_a,face_a):a\in A\} +=sort\{(\theta_b,face_b):b\in B\}. +$$ + +It ignores witnesses, payloads, and manifest identity. It compares sorted +angle-face pairs rather than chronological anchor order. Chronological +testimony order remains readout-bearing in the ordered witness-bundle hash. +The module preserves this split as `hmmm`; a website must not silently replace +it with a stronger ordered UCNS equivalence claim. + +EDCM measurement equivalence first requires carrier equivalence and equal +manifest hashes. It then applies one closed readout scope: + +| Scope | Additional exact comparison | +|---|---| +| `operator_scope` | ordered readout-bearing witness-bundle hash | +| `payload_scope` | sorted `(content_hash, reduced_carrier)` tuples | +| `cadence_scope` | cadence carrier plus ordered cadence `(lattice_n, ordinal, theta)` tuples | +| `field_scope` | exact field-chain tuple | +| `bridge_scope` | no additional identity comparison; validator diagnostics remain observational | + +The `bridge_scope` diagnostic vocabulary remains unresolved and growing. No +runtime scope-registration surface exists; extending the registry requires a +manifest revision and epoch break. + +### Validation, polarity, and epochs + +`witness_geometry_consistent` checks origin constraints, nonzero bone phases, +one-to-one bone/witness pairing, exact gauge and residue agreement, stable NFC +canonicalization of turn/source ids, and existing payload targets. A mismatch +emits a Bridge diagnostic rather than an alternate reading. + +`gauge_audit` considers bone faces only. No differences passes; a difference +at every paired face is reported as `gauge_mismatch`; a partial difference or +different face-sequence length is `measurement_divergence`. This is a +diagnostic classification, not proof of empirical equivalence. + +The window identity used in epoch chains hashes, in order: + +- serialized anchor role, family, lattice, ordinal, angle, and face values; +- the ordered witness-bundle hash; +- sorted payload content hashes; +- the exact field-chain tuple; and +- the manifest hash. + +The five components are pipe-joined before SHA-256. Anchor records are +semicolon-joined; payload content hashes are sorted then comma-joined; field +chain entries retain their exact order. These identities detect implementation +drift but do not authenticate a producer. + +A manifest rotation seals the old segment and records old manifest, new +manifest, and optional boundary-window identities before opening the new +segment. Cross-epoch comparison emits `cross_epoch_lens`; it is not a raw +delta. Adoption of `non_origin_residue_v031` is itself recorded as an epoch +break. + +### v0.3.1 unresolved boundary + +The following remain non-operational `NotImplementedError` surfaces with +named falsifiers: contact convergence, residual-primality / $DA_{geom}$ +correlation, and cadence admission from transcript text. Corpus parallel-run +conclusions and operating-state empirical validity also remain frontier. + +Additional source-level `hmmm` boundaries remain visible: + +- `constraint_governance` is an opaque readout-bearing string; +- the cadence origin collision described above is unresolved; +- `bridge_scope` compares manifest/carrier identity while its diagnostic + vocabulary is still growing; +- the kappa ledger reads open-payload tension only; +- bone emission from raw text is outside this encoder and is identified only + by the manifest's upstream emission-policy version; and +- v0.3.1 carrier equivalence sorts angle-face pairs while witness identity + retains chronology. + +## 11. Controlled goal-vector candidate For a declared goal with $d$ components, each available component state is `toward` $(+1,1)$ or `away` $(-1,1)$. An unavailable component is `NA`; a turn @@ -673,7 +978,7 @@ The sealed v0.1.0 fixture produced: This is controlled candidate-measured evidence: eight supported findings, zero falsified findings, and no canon selection. -## 11. Initial joint experiment candidate +## 12. Initial joint experiment candidate The historical v0.1 experiment also retains a transparent, noncanonical sequence candidate. For each turn $i$, phrase-hit signals @@ -887,7 +1192,7 @@ versioned in `edcm/ucns_edcm_experiments_v2.py` through `edcm/ucns_edcm_experiments_v4.py` and `experiments/results/`. None replaces the maintained baseline equations or selects joint canon. -## 12. Exact UCNS observation boundary +## 13. Exact UCNS observation boundary The current profile supplies exact ordered word-gonol observations with one unit of support per speaker turn. It retains exact Unicode source values, @@ -905,7 +1210,7 @@ Those quantities are `NA`, not zero. A UCNS observation digest establishes deterministic content identity under its schema; it is not signed producer authentication and transfers no theorem or proof status into EDCM. -## 13. Identity and reproducibility mathematics +## 14. Identity and reproducibility mathematics EDCM evidence records use canonical JSON bytes @@ -925,7 +1230,15 @@ $d(x)$ and then attached to the report. The immutable evidence file also has a SHA-256 over its exact serialized bytes. These identities detect drift; they do not prove truth, authorship, or empirical validity. -## 14. What is not yet mathematics +For `edcm.shared-stack-result/1.2.0`, `epoch_identity` is $d(x)$ over the +METAPAT canon/provenance digests, UCNS profile identity/scope/source/options, +EDCM manifest hash, and selected semantic-authority, UCNS-profile, and +measurement implementations. `result_identity` is $d(x)$ over that epoch +identity plus source evidence, the complete UCNS profile observation, EDCM +readouts, factorization evidence, and status evidence. Geometry absence remains +a typed compartment and does not become a fabricated geometry identity. + +## 15. What is not yet mathematics The following are deliberately not filled with convenient equations: