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/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 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 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. 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 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.

12. 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.

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, 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.

14. 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.

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:

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:

python -m edcm.integrity
python -m pytest -q

For the controlled goal-vector candidate:

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:

change the owning source and its tests;
update this reference in the same change;
version any changed candidate or evidence schema;
preserve old sealed reports unchanged;
rerun integrity, metadata, complete tests, build, and wheel checks;
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.

EDCM mathematical reference

Authority and scope

Status vocabulary

1. Transcript and round domain

2. Common operators and text statistics

Clamp

Type–token ratio and repetition

Shannon entropy

Repeated n-gram density

Pattern density

Novelty

Bag-of-words cosine similarity

Jaccard similarity

Correction fidelity

Per-100 normalization

3. Maintained baseline vector

Fixation

Loop risk used by escalation

Escalation

Deflection

Noise

Confidence polarity

Coherence loss

Progress proxy

4. Dissonance and circuit recurrence

5. Auxiliary risk proxies

Broken return

Escalation or shutdown risk

Stagnation

Fixation and loop

6. Agent-facing projections

Turn-balance Gini

7. Alerts and risk crosswalk

8. Matrix identity and present duplication

9. Signed-ternary EDCM construction

Constraint field

Field motion

10. Implemented v0.3.1 architecture layer

Manifest and family gauge

Non-origin residue and anchors

Mass, carriers, shares, and field load

Turn and payload absence

Chronological append and reserved interaction product

Exact implemented equivalence

Validation, polarity, and epochs

v0.3.1 unresolved boundary

11. Controlled goal-vector candidate

12. Initial joint experiment candidate

v0.2 occurrence, coverage, and latency candidate

v0.3 assertion and local-scope candidate

v0.4 discourse-graph candidate

13. Exact UCNS observation boundary

14. Identity and reproducibility mathematics

15. What is not yet mathematics

Usage guidance

hmmm

Source identity and drift boundary

Usage guidance

hmmm