# UD native pre-event projection obstruction v0.1

**12 October 2026 UTC. EXACT formal factorization criterion and scoped source-interface countermodels; OPEN native dynamics. Constructor verification plus separate AI audit of the earlier comparison model. Physical promotion 0.** This does not assert that either formal completion occurs in nature.

## Source lock and typed question

The [Paper I review draft v1.1.1 §7.4](https://github.com/ud-tetra/UD/blob/main/captures/2026-10-07T191951Z-codex-ud-bootstrap-5170f8b8/browse/dist/papers/UD_PAPER_I_REVIEW_DRAFT_v1.1.1.md) leaves the native source of an event receipt open. [Paper II review draft v1.1.1 §8.3, II.M1](https://github.com/ud-tetra/UD/blob/main/captures/2026-10-07T191951Z-codex-ud-bootstrap-5170f8b8/browse/dist/papers/UD_PAPER_II_REVIEW_DRAFT_v1.1.1.md) proves the linear visible quotient criterion `PA=FP iff ker P is A-invariant`. The admitted `UD_THETA_FLIP_DIRECT_EVENT_INPUT_SOURCE_ADDENDUM_v0.1.md` (26 August 2026, local SHA-256 `afef7b56d187f4e6aa7dc7debd7d6fb36076f45b2630286d3716796afad93b06`, §§Event input–No claims) gives `Theta+ = P_g Theta- XOR xi`, with externally supplied `xi in F_2^3` and no flip rate, probability, or autonomous microdynamics; [the October 10 source audit](https://github.com/ud-tetra/UD/blob/main/captures/2026-10-10T170752Z-codex-theta-closure-245626d6/REPORT.md) specifies provenance and separate edge transport limits. The supplied coefficient ledger v0.39(2) (22 August, SHA-256 `1281aa8454013fbbdbcf8ada07af0aefe81014003f25a27f3929ad43afffae63`, Q156/Q167/Q169/Q173) has a native global skew chain generator and conditional hard masks, but no source of `xi` or local factor transition. The attached CRL-2 subdivision v1.0 is a governance **proposal**, not an independent review receipt.

The mathematical question is whether the currently declared native **pre-event** packet/cochain state determines the next pair state or six-edge hard mask, before consulting an external flip receipt or a post-event closure/local-transport receipt. The native chain state, pair bits, closure predicates, transport predicates, their spaces and operators remain differently typed.

## General deterministic factorization criterion

Let `N` be a nonempty set of native pre-event states, `W` a set of source completions, and `R(n) subset W` the **nonempty** set of completions admitted by a declared source contract at every `n in N`. Let `O(n,w) in Z` be the requested next readout. A single deterministic function `f:N -> Z` agrees with **every admitted completion** exactly if

\[
\boxed{\forall n\in N,\quad |\{O(n,w):w\in R(n)\}|=1.}
\]

**Proof.** If `f` exists, every completion at a fixed `n` equals `f(n)`, giving a singleton. Conversely a singleton nonempty output at each `n` defines `f(n)` unambiguously. No metric, probability, physical time or regularity assumption enters. Outside this theorem's domain, `R(n)=empty` is a separate **hold/no-source** case, not a proved no-event physical outcome. This set-valued result is the nonlinear/relation counterpart of the fiber principle behind Paper II II.M1; it is not an amendment to that linear theorem.

If `j:N -> J` is any further statistic computed only from the same native state, two admitted completions at an identical `n` also have identical `j(n)` and cannot be separated by it. For a fixed native generator `A` and chain state `c`, all pre-event jets `c, Ac, A^2c, ...` and the same pre-event trajectory `exp(sA)c` are functions of `c`. Adding arbitrarily many of **those** jets cannot resolve a branch whose cause is an independently supplied event input. This says nothing about a new coupling that changes `A`, a new source state, or a new admissibility axiom.

## Application 1: pair-state event occurrence

Fix one labeled filled K4, oriented native chain state `c in C_0⊕C_1⊕C_2⊕C_3`, pre-event `Theta in F_2^3`, and sourced frame `g=id`. The direct-input interface admits the conditional calculation

\[
\Theta^+_\xi=\Theta\oplus\xi.
\]

Consider two **hypothetical, type-correct formal source completions**, `xi_0=(0,0,0)` and `xi_1=(1,1,1)`, with distinct stipulated external providers. The interface does not itself supply or authenticate either provider. If both completions are admitted at the same native pre-state, they give distinct next pair states despite identical pre-event cochain jets. Both constant masks are invariant under the matching `S4 -> S3` action, so pair-relabeling covariance alone does not choose one. This is a logical countermodel to **derivation from the currently stated interface**, not a demonstration that two actual provider receipts or physical histories exist for one preparation. A missing receipt instead produces `THETA_UPDATE_DEFERRED`, a third operational status that must not be silently identified with a zero-flip event.

Thus **NO-GO for a theorem from the currently stated native-only inputs across all type-correct formal source completions**: the interface does not force a unique pair endpoint. A future native causal theorem or verified provider constraint could restrict `R(n)` to a singleton and reopen this branch. This no-go is about logical entailment, not a physical impossibility theorem. Until then an endpoint-derived `xi=Theta XOR Theta+` is retrospective.

The stochastic alternative is also not determined. At one fully pair-symmetric input, **conditional on an applied receipt**, define solely as formal distributions over the type-correct masks, for `p in [0,1]`:

\[
\Pr_p(\xi=000)=1-p,\qquad
\Pr_p(\xi=100)=\Pr_p(\xi=010)=\Pr_p(\xi=001)=p/3.
\]

Every such distribution is normalized and invariant under the pair action at that input, but `p=0` and `p=1` give different **nonzero-switch probabilities conditional on a receipt**. A zero mask is an applied receipt, not `None`. To represent the separate missing-receipt status, one may also stipulate `Pr(receipt=None)=1-q` and multiply each displayed applied-receipt probability by `q`, with independently free `q in [0,1]`. This changes **receipt availability** and the operational rate of recorded switches (`qp`) without identifying a physical event rate. These fiberwise examples do **not** construct a globally defined stochastic UD evolution on all native states. They are **countermodels to stochastic identification**, not UD-approved physical kernels. The direct-input source explicitly defines no flip probability, receipt-arrival law, or physical clock. Admissibility and symmetry can restrict *what* may happen without supplying *how often* it happens.

## Application 2: edge-mask factor source is separate

For a local edge, the declared readout is `h_e=C_e T_e`, with `C_e` an edge closure predicate and `T_e` an edge transport-integrity predicate. The [mask-source readiness v0.1, adversarial fixtures](https://github.com/ud-tetra/UD/blob/main/captures/2026-10-10T163105Z-codex-source-readiness-3c72f65b/REPORT.md) keeps the same **reduced pre-factors** `(C,T)=(1,1)` and unresolved primitive event token, while displaying formal completions `(C',T')=(1,1)` and `(0,1)`. They yield `h'=1` and `h'=0`. This proves no deterministic rule from **those reduced inputs alone**. It does not prove failure of a rule on a richer complete native state: a future sourced cochain-to-receipt mechanism might distinguish them. No such mechanism is defined in that audit. This is a **separate typed** obstruction; it is not obtained by identifying edge closure with `1-Theta_p` in every context. The [direct-Theta pushforward v0.1](https://github.com/ud-tetra/UD/blob/main/captures/2026-10-10T170752Z-codex-theta-closure-245626d6/REPORT.md) proves a particular pair-lift formula only after `xi` is supplied and, for hard-mask counts, under fixed local `T`.

A **predeclared fixed-structure certificate** that all relevant closure receipts and local transport predicates remain constant through an interval does prove `h^+=h^-` there. Such a certificate is additional model information, not an inference from the current cochain value or negative signed source. [Structural eligibility boundary v0.1 §§The sourced negative certificate–Adversarial contrast](https://github.com/ud-tetra/UD/blob/main/captures/2026-10-10T182115Z-codex-structural-veto-ef5beee2/REPORT.md). Nor can one universally substitute a compression of native `exp(sA)` for the internal edge map; the fixed-map countercompletion is documented in [native projection boundary v0.1 §§Why a local contractive step misses the return–Frozen-null test](https://github.com/ud-tetra/UD/blob/main/captures/2026-10-11T010749Z-codex-native-projection-c9c95ae7/REPORT.md).

## What an admissible positive repair must supply

The next proposal must declare a new source state or source law with a **pre-event** domain, causal order and retained null windows, then show that the projected next pair/edge output is single valued on every in-domain input, or give a fully normalized stochastic transition kernel with its event-count/physical-time distinction. It must state how the source state is obtained from packet/cochain/defect variables (or label it an independent axiom), how local closure receipts and typed edge maps update, and what happens under simultaneous contacts and symmetry. A future observable dictionary needs units, uncertainty, baseline and falsifier. Simply appending `xi`, the next `C/T`, or an endpoint-derived address to the pre-state relabels the answer unless their independent prior source is demonstrated.

The [bounded comparison law v0.1](https://github.com/ud-tetra/UD/blob/main/captures/2026-10-12T001121Z-codex-k4-pre-event-40c08e54/MODEL.md) is complete **after** preparing clock and fuel bits. Its independent finite audit below supports internal consistency, not the missing map from native UD state to those bits. The [OP03 producer handoff v0.1](https://github.com/ud-tetra/UD/blob/main/captures/2026-10-11T020241Z-codex-op03-producer-handoff-23f7e091/PROVIDER_HANDOFF_v0.1.md) still needs an independently generated same-carrier endpoint and all null windows for any held-out score. No target was exposed here.

## Verification and disposition

`verify.py` checks the direct-input algebra and S4 pair action over all `8*24*8=1,536` state/action/flip cases; eight conditional endpoints for each fixed `Theta`; two distinct covariant deterministic completions; 72 invariance checks for three exact-fraction conditional flip kernels; 216 checks for receipt-availability/flip mixtures that keep `None` distinct from `000`; and a separate edge-factor ambiguity. These are finite formal checks of the written source-interface reasoning. They do not establish physical attainability or replace the general set-valued proof.

**EXACT scoped:** factorization criterion and the conditional algebra/covariance cases. **NO-GO scoped:** the current direct-input interface does not logically force a deterministic native-only next `Theta`; reduced pre-edge factors do not determine next `h`; symmetry does not identify a flip/receipt-availability probability. **OPEN_GATED:** whether a *complete* native cochain/defect state supplies either transition, and whether a new constitutive source axiom makes independent predictions and a physical bridge. No AUTO_LOCK of a UD event mechanism; no empirical score; physical promotion **0**.
