Cancellation examination: whole-contract grade

---

Grade: void for present acceptance. Exact accepted independent weight: none. The unresolved requirement is a distinct eligible ruling on this grader's disclosed exposure. This record does not waive that exposure or authorize a tier. The inspection found the frozen report's mathematical coverage and its reviewer's independence supported by the supplied evidence; those findings are retained below for the whole commissioned subject. They do not turn this unresolved grading eligibility into an acceptance.

The report being graded records refutation-failed for the full cancellation premise P, its essential source Sections 2–5 proof, and its actual signed application interface, relative to three stated classical premises. No mathematical counterexample or missing essential P deduction was found in this grading. The disposition is not refuted-as-stated, and it does not assert proof defective; statement unresolved about the source argument.

Examination date: 2026-10-15 UTC. Mathematical subject freeze: 2026-10-15, 14:29 UTC; neutral extraction prepared at 15:09:22 UTC. Report examined: the settled examination delivered on 2026-10-15, preserved with the listed mechanical maintenance at report.md. This is a grade of that report, not a new review cycle, a repaired proof, or a grade of later text.

Roles: the report's mathematical examiner and this grader were separate fresh contexts, both disclosed as OpenAI gpt-6-astra with max reasoning. This grader was neither the source author, the reconstruction's author or collaborator, the extraction preparer, the mathematical reviewer, nor the commissioner. A shared model provider is disclosed and is not represented as different-provider independence. The source mathematics is attributed to OpenAI, Weighted dilation graphs, smooth shifted primes and totient fibers, release of 24 September 2026, an unrefereed manuscript. The project reconstruction, examination, and grading work are credited to Plasma AI.

Subject, reading, and eligibility

The complete retained mathematical package is:

Both docs/verification.md and campaign/guides/verification.md were read in full. The required Claims, Evidence, Tiers, and Project claims passages of docs/anatomy.md were read, together with the full README, campaign rules, evidence, approach-vetting, mathematical-authoring, and weaving guides. Operating pages were compared with their supplied frozen counterparts before semantic use. Generic links were not followed beyond the commissioned set.

The historical evidence was treated as inert data. The original commission, effective-settings record, configuration, mathematical inputs, relevant seed instructions, all recorded reviewer tool calls, their output/reading coverage, communication records, settlement paths, and relevant continuation receipts were inspected. The native records were parsed in full for events and calls; the mathematical write bodies were assessed through the settled report and keepers. This does not claim a word-by-word reading of every repeated runtime line or hidden compaction payload. A recorded encrypted compaction item is opaque; its surrounding primary record contains the permitted commission and the reviewer's own continuation, with no additional exogenous mathematical message. Startup record prefixes were compared with the final records.

Historical reviewer's eligibility ruling

Supported by the supplied primary evidence. The reviewer was commissioned to refute the entire P reconstruction, not to confirm the application pair. The extraction was supplied before that context began. Its three mathematical files are identical to the report's retained assets. No earlier verdict, standing paragraph, or private advocacy appears among those mathematical inputs. The small omission markers do not remove an essential deduction of P: the full relevant source Sections 2–5 accompany the reconstruction.

The initialization probe had only an acknowledgment request and no tool calls or mathematics. The distinct examination record begins with operating instructions and the full commission. Its recorded calls read the supplied extracts, permitted operating pages, and its own continuation/output. They show no source-checkout extraction, inbox/feed access, outside search, native subagent, author communication, or mathematical execution. The messages are outbound progress and delivery notices. Empty subscription records at launch, the first boundary, after startup, and closure corroborate this history; emptiness alone is not the basis of the ruling.

The original native configuration remains an intact prefix of the recorded configuration, with only the expressly permitted project-trust append. The startup and final configurations coincide. The effective recorded model and reasoning settings match the commission. The automatic closing save changes only private continuation and delivery records; no corpus edit by the reviewer is inferred from it. The closing status, descendant record, and scoped writer observation support settled delivery; the completion label itself supplies no mathematical warrant.

The preparer's historical repository gate occurred before the reviewer started. That gate output is absent from the reviewer's recorded reads and was not a mathematical input to its report. It must not be attributed to the reviewer merely because it is included in this grading packet.

Grader's own exposure and unresolved ruling

After the mathematical files and keepers had been read, this grader inspected the expressly enumerated historical launch record, retained in private provenance custody. Its preparer-gate output unexpectedly displayed standing and reading-depth summaries for unrelated claims. The display was truncated. No cancellation/P verdict or commissioner advocacy was visible in the displayed portion. No original claim page, live ledger, unlisted file, or linked source was opened. The exposure was disclosed immediately through the authorized outbound channel; the exact source, visible examples, display limitation, and receipt are retained privately. The remaining standing rows were not pursued.

No immateriality ruling is made here. In particular, the timing of the exposure and the absence of a visible P verdict are evidence for an eligible decision maker, not this grader's permission to waive it. The complete mathematical findings below remain available, but this grading record cannot be relied on as independent acceptance until a distinct eligible party applies the content test: whether the findings could only have come from the exposure, or whether the attack direction or strength of the refutation charge followed it. If that test finds material contamination, a fresh distinct grader is required. The coordinator owns obtaining that ruling and any replacement.

On resumption, the grader's own operating-configuration bytes also failed their original manifest comparison. The changed configuration was not semantically read or edited. The mathematical packet and static operating pages still matched. This separate administrative identity discrepancy was reported and remains for the operator to reconcile; a changed time allowance does not by itself identify all changed configuration bytes. It is not a change to the report being graded.

Restatement fidelity and exact mathematical scope

The report's restatement agrees with the frozen consumed statement. It keeps the following distinctions, each of which could have invalidated an apparent application-only pass.

Let $L=\log x$, $T=\log L$, and $W=\exp(\sqrt L)$. The fixed geometric data satisfy $0<a<b<c<d<0.47$, the number of small groups and the number of big groups each lie between $c_0T$ and $C_0T$ for fixed $c_0,C_0>0$, and every harmonic group mass $V_g$ lies in $[v_-,v_+]$ for fixed $v_-,v_+>0$. Small groups are arbitrary prime subsets of $[\exp(L^a),\exp(L^b)]$; big groups contain all primes in an interval in $[\exp(L^c),\exp(L^d)]$. Groups are disjoint. The data may vary with $x$. The conclusion is eventual and uniform over admissible data, with thresholds allowed to depend on the fixed parameters. It does not assert existence of groups for incompatible specified constants.

For $0<q<1$ and fixed integer $\ell\ge1$, $n_*$ removes all group-prime factors, $\omega_g$ counts distinct primes, and

$$\mathcal W_\ell(n) =\prod_g q^{\omega_g(n)-\ell} (\omega_g(n))_\ell/V_g^\ell,$$

with the factor zero when $\omega_g(n)<\ell$. Endpoint coefficients have the full form

$$F_0(n)=\sum_{mpr=n_*} \alpha_m\chi_0(m)m^{i\sigma_0} \mathbf1_{p\in I_p,\ P^-(p)>W}p^{i\sigma_1}c_r.$$

All factor and summation variables here are positive integers, with $P^-(1)=\infty$. In particular $p$ is an integer, not a prime variable. Fix $C>0$. The interval $I_p$ is any interval contained in $[x^\tau,x^\eta]$, and $0<\tau<\eta<1/4$ are fixed. The original $\alpha_m$ is supported on $W$-rough integers, and $|\alpha_m|,|c_r|\le L^C$. The residual $c_r$ is arbitrary complex; it has no roughness, distribution, or multiplicativity hypothesis. The modulus of $\chi_0$ is at most $L^C$, and the real $\sigma_0,\sigma_1$ have absolute value at most $L^C$. The two endpoints may have unrelated sequences, intervals, characters, and twists within these common bounds.

On one endpoint only, the original restricted $\alpha$ satisfies

$$\left|\sum_{m\in I}\frac{\alpha_m\chi(m)m^{iu}}m\right| \le L^{-B} \qquad(\mathrm D_B)$$

for every interval $I\subset[1,x^2]$, every character of modulus at most $L^B$, including principal and imprimitive characters, and every $|u|\le L^B$. It is not a discrepancy condition on an arbitrarily altered convolution coefficient.

For each fixed desired saving $D_0$, fixed outer bounds and cutoff constants, one fixed sufficiently large $B$ gives

$$\left|\sum_{z>0,\ z+k>0} \frac{\Psi(z/Z)}z z^{ia_1}(z+k)^{ia_2} \overline{F_0(z)}G_0(z+k) \mathcal W_\ell(z)\mathcal W_\ell(z+k)\right| \ll L^{-D_0}.$$

The ranges include both integer signs $k\in\mathbb Z$, $0<|k|\le L^C$, $xL^{-C}\le Z\le xL^C$, real $|a_1|,|a_2|\le L^C$, and smooth $\Psi$ on a fixed compact positive interval with $\|\Psi^{(j)}\|_\infty\ll_j L^{C(j+1)}$. All these data are uniform after the fixed bounds are chosen. Interval restriction and conjugation of the original discrepancy sequence are legitimate. A further fixed twist is paid for by the eventual choice of $B$; the report does not claim unchanged-exponent discrepancy under arbitrary new twists.

The complete endpoint class, rather than its special application pair, is used in the Section 5 inspection below. In particular, the reciprocal convolution and sparse Gram arguments retain arbitrary $c_r$, and the rough-integer estimate remains uniform on every $I_p$, including intervals containing one integer or none.

Full source-proof coverage

The following rulings assess the proof and independent reasoning already in the frozen report. They do not insert a replacement proof. The source result numbers refer to the retained Sections 2–5. Each row was checked against the report's deduction census and the indicated keeper or bridge calculation, rather than accepted from the census label alone.

The multiplicative large sieve, source Theorem 2.3, is not used by this chain. Its statement was read, but no proof acceptance is claimed. Historical comparisons in the source bibliography do not replace the checked projection, sieve, moment, or memory deductions. The order of dependence is acyclic: elementary Section 2 bounds; conditional transfer in Section 3; its ideal antecedent in Section 4; Section 5 endpoint and time estimates; P; then the application interface.

Weakest steps and strongest refutation attempt

The report independently rederives three consequential families of steps. Their warrant is the retained calculations, not their agreement with a final source formula. The following checks explain why the derivations address the failure surfaces they claim to address.

Memory transfer and a dead-pivot collision

The first-prime expectation in (M1)–(M3) uses a single residue throughout a lifespan. Giving each visit an independent residue would be a different model. Likewise, giving every visit a new $1/p$ factor would create false decay. The keeper instead has one fresh-birth measure and deterministic damping during the intervening visits. Its factorial adjoint accounts for ordered retrievals and unordered continuing memory; the pending-residue coordinate has counting measure. These conventions agree with the source's absolute row and column bounds and with reversed stores.

The rare-transfer argument has a concrete injection. Conditional on the eligible big data and free labels, an omitted small product $U$ is one of $\binom{J+\ell}{\ell}^{|\mathcal S|}$ distinct integers. Each is smaller than any relevant big prime. The congruence

$$r\pm kD_{\mathcal B}F/U\equiv0\pmod p$$

therefore permits at most one $U$ per pending particle, with no sign restriction. Conditioning is legitimate because the coefficient depends only on the big labels. This supplies the improved row estimate; a column estimate alone would not establish the stated operator bound. The clean estimate independently checks that small-state maps and pending contractions do not introduce a later-$J$ dependence into the target ideal exponent.

The strongest attempted refutation is the global distinctness restoration. An early numerical prime may disappear from memory and be reborn much later. Simply deleting all colliding paths by an absolute union bound is inadequate: $\log P_*=L^c$ is smaller than $N\log L$, so a single $P_*^{-1}$ cannot absorb an absolute path cost $L^{CN}$. This is an actual failed estimate, not a counterexample to P. Both the failed bound and the successful distinction are already in the submitted keeper.

For equality rank $r$, the number of affected birth addresses is at most $2r$, and the total absolute partition coefficient is at most $A_*^{2r}$, where $A_*$ is polynomial in $L$. Large rank pays a fresh-atom factor for each nonpivot birth. Retaining a pivot value in chronological conditioning does not require it to remain in the live state; uniform absolute transition bounds give

$$L^{C_h(N+1)}(C/P_*)^r.$$

Small rank is handled differently. Fourier phases representing equality are attached at the two births. They do not propagate a dead prime through unmodified state operators. Only the affected birth operations lose their signed estimate; whole pattern sums and symmetrizations remain on the other edges. The bound is

$$O\left(L^{(-G+C_v)N+C_v+2r(G+C_a)}\right).$$

With $r_0=\lceil C''N\log L/L^c\rceil$, $r_0/N\to0$. Above $r_0$ the fresh-atom factors dominate the absolute path cost; below it the modified-edge cost and $A_*^{2r}$ are $L^{o(N)}$. Choosing $G>E+C_v+3$ first and $C''$ large makes both sums negligible against $L^{-EN}$. This is the retained source argument and its independent rederivation, not a missing step supplied by this grade. The attack therefore fails for a reason that applies to the whole path family, including both orientations and repeated numerical values.

The return to integer roots is also essential. Active-prime damping is removed before the relative CRT/Bonferroni estimate, so a potentially tiny deterministic factor is not lost in an absolute error. The subsequent Gram-trace inequality uses the coefficient norm in the unnormalized $u_n$ expansion; it does not mistakenly assume equal or unit fiber norms. These checks close the two ends of the transfer, beyond proving only an ideal-label cancellation statement.

Arbitrary tuple tests and concentrated cells

The tuple-to-product estimate in (I1) follows by Cauchy–Schwarz on each fiber. Repeated labels affect the fiber probability, which is bounded by $L^\kappa/n$, rather than justifying a restriction to product-dependent tests. The integer bilinear estimate then applies to the collapsed coefficients in their actual norms. This rules out a change of test class hidden in the comparison.

For a retained log cell of mass $\nu$, the comparison kernel includes $1/\nu$. In conditional probability the character Gram matrix has diagonal one and off-diagonal error $O_D(\nu^{-1}L^{-D})$. Returning to original probability multiplies both squared norms by $\nu$; it does not create an additional inverse-cell-mass operator loss. The cutoff $\nu\ge\xi$ and the later choice of character-estimate precision control the Gram norm.

A concentrated test in a discarded cell is not handled by claiming that restriction to a small set has small $L^2$ norm. The retained proof uses

$$\mathbb E\bigl[\mathbf1_E|f(X_B)g(X_A)|\bigr] \le \mathbb P(E)^{1/2}\|f\|_2\|g\|_2,$$

because the two full tuple spaces are independent. In the asymmetric construction they become separated after conditioning on the other blocks. An arbitrary joint test would invalidate this use; such a test is not the conditional object in the proof. This distinction resolves the report's concentration attack without removing arbitrary endpoint tuple functions.

For rational major frequencies the primitive character list reproduces every induced character on the large-prime products, which are units. The error includes both matched log products and the kernels' absolute masses. For larger denominators the integer bilinear estimate applies to both the raw and projected tests. The ordered choices in (I8) therefore cover all additive frequencies, not just the major arcs.

Finally the symmetric projection fraction is exactly $(j)_m(M-j)_\ell/(M)_{m+\ell}$. Its bound comes from maximizing $u^m(1-u)^\ell$ on $[0,1]$; it is not inferred from a neighboring count. Alternating cancellation is an identity on the nonexceptional components. The full-probe components are combined before taking absolute values, avoiding a spurious growing subset loss. These facts substantiate the complete ideal comparison, including entangled tests.

Mellin reduction and the complete endpoint class

The Fourier-to-Mellin step keeps the center of the smooth window in a fixed positive compact range. Writing $h=H/Y$ and changing variables to logarithmic coordinates gives the normalization $H^{-2}Yh^2=Y^{-1}$. The replacement of the local kernel has a controlled squared error, and the conversion from $Y^{-1}$ to reciprocal coefficients keeps the smooth factor $w/Y$ in the separation. It is not a pointwise bound on an oscillatory sum obtained by discarding that factor.

Extracting one small mark leaves a four-factor reciprocal polynomial. The small-prime factor has length at most $\exp(L^b)$, the long rough-integer factor has support at most $x^\eta$, and the remaining factor has length $U=Y^{1-\eta-o(1)}>Y^{0.6}$ for every allowed $\eta<1/4$. The residual coefficients retain only their stated bound and fixed divisor-moment square norm. No cancellation or roughness of that residual is used.

There are two different high-time mechanisms. Outside the exceptional small-prime set, its logarithmic saving combines with an ordinary mean-square bound for the other factors. On the exceptional set, the growing moment counts $Y^{o(1)}$ occupied unit intervals. That count by itself is too large to multiply by any fixed logarithmic saving. The report explicitly avoids that invalid estimate: the sparse residual Gram kernel is bounded by

$$\frac{U}{1+|t-t'|}+Y^{1/2}.$$

Unit separation bounds the first term's row sum by $O(U\log Y)$, while $Y^{o(1)}Y^{1/2}=o(U)$ controls the second. Combined with the actual residual square norm, this bounds the sum of interval suprema by a fixed logarithmic power even for adversarial complex residual coefficients. The long factor's saving is then sufficient. This is the load-bearing protection of the entire endpoint class, not only of the residual appearing in the application.

For that long factor, the block sieve has nonnegative overcount and level $D=W^{4h_0+2}=x^{o(1)}$ with the stated growing even truncation $h_0$. After character-class splitting the long progression length is still a positive fixed power of $x$. At lower oscillatory times the first derivative test applies. At higher times finitely many overlapping derivative ranges, followed by at most $K-2$ differences, reach a second derivative in the allowed range. Each intersected interval remains an interval, so the estimate is uniform under all further restrictions of $I_p$. Negative times only reverse the derivative sign; the first-derivative interval adjacent to zero is then $(-1,0)$. Choosing the high-time threshold above the fixed endpoint twist prevents $t+\sigma$ from being near zero there. No short-interval asymptotic for rough integers is assumed.

The remaining low-time range uses $(\mathrm D_B)$ on the original $\alpha$, after interval intersections and all fixed character/frequency costs. It does not use it on the residual or on the whole convolution. The three terms in (F18) have exponents

$$-2A_s+K_1,\qquad -2A_\ell+K_2, \qquad -2B+B_0+K_3.$$

The fixed losses are determined before choosing the final $B$ and proxy precision. The report's choices make each term smaller than the required target. Thus arbitrary intervals, all characters, unrelated endpoints, and both signs are genuinely covered by the retained derivation.

Physical lift and actual signed application

The physical lift is checked before accepting the application. Its endpoint norms use fixed convolution moments and the harmonic sum of marked lists; the exponent needed before $J$ is selected is independent of $J$. Removing shared labels turns their normalization into harmonic draws and produces exactly the marked weight for the raw pattern. Overlaps with a shared prime cost a very small atom. When a free prime divides both endpoints because it divides the shift, one divides the integer variable by that prime and uses the divisor norm; treating the two divisibilities as independent would be wrong. The report uses the former argument. These steps justify transporting the proved operator estimate to the actual shifted correlation.

For the application, expanding the same square gives

$$mn=2eh-1,\qquad m'n=2eh'-1,$$

and, with the report's sign convention,

$$m'-m=-2ek,\qquad h'-h=-kn,\qquad mh'-m'h=k.$$

Consequently $z=m'h$ and $z+k=mh'$ are both positive. The converse also holds with both signs under the stated roughness, $0<|k|<W$, $m'\equiv m\pmod{2|k|}$, and $e=(m-m')/(2k)>0$. From $m(h'-h)=-k(2eh-1)$ and $(m,k)=1$ one recovers a positive integral $n$. No extra assumption $(m,m')=1$ is needed or silently imposed.

The exact pulled-back variable is

$$\frac nV=\frac1V\left(\frac{(m-m')z}{kmm'}-\frac1m\right).$$

The $-1/m$ term is retained. Both rough variables are units modulo $2|k|$, so character orthogonality uses all characters with the factor $1/\varphi(2|k|)$. Smooth separation has fixed logarithmic costs after the diagonal parameter is selected; interval restrictions remain on the original $\alpha$.

The actual endpoints in the report have the same restricted $\alpha$, the same rough-integer interval $I_{**}$, and the same conjugated residual:

$$\begin{aligned} F_0(v)&=\sum_{mpr=v_*}\alpha_m\chi(m)m^{i(\varrho-\xi_2)} \mathbf1_{p\in I_{**},\ P^-(p)>W}p^{-i\sigma}\overline{c_r},\\ G_0(v)&=\sum_{mpr=v_*}\alpha_m\chi(m)m^{i(\xi_1+\varrho)} \mathbf1_{p\in I_{**},\ P^-(p)>W}p^{-i\sigma}\overline{c_r}. \end{aligned}$$

Conjugating the first endpoint supplies the conjugates required by the square. With $a_1=\varrho+\xi_3$, $a_2=-\varrho$, and $\Psi(t)=t\psi_Z(t)$, the separated unweighted correlation is exactly $Z$ times the harmonic P sum. Missing that factor would invalidate the application's claimed saving. The bound on $I_{**}$ is a fixed $0<\tau_*<\eta_*<b_*/4<1/4$, so it lies in the full endpoint class.

The slot construction's growing number of cutoffs has total Fourier mass bounded by a fixed power of $L$. Its early frequency and coefficient costs are independent of the later diagonal threshold $K_0$. The leftover small band gives $EL^{-C_s}\le e\le E$ with $C_s$ fixed before $K_0$. The diagonal estimate uses a fixed divisor moment, allowing $K_0$ to be chosen before the later separation precision. The resulting order is fixed geometry and early exponents, then $K_0$, then separation costs and $D_0$, then P's $B$, then proxy precision. These are the particular early bounds needed for the P interface; checking them does not certify the separate E estimates or the whole application theorem as an unconditional result.

Premises and source boundaries

The dependency census was independently derived from the frozen statement, proof, and consequence sentences on 2026-10-15 UTC. No established native L-claim is consumed. P and source Theorem 5.1 are targets, not premises of their own reconstruction. The quoted definitions are well-defined using the absolute estimates, without assuming later cancellation. Therefore no live native-claim ledger read is needed or authorized. The unrelated historical standing summaries in the grader's exposure were not used as premises.

There are precisely three designated non-elementary external boundaries:

For each boundary the statement and application were checked in the supplied transcription. The original cited text, its proof, and the bibliographic/PDF fidelity were not independently read. The original commission expressly allowed these as exact classical premises. The report is therefore honest about the relative scope it claims; it does not present unread classical proofs as independently verified. No essential same-paper deduction is moved to that boundary by this grade.

Finite character orthogonality, CRT, elementary Dirichlet approximation, Fourier inversion/Plancherel, Cauchy–Schwarz, and the displayed Hilbert-space inequalities are used in their explicit standard roles. The report reconstructs the needed sieve, projections, moments, and memory estimates instead of importing stronger results under the names in the bibliography.

Source Section 6 is absent. Accordingly the assertion that the signed application equals the source's Theorem 6.1 with precisely the stated changes remains unverified historical source fidelity. The report explicitly says so. Its direct signed identities and P substitution do not depend on that equivalence. This is a real retained limitation, but it is not missing Sections 2–5 warrant for the commissioned P reconstruction. A claim of that historical equivalence would require its own permitted exact Section 6 input and examination.

Report-contract rulings

These are content and historical-reviewer rulings. The unresolved eligibility of this grader prevents them from carrying independent acceptance at present.

Canonical failure modes

Named patterns

Erdos-specific checklist

The neighboring evidence-coverage discipline is met by the source-by-source mapping and the complete retained calculations. Correlated-sample adjustment is inapplicable because no statistical inference is made. Grading this report does not constitute a second independent mathematical review cycle, so it does not claim a second disjoint cycle's reliability weight. The requirement for a structurally different computational batch route is also inapplicable.

Execution, reconstruction, and presentation findings

The report and its README assert a mathematical reading/rederivation route, not an executable mathematical verifier. The primary command record confirms that no mathematical program or diagnostic was run. Consequently there is no mathematical execution result requiring a numerical reproduction, no missing mathematical implementation, and no assertion of an installed Python or project-package environment to validate. This grader likewise used no mathematical execution. No program was reconstructed from historical writes and run, and no historical command was replayed.

The reviewer's administrative package checker read exact input bytes, relative links, descriptions, table shapes, and equation/checklist inventories. Its initial predicate classified every line beginning with a vertical bar as a table row, falsely rejecting two displayed absolute-value formulas in the ideal-comparison keeper. The corrected predicate requires table-row framing. The original failed checker, its failed receipt, corrected source, and successful outputs are supplied. The primary record also shows a rejected duplicate-target checkpoint patch and its subsequent successful replacement. These are actual disclosed failures; neither is a missing analytic estimate or an unexecuted required mathematical check. Their success counts carry no mathematical weight. This grade inspected the code and primary outcomes; it does not claim to have replayed that administrative checker verbatim.

Exact displayed-output comparisons substantiate the reviewer's full reading of the three mathematical extracts and both verification guides. An initially truncated evidence-guide display was subsequently displayed in full. A later large source/application reread also truncated, but the full earlier source reads and a smaller application reread supplied the affected content. Merely requesting an unseen file would not establish reading; the ruling here rests on the recorded displayed bytes and the retained reasoning.

There is a minor presentation defect in the submitted keepers: four literal carriage-return bytes occur where a roman-font escape was intended. They label the big-prime product in the memory keeper, the two cell indicators in (I3), and occupied intervals in (F13). The surrounding prose and corresponding source formulas uniquely specify these indices. No missing bound or new hypothesis is supplied by reading those labels in that context. The submitted mathematical content is retained; the record index identifies the purely mechanical typesetting corrections in the filed copies. A filing owner may document a purely mechanical typesetting correction while retaining the examined snapshot; this grade performs no such correction and the format checker did not prove the mathematics.

The eight mathematical delivery files are preserved at the paths above, with only the path and typesetting maintenance listed on the record index. There are no code edits or changes to the mathematical assertions or checks. The reconstruction instructions give the complete retained route. Administrative parsing concatenated the listed native-log parts with no separator into private scratch; those copies neither enlarged the read set nor became mathematical inputs. Exact scripts, outcomes, custody comparisons, and the exposure/configuration disclosures remain in private accompaniment.

Accepted weight and unfinished obligations

The whole-contract disposition of this grading record is void for present acceptance, with zero accepted independent mathematical weight. It must not be cited as an unqualified PASS or used to promote P. This is the precise consequence of leaving the grader's exposure unresolved, not a mathematical refutation of P or a finding that the frozen report omitted its full endpoint class. No favorable outcome is a completion condition for this assignment.

The retained content findings cover the full P statement, every essential deduction in supplied source Sections 2–5, both signs, and the actual signed application interface, relative to the three quoted classical premises. If a distinct eligible ruling permits these findings to be accepted, that is the maximum scope available from this report. It would still not establish any proxy's $(\mathrm D_B)$, the separate E estimates, an unconditional Problem 824 conclusion, or a second independent review cycle.

The remaining obligations have separate owners and meanings:

No further essential P range or same-paper inference was identified as missing from the frozen report. The coordinator owns intake and allocation of every remaining obligation; the project owner retains them if this commission ends. The unchanged keepers, including the useful failed absolute collision estimate, remain reusable regardless of the eligibility ruling or any later acceptance.