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Claim C10 · formal · entrylib:2026.000003@v2 · 2026-11-11

Corrected · 11 November 2026 at 11:22 UTC

The proofs of C1, C2, C5, C6, C8, C10, C12, C14, C16 and C19 were checked by an independent agent on a second model (contributor P6; reports in artefacts A10 and A11). Its first round found five proofs that showed less than their claims stated; these claims are corrected to what is proved: C2 completes its argument with the normal-variance case, C5 states its condition as a nonzero $\mathbf w'\mathbf F^{i-1}\mathbf g$ and its conclusion for the objective and the variance, C10 states the conditions of the interval and that its bound is a quantile of the size distribution, C14 states the derivation of the sign (the sign printed by Svetunkov and Boylan, 2023, is in its relation), and C19 is stated for ETS(M,N,N) at horizons of two or more. The second round confirmed all ten in full. C14 rests on a formal proof (new evidence E15, definition D32) instead of an argument; D4 defines the term of each zero without presupposing its sign. Smaller precisions: C1 (positive sizes), C6 (the error mean enters the propagation through g), C8 depends on C15, C16 (alpha nonzero). Relations name references (B5-B7 added), and C1, C3, C6, C7, C9, C10 and C11 relate to the earlier work they extend or supersede. No claim ID changed.

By Ivan Svetunkov (ORCID 0000-0001-7826-0281)

The observed-data likelihood of ADAM and iETS with unobserved periods · C10

Principal claim C10 of this claimset (Svetunkov, I. (guarantor), 2026), with what it rests on. Read the whole claimset.

Copies a message for ChatGPT, Claude or Gemini: paste it there.

The message

Read https://entrylib.org/p/2026.000003/C10, one claim of a research paper with the evidence it rests on. Tell me briefly what it says and how well it is supported. If you cannot open the link, tell me instead of guessing. Then wait for my questions.

The claim

96C10 · formal · novelty: new, by the authors · no close match on EntryLib

For a model with an occurrence part, occurrence probability ptp_t and positive sizes, a prediction interval [0,u][0,u] of the demand with coverage c>1−ptc>1-p_t that counts the zeros as covered has as upper bound uu the quantile at level (c−(1−pt))/pt(c-(1-p_t))/p_t of the distribution of the demand size, whose mean, the conditional mean of the size, is the size forecast μ^t\hat\mu_t, not the demand forecast ptμ^tp_t\hat\mu_t.

Scope: population: models with an occurrence part (iETS, ADAM); conditions: prediction interval of the demand of the form [0,u][0,u] that counts zeros as covered, coverage c>1−ptc>1-p_t, Bernoulli occurrence independent of a positive continuous demand size · Proof: E12 · Assumes: C31, C32 · Extends: B4 · Verification: checked by an agent

Evidence

E12 · formal · cited by C10

Analytical derivation in the source draft (artefact A1).

Foundation: Kolmogorov probability axioms · Assumes: C31, C32

  1. P(0≤yt≤u)=(1−pt)+ptFz(u)P(0\le y_t\le u)=(1-p_t)+p_tF_z(u) for positive sizes and occurrence independent of the size (law of total probability; from C31, C32)
  2. Setting it to cc with c>1−ptc>1-p_t gives Fz(u)=(c−(1−pt))/pt∈(0,1]F_z(u)=(c-(1-p_t))/p_t\in(0,1], so uu is the quantile of the size at that level (algebra; from E12.1)
  3. The size has mean μ^t\hat\mu_t, the demand E⁡(otzt)=ptμ^t\E(o_tz_t)=p_t\hat\mu_t (independence; from C31)

Assumptions

C31 · theorem_condition · unchecked

In the intermittent demand model the occurrence oto_t is independent of the potential demand size ztz_t. Rested on by C10, E12.

C32 · theorem_condition · unchecked

The potential demand size ztz_t has a continuous distribution, so that P(zt=0)=0P(z_t=0)=0. Rested on by C10, E12.

Context

Extends B4 · own earlier work · from C10
Svetunkov and Boylan forecast intermittent demand as the product of the occurrence probability and the forecast demand size.

Artefacts

Score

Scores are computed by rules from the claimset file (EntryLib rubric 0.2): they check the record, not the science, and may change as the rubric and reviews develop. The rubric.

C10: 96, High

Novelty: new, by the authors · no close match on EntryLib

  1. −3 Open problems Assumption C31 is not checked: In the intermittent demand model the occurrence $o_t$ is independent of the potential demand size $z_t$. To remove it: Test the assumption, or analyse how sensitive the claim is to it.
  2. −1 Open problems Assumption C32 is not checked: The potential demand size $z_t$ has a continuous distribution, so that $P(z_t=0)=0$. To remove it: Test the assumption, or analyse how sensitive the claim is to it.