祝融说。

Start from an Actual Question

This appendix is a set of record structures, not a set of already-filled-in probability answers. To use it, first select a question that actually requires judgment, and save according to the corresponding relations; simple tasks can be recorded briefly, and fields can be expanded when material is ambiguous or evaluation is complex.

The field descriptions in the tables serve to organize the reader's own records; they do not require every item to have a numerical value. Unobtained, unadopted, and pending-check items should be preserved as they are; do not manufacture content just to fill a table. An empty template slot is not the same thing as a judged probability of zero.

All quantities and characters in Chengwan are fictional. The case index serves to check this book's internal continuity; it cannot become a sample for the reader's real tasks. Formulas work only on inputs satisfying the corresponding conditions; they do not make the inputs real.

Event Card: Let the Outcome Be Adjudicable First

First test whether another reader, given these conditions, could adjudicate with the same material. If they would still be answering different questions, add definitions; if the definitions are already explicit but the material is insufficient, keep the material gap open rather than continuing to widen the event until an answer appears.

R17's affirmative event is explicit and complete acceptance, within the original window, of the scope of keeping the first version, the payment conditions, and the receiving time slot; the window includes Friday 17:00 as a boundary time point. Payment arriving, repair completed, and worth taking on are other objects; their later outcomes cannot be substituted for this card.

Material Page: Separate the Original from Its Use

A piece of material can support a narrower fact yet be insufficient for a broader conclusion. A subject being direct does not mean its use is unlimited; a newer time point does not mean it automatically overrides older material. In disputes, first check by subject, version, time, and original wording, then decide on adoption.

Multiple people re-reading the same original can increase verification of use, but it does not increase the number of originals. New originals may also share the same conditions; one cannot assume mathematical independence merely because the item count increases.

Sample Page: Sets and Denominators Have Places

Record the entered scope, the obtained scope, the applicable scope, and the corresponding classification of outcomes. If display material or search filtering exists, explain how they were formed. Different scopes may overlap; quantities cannot be added together without identification.

Applicable exclusions should have object-level or field-level reasons, not be decided by whether the outcome is favorable. If material is later recovered, note the basis of acquisition and classification; a new scope can form a new table while the old table keeps its original position.

Among the eight historically comparable items, five are A and three are non-A. The non-A includes two items with no complete confirmation obtained within the window and one item that proposed modifications; they cannot be collectively called explicit rejections, nor is a specific reason that was never given to be assigned to each number.

Conditions Table: Check the Same Classification Rule

B means that, after 10:00 on each item's respective Thursday and up to 11:20, an explicit message stating the list was received arrived via the agreed channel. All eight items have material sufficient to classify B; missing material is not misfilled as non-B.

In the table, the B group has four items with three A; the non-B group has four items with two A. This is a descriptive conditions table; it does not by itself prove that requesting a reply causes confirmation. The complete fields for the actual order of receipt, and the times still pending, of each item's historical A and B remained unfilled at the end of the book; the short-window label does not substitute for chronological verification.

Adoption Page: Separate the Actual Report from the Candidates

It can be handed over in one paragraph: as of the recorded time point, for the specified event, the recorded report is provisionally adopted; the grounds and additional assumptions are open to revision; the undecided restrictions are listed concretely; reopen when the recorded changes occur. The format is not a guarantee; the content must correspond to a real task.

R17's first actual point value was the 0.5 issued at 21:20 on Thursday, with information up to 21:00. The two subjective working models had provisional values of 3/4 and 1/4, each weighted 1/2; the latter and the equal weighting were not statistically verified. It is not the 10:00 a.m. forecast, nor a direct transplant of a historical candidate.

With the higher model's weight varying between 1/4 and 3/4 while the two model values are held fixed, the weighted result ranging from 3/8 to 5/8 is this round's sensitivity range. The weight bounds are a check choice, not a proven true range, and still less a confidence interval.

Adjudication Page: Separate the Outcome from the Check Time

Save the original window, the received scope, the original content, the basis of adjudication, the check time point, and the undecided status. If sufficiently established, record it as holding; if not sufficiently established and the window has not ended, do not prematurely judge the whole future segment as not holding. If material is insufficient after the deadline, do not casually fill in a negative.

If recovered original material shows the adjudication was wrong, generate a correction relation; if a new event merely occurred later, record it separately as a follow-up rather than extending the old window. A corrected adjudication affects the corresponding scoring, but it does not change what the original forecast knew at the time.

The main line explicitly sets the corresponding receipt records as complete, with no omissions of window-relevant content, and none of the three original replies completely accepted the first version; hence Y=0. The check time is not the receipt deadline; next week's proposal has not yet formed a second version. Nor are the historical gaps resolved by the current adjudication.

Revision and Handover: Write the Changed Object Clearly

A revision record first indicates the affected layer: material use, event version, model inputs, the number, the applicable scope, or adoption status. Then it writes the new grounds, the current status, the relation to the old version, and the next question. Do not merely write that things got worse and leave the successor to guess what changed.

The successor may accept the original report without independently endorsing it, and may also form a new adoption separately. Consensus preserves the object and the checkable relations; it does not force everyone to report the same number. When the original outcome already has support, material is not denied for the sake of displaying independence.

Formula Quick Reference: Conditions Cannot Be Omitted

Conditional probability P(A|B)=P(A and B)/P(B), requiring P(B)>0. The conditional denominator contains only the objects satisfying B; one must not misread "how much of A is B" as "how much of B is A."

Let p=P(A), q=P(B|A), r=P(B|not A); then, when the denominator is positive and these conditions correspond, P(A|B)=pq/[pq+(1-p)r]. In the historical table, p=5/8, q=3/5, r=1/3, and the result is 3/4; this is a computation consistent within the same table, not an independent verification.

When 0<p<1, r>0, and the updating conditions apply, the posterior odds may be written as the prior odds times q/r. Odds are p/(1-p); the relative evidence q/r comes from comparing B under the two classes of conditions, not from B's absolute rate of occurrence. Zero-probability boundaries need separate handling; a zero cell from a finite sample must not be treated directly as impossible.

For not-B, use its own relative evidence (1-q)/(1-r), and update again when the conditions hold. In the historical example it is 3/5, not the reciprocal of B's relative evidence 9/5. When combining multiple sources, check the joint conditions; do not default to multiplying all marginal weights together.

Binary calibration is written, in the probabilistic framework adopted by this book, as P(Y=1|p)=p. Finite grouped frequencies are diagnostic material; they do not directly amount to the property having been proven. Agreement of a population mean does not complete the check for every probability group or ex-ante conditional subgroup.

This book's individual Brier loss is (p-Y)^2, with the average being the sum of the corresponding individual losses divided by the number of reports; smaller is better. The sum of squared differences over all classes in the binary case is twice that; scales and directions must not be mixed. For R17, p=0.5 and Y=0, giving an individual loss of 0.25.

The q in scoring refers separately to the affirmative probability the recorder seriously adopts; its role differs from the q in the preceding conditional formulas. The expected loss compared against q is q(1-p)^2+(1-q)p^2=(p-q)^2+q(1-q); with q fixed, p=q is the unique minimum. It does not guarantee winning every actual outcome, nor does it prove that q is already accurate.

Entry Points to Primary Sources

These links help check specific technical relations; they do not supply external authenticity for the case quantities. When using the methods in these sources, the task and premises still need checking; this book does not import any of their medical, industrial, or other empirical statistics as the basis for Chengwan.

After Saving, Do One Minimal Review

First confirm that one number corresponds to one explicit event and one issuance time point; then confirm when the material was obtained and how the outcome was adjudicated. If there was an update, check that the old version is still returnable; if there is a scope, check that the name matches its formation rule.

When preparing a summary, state the full entry set, the actual adoptions, the adjudicated, the pending, and the excluded scopes. With multiple people or multiple forecasts, identify the differing event counts at the same time; do not infer an independent sample size directly from row counts. Preserve the provenance of groupings and of weight changes.

Finally, check whether revisions target concrete relations. Sufficient adverse outcomes are not removed from the record; unknown causes are not filled with hidden stories; the current adoption does not become authorization for action. Only after completing these relations should one decide what finer statistical tools are needed.

This appendix cannot make every task immediately answerable. It lets the positions without answers also be handed over, lets the positions with answers have grounds, and lets later material, upon entering, make known what should change. This is the minimum requirement for a continuous record to be continuable.