祝融说。

Both of Them Say It Has Been Received

At 12:50 on Thursday, Tang Ke showed Ye Cheng the original text of the reply R17 obtained at 11:20. After reading it, Ye Cheng told Gu Ning that the message did indeed say the checklist was received and the reception time still needed verification. Tang Ke also said this was exactly what she saw.

Gu Ning now has two people's reading accounts, but no second independent reply from the client. Both return the same original message; what is added is a re-check, not B occurring a second time for R17. The change in the number of people and the change in the original observation must be kept apart.

This chapter continues the fictional Chengwan thought experiment. The previous chapter only preserved a candidate model computation, not adopted as R17's final prediction; complete confirmation is still not obtained. Ye Cheng's reading does not turn the pending reception time into available, nor does it add accepted material for scope and payment conditions.

The source question is finer than whether a judgment repeats words. The same wording may come from different observations, and different wordings may share the same observation. We must ask how material was obtained, how it was transmitted, and at which layer new support is added—not merely count by speakers' names.

A Source Can Denote Four Different Positions

Tang Ke is Gu Ning's direct route to the current message; the client is the issuer of the original utterance; the agreed channel supplies the received material; and Ye Cheng is a later reader of this material. All may be called "sources" in everyday language, yet they occupy different stages.

If the prediction uses the observation "checklist-received message," the statistical unit cannot become four sources each giving one B. One act of issuance, preserved by the channel, obtained by Tang Ke, and re-checked by Ye Cheng, still revolves around the same original record. The number of stages is not automatically the number of pieces of evidence.

The path can be written as: the client's original utterance enters the agreed channel; Tang Ke obtains it and hands it to Gu Ning; later it is handed to Ye Cheng to read; Ye Cheng tells Gu Ning what he read. This is not a ranking of each person's credibility but a way for support to return to the actual object.

Gu Ning's own candidate model, in turn, organizes judgment downstream of this path. That she computes a scenario, that Tang Ke agrees, and that Ye Cheng understands the computation do not give the same model output three external validations. Keeping raw material, reading, and inference separately preserved is how one knows which layer truly added information.

Different Names Do Not Prove Different Observations

As a transmission comparison: suppose Tang Ke condenses the original utterance into a short summary, another member reads it and relays, and a third hears it from the second and expresses agreement. All three may be sincere, and the original utterance may be true, yet their shared basis is still one summary.

If the summary mistook "received" for "accepted," the latter two may continue explaining along the same error. They did not collude, nor did they say they were lying; sharing the intermediate material suffices for the error to enter together. A larger number of people cannot offset this provenance problem.

Conversely, two people's differing wording does not guarantee a new observation. If one says "there has been progress" and the other "it should be arrangeable," both having read only the original B, these may be merely two interpretations of the same material. A richer descriptive vocabulary has not produced another condition for the client.

What Tang Ke hands Ye Cheng in the main line is the original text, not a summary proven erroneous. The shared-misreading comparison illustrates a mechanism the source graph can check; it does not record a hypothetical miswriting as a problem that has occurred in Chengwan.

Re-Checking Still Has Its Own Value

Ye Cheng's second reading can help Gu Ning check whether the original utterance dropped words, whether B's meaning is accurate, and whether the pending clause is preserved. If a relay omission is found, Gu Ning can correct the material's correspondence. One cannot declare the re-check worthless merely because it is not an independent client reply.

But the value corresponds to reading and recording quality. It is not the same as obtaining another B that appears independently under A and not-A. Gu Ning can be more confident that she correctly understood the original message, while still not being confident that the client will accept the full first version within the window.

The same original text also does not prove that the issuer's statement matches reality. Both readers reading correctly does not mean the checklist has actually been verified item by item, still less that arrangements will not change later. The original utterance's content, its truth, and future events remain different objects.

If one wanted to build a numerical model for how re-checking reduces misreading, one would need to state separately the reading error, the shared material, and detection methods; this chapter has no such inputs. Preserving the re-checked object is therefore more suitable than carelessly adding another likelihood ratio.

What Probabilistic Independence Actually Requires

Independence in the probabilistic sense is a relation among events within the same model, not the mutual non-influence of two personalities, nor two documents being stored in different places. If the observations are B and C, independence requires the joint probability to equal the product of the separate probabilities.

In updating, what matters more is often conditional independence. Given A, do B and C still provide additional appearance information about each other; given not-A, is it the same. Only when the corresponding relation holds in both comparison classes can the two likelihood ratios, conditioned on neither the other, be multiplied directly.

The relation given A is written:

$$ P(B\cap C\mid A)=P(B\mid A)P(C\mid A) $$

A given must have positive probability, and the not-A side must also be checked separately. For the definition of conditional independence and the fact that it and unconditional independence do not guarantee each other, see the independence section of the MIT Introduction to Probability textbook summary.

The terminology does not supply the relation on site. Two observers working separately is only one piece of material for checking an independence assumption, not proof that the definition already holds; they may still depend on the same device, the same condition, or the same communication entrance.

Duplicate Messages and Independent Messages Multiply Differently

As an explicit hypothetical comparison, let C be entirely a duplicate of B; in the model the two are the same observation. If B's probability under A is three-fifths and under not-A one-third, then B and C occurring together are still three-fifths and one-third respectively, not the two probabilities each squared.

The joint observation's likelihood ratio is still 1.8. If one mistakenly multiplies according to two conditionally independent items, the joint probability under A becomes nine-twenty-fifths and under not-A one-ninth, yielding a ratio of 3.24. The multiplication itself is correct, but the model described has been swapped.

Another independent comparison can explicitly assume that B and C are conditionally independent under both A and not-A, with their separate message probabilities also taking the two numbers just given. Only then do the squaring and the ratio of 3.24 match the setting. The two models share the single-item probabilities yet have different joint-occurrence relations.

This chapter does not posit that Chengwan actually obtained C, nor fit Ye Cheng's reading into this independent model. The comparison shows only that knowing each clue's separate appearance probability is still insufficient to determine their combined role; the joint relation cannot be computed from the number of names.

How to Preserve Old Conditions When There Is a New Observation

If B has already been observed and C is then obtained, the correct continuation is to compare how C appears given B and A, with how C appears given B and not-A. When the corresponding conditions and denominators are definable, one can write:

$$ O(A\mid B,C)=O(A\mid B) \frac{P(C\mid A,B)}{P(C\mid\neg A,B)} $$

This continues updating by the new observation without first assuming B and C conditionally independent. If the independence relation has grounds, the added ratio can be simplified into C's ratio without conditioning on B; if not, B stays in the condition. For the independence simplification of sequential updating, see MIT 18.05, Lecture 12.

A C that entirely duplicates B is certain to appear once B is known; both given conditions yield one, so the incremental ratio is one. It will not change the observation's relative support for the target again. What is discussed here is exact duplication within the model; one cannot compress all superficially similar messages into the same event without checking.

If there are no probabilities for C under the two conditions given B, Gu Ning can first state the added content and the possible relation, without entering a fabricated weight. Preserving a dependence does not prove updating cannot proceed; it states what kind of correspondence the further computation requires.

Different Materials May Also Share Measurement Error

As a device comparison, two members separately read a reception-period table, so the acts of obtaining material look different. If the table itself is an outdated version, the two may consistently report a period no longer applicable. Each reading the same old table correctly cannot offset the table's shared problem.

If the two tables were copied from the same original schedule, different filenames and responsible persons still cannot guarantee independence. One must re-check the original schedule's version, copy time, and applicable objects. Shared measurement or preservation methods may make the two materials' biases appear together.

Conversely, independent re-checking may also discover a problem at the common entrance. If someone stops merely re-reading the old table and checks the original schedule's updates, this may add version material. Distinguishing independence is not about rejecting common sources wholesale, but about knowing at which layer the new support occurs.

These comparisons do not obtain an available reception period for R17. The main line has only the pending-verification statement; the device and schedule example illustrates the common entrance to be checked along the source path, not a record that Chengwan has discovered the table outdated.

Without Relaying, There May Still Be Common Conditions

Even if two observers do not pass material to each other, their observations may depend jointly on some state. If the same matter's degree of preparation affects both the checklist reply and the period statement, B and C may be correlated; knowing one changes the judgment about the other. However, the existence of such a common condition at the level of description does not automatically mean the two observations are statistically dependent within both outcome groups, nor that they cannot be simplified under stated assumptions.

Given A, whether the common state is already fully explained by A cannot be assumed directly either. A indicates only that complete confirmation holds within the original window; it does not guarantee that all A objects had the same preparation process. Not-A likewise has different origins within it, a limitation already preserved in the previous chapter.

Updating therefore requires checking whether important dependence still exists within the two outcome groups A and not-A, not merely checking that B and C look weakly related overall. Condition changes can change event relations; an observation in one scope cannot hold for another given scope.

This only raises the mechanism that needs checking; it does not, on the possibility of a common condition, declare all sources permanently dependent. A model may adopt a justified simplification, but should state its scope, so that an important dependence discovered later can be returned to and revised.

The Two Independences Cannot Be Merged into One Sentence

Saying in daily life that Ye Cheng judges independently may mean only that he did not answer with an eye to Gu Ning's conclusion; probabilistic conditional independence concerns the joint distribution of two observations given the outcome. The former division of labor may be reasonable and still not automatically supply the latter's multiplication rule.

Likewise, two members not knowing each other may reduce mutual relaying, but cannot exclude shared original data, a common device, or environmental conditions. Two who do know each other need not make every observation identical; the degree of familiarity cannot become a mathematical parameter directly.

Gu Ning can record whether each first saw the other's conclusion, which materials were used, and whether there was a common entrance, then treat these as support for or limits on the independence assumption. She need not affix a permanent label of independent or dependent to a person; the judgment targets this round's material and use.

This lets division of labor and evidence coexist. Independent work is worth preserving, and actually shared bases are also worth preserving; only by writing out both will the recipient avoid mistaking the number of expert members for the number of independent samples.

A Common Conclusion Can Expose New Reasoning

Two people using the same original utterance need not merely repeat mechanically. Ye Cheng may discover that Gu Ning compressed B's meaning too broadly; Tang Ke may point out the reception time still awaits verification. What is added is a correction of interpretation, which can make the model's scope more accurate rather than yielding another client signal.

Two competing readings may also be preserved, stating what the raw material supports and what is still lacking. If the agreement arises only because both saw the same summary, it cannot be called independent discovery; if each returned to the original and obtained the same limited interpretation, a reading re-check can be stated, but it is not elevated into a second weight for future confirmation.

The same holds for Gu Ning's computation and Ye Cheng's arithmetic re-check. Two correct computations can help find errors; obtaining the same result from the same input does not become two external observations proving the input applicable. Reasoning checks and reality-material checks should each leave their own product.

The source graph does not merely count root nodes; it must state what each step adds for which question. Making the roles concrete is how one avoids discarding genuine corrections while avoiding duplication.

How to Draw a Source Graph Well Enough

Gu Ning need not trace everyone's full social relations. A currently sufficient graph at least connects the original message, copies or summaries, obtainers, readers, and inferences; each node notes the object and time, with arrows indicating actual transmission rather than guessed connection based on agreement of opinion.

The main line can confirm that Tang Ke obtained the original reply and gave it to Gu Ning, and at 12:50 handed it to Ye Cheng to read; Ye Cheng reported the limited original meaning. If another source's provenance is still unknown, it can be marked temporarily unknown; one cannot, to make the graph tidy, attach it to the original message or draw it as another independent root.

If the same source provides observations of two different objects, their contents are still preserved separately. The same original author does not prove two observations necessarily have no increment, nor do different authors prove them necessarily independent. The graph helps identify provenance; the actual probabilistic relation still needs model and material support.

"Sufficient" means being able to answer whether this update duplicates, which entrance is shared, and what is still lacking. More material later extends the graph; one neither treats tracing all relations as a threshold no computation can ever cross beforehand, nor declares all real relations exhausted once the graph is drawn.

An Increase in Information Can First Change the Adoption Scope

If it turns out that several materials share the same original utterance, Gu Ning can narrow the claim of independent support while retaining the original utterance itself and the reading re-check. If a genuinely different observation is found, first check which condition it adds, then discuss whether the model inputs need modification.

Dependence should not be handled by blanket deletion. A common source may be genuinely reliable, just not usable as several independent appearances. Nor should every suspicious source be casually discounted by half, pretending a verified correction parameter has been obtained.

When the limited relations are unclear, one can deliver separately the confirmed original observation, the shared re-check, the unknown-provenance items, and the hypothetical conditions. This way the current judgment can keep being generated while the adoption scope matches the support, rather than jumping abruptly from great confidence to believing nothing.

This volume does not yet configure verification budgets or action investment. What is handled here is whether the judgment account can be faithful to provenance; the later volume will consider how much resource to spend and what loss to bear for a piece of new material.

How Source Checking Keeps the Feedback Entrance Open

RC understands ideas and consensus as representation formation within limited observation. Realized for this problem: multiple relays can make one interpretation more familiar and more readily adopted, yet it does not gain new real-world correspondence merely from a growing number of people.

If a shared interpretation refuses to return to the original utterance, treating whoever points out the shared entrance as uncooperative, the judgment may ossify in transmission. Conversely, allowing readers to point out omissions, letting new observations enter the correspondence, and narrowing the multiplication when the independence assumption is insufficient lets the consensus accept concrete feedback.

This chapter does not automatically call a reasonable client "evaluation alienation," nor treat all agreement as contextual contamination. Division of labor can increase testing capacity; the key is whether scope and provenance can be re-checked and whether corrections can change the actual representation—not prescribing that everyone must obtain all material personally.

These application interpretations unfold from RC's internal starting point, without using a source graph to prove that a philosophy or statistical model has been empirically verified. The graph makes limited judgment more returnable; it does not create new client acceptance.

The Forwarding Time Point Does Not Change the Original Observation's Time Point

The original reply was handed to Ye Cheng only at 12:50; one cannot say the client stated the checklist received a second time at 12:50. The graph should preserve separately the original message's acquisition time, the handoff time, and the re-check report time. The transmission occurred later, and the state the message refers to did not automatically update.

If a screenshot shows only the forwarding time, the recipient may mistake it for the original channel's receipt time. Gu Ning must return to the raw material to check; if the original time cannot be obtained, she should mark the time provenance as insufficient, and cannot adjudicate B's holding within the specified window based on the forwarding time.

Likewise, older material spread later need not be more applicable than newer material obtained earlier. New and old depend on the times of the observation and the object, not merely on who spoke most recently. Chapter 12 will concretely compare material time points; here the source graph first preserves enough temporal layers for later checking to begin.

This does not require screenshots to be forever useless. They can preserve content or help locate the original message, but which adjudication they bear requires separate checking of support. A material's serving one use does not win it all fields; when the original provenance lacks a time, the file's mere existence cannot supply the time.

The Same Issuer Has New Material Later

As a future comparison: if the client later explicitly states that the reception time has been verified, this may add the current condition and cannot be treated as carrying no information merely because the author is the same. But how the new reply relates to the original reply must be judged against the original known B and other background.

It may have appeared after the original communication advanced, rather than being a message drawn afresh from the same population independently of B. Gu Ning should preserve the content change and the time point, then ask how the added state appears under A and not-A; one can neither delete both messages wholesale because they come from one person, nor default to conditional independence because he issued two.

If the later message merely repeats the original wording, without new content or a reliable state time, the incremental role may differ again. Whether identical wording indicates recent re-verification must have material; Gu Ning cannot supply a renewed checking process for the issuer on her own.

All the above are comparisons and add no reply to the R17 main line. They keep source checking open: the same author does not decide the information content; what decides is the new observation's content, its acquisition process, and its correspondence with known conditions. A source graph both prevents duplication and must be able to admit genuine change.

Different Historical Objects Are Not Statistical Independence

The eight historical requests are preserved by request number, which suffices to prevent multiple materials of the same request from being treated as multiple objects. But different numbers only settle the statistical unit; they do not guarantee the requests share no common conditions. They may share some process, the same acquisition entrance, or similar-period states.

This book has not set whether these eight were submitted by the same client, nor whether the items were randomly drawn or mutually independent. Describing the five confirmations and the message correspondence does not require pretending these facts have been obtained; if some later estimation method needs a sample-independence assumption, its grounds and limits must be stated separately.

Source checking therefore targets not only multiple relays of the current message but also the common entrances of different objects. It does not automatically merge the eight into one, nor give some effective sample size without a model. Different requests can each preserve their outcomes, with common conditions recorded as applicability statements and further checking questions.

This connects with Chapter 3's identification of units while adding the boundary of statistical relations. Non-duplication of objects is a necessary compilation discipline, but one cannot derive estimation precision or independent multiplication from it directly. Preserving objects and preserving dependence clues are two consecutive tasks, both returning to actual material.

Provenance of the New Support

At 13:10 on Thursday, Gu Ning saves the source account. R17's original reply is still the one obtained at 11:20; Tang Ke's and Ye Cheng's readings revolve around the same material; the 12:50 addition is a re-check, adding no independent B or complete confirmation.

The candidate computation is still preserved only as a scenario, and because both read "checklist received," it is not updated repeatedly from three-quarters to twenty-seven thirty-seconds. The complete current original utterance's pending reception time carries no additional historical weight, and source checking has not fabricated a new likelihood for this part.

The account separates the original observation, the reading re-check, the inference, and the independence assumptions, preserving the shared entrance and the positions of unknown provenance. The judgment Chapter 11 yields is that the quantity of evidence is identified by observations and conditional relations, and cannot be multiplied directly by the number of people, files, or degree of agreement.

The next chapter faces inconsistent material: some original text is direct, some is newer, some concerns different objects, and some may be misread. Clear source relations do not guarantee that every content agrees. Judgment must also check quality, so as to decide which condition the conflict actually changes, rather than simply averaging several voices.