Why Can Three Geometric Rules Recover Nearly 90% of Jiayi Jing Acupoint Indications?

If more than three hundred acupoints each had an independent set of indication rules, the best way to understand the Zhenjiu Jiayi Jing might simply be to memorize them one by one.

But if many indications are repetitions of only a few geometric relations, the problem changes completely.

What we really want to find is: what is the smallest number of rules needed to explain the largest number of “acupoint–specific symptom” relations?

This is a classic razor problem.

First make the denominator clear

This round does not use “how many times a symptom occurs” as the denominator.

The formal calculation uses 625 unique acupoint–specific-symptom pairs that can be independently localized in space. For example, “Jinggu–headache” is counted as one pair even if it appears repeatedly in the text.

This prevents high-frequency symptoms in the ancient text from inflating model performance.

For each of these 625 pairs, we ask whether each geometric rule can independently include the symptom’s spatial domain in its prediction.

Rule 1: equal-distance phase equivalence

The strongest current coverage comes from RULE_05, equal-distance phase equivalence.

Its core idea is not that “two points are the same number of centimeters away,” but that under the same harmonic n, control points in different wave lobes that occupy similar local λ proportions—that is, similar local phases—tend to share part of their indicated spatial domain.

This rule alone fully hits:

495 / 625 = 79.2%

of the formally testable specific-symptom pairs.

That is a high recall, but it has a cost: equal-phase relations often generate relatively broad candidate domains. It therefore behaves more like a main candidate generator than a final unique classifier.

Rule 2: cross-node / cross-lobe symmetry

RULE_04 describes another situation.

After a location crosses a node and enters an adjacent or corresponding wave lobe, it may preserve certain control functions if its relative phase remains similar.

Its standalone coverage is lower than RULE_05, but it rescues a group of relations not fully covered by RULE_05.

This resembles taking “same phase” beyond simple periodic translation and adding a cross-lobe topological condition.

From a first-principles perspective, RULE_04 and RULE_05 may therefore not be two completely unrelated natural laws. They may be two expressions of the same phase-equivalence relation under different wave-lobe topology.

Rule 3: full-length mirroring

RULE_01 is the most visually intuitive:

Along the same channel pathway, use the Jing-Well point as a reference and reflect position across the full length, approximately x → 1 - x.

This is not phase translation but reflection.

By itself, it fully hits far fewer specific symptoms than RULE_05. But even after RULE_04 and RULE_05 are present, adding RULE_01 still rescues a new group of pairs.

This means “translation equivalence” cannot completely absorb “mirror equivalence.”

In a simpler geometric language, the multiple rules can be compressed into two basic operations:

• phase translation / equal-phase equivalence: RULE_05 as the general form, RULE_04 as the cross-lobe form;
• phase reflection / mirror equivalence: RULE_01 at full-channel scale, with the original within-lobe symmetry interpretable as a local-scale reflection.

Three rules already reach 88.96%

Combining RULE_01, RULE_04, and RULE_05 fully covers:

556 / 625 = 88.96%

of the 625 specific-symptom pairs—nearly ninety percent.

Adding peak anchoring, RULE_02, raises this to:

564 / 625 = 90.24%

only 8 additional pairs, an improvement of 1.28 percentage points.

Adding RULE_03, within-lobe symmetry, produces no further increase in specific-symptom coverage.

This is why the present hierarchy is better kept simple rather than presenting seven rules as equals:

Main trunk: equal-distance phase equivalence.

Topological supplement: cross-lobe relation.

Reflection supplement: full-length mirroring.

Special fixed-point patch: peak anchoring.

Nearly ninety percent does not prove causality

The number is high, but it is still retrospective coverage on the same corpus of ancient material.

More importantly, the best harmonic n was selected in an earlier stage using observed data, so model-selection bias remains.

The safest current statement is therefore not “three rules prove acupoint indications,” but:

A large number of apparently scattered acupoint indications in the Jiayi Jing can be highly compressed by a very small set of phase-geometric operations.

That is already enough to change the research question.

The next step should not be to invent RULE_08, but to freeze these core rules and test them on held-out channels, held-out passages, or new external acupuncture data.

In the next article, rather than percentages, we look at direct examples: why can a point on the foot form a stable geometric relation with the head, neck, and throat?