Part 1: The Theoretical Framework
I propose a reexamination of mathematical observation through what I call the Zero Point Perspective (ZPP).
Core Axioms:
• Zero is not “nothingness” but an anchor point—a coordinate origin of self‑coincidence. Each reference frame generates its own zero. Thus, 0F1 may ≠ 0F2.
• π is not merely a ratio but a principle of minimal informational complexity. It encodes “straightness” itself—the least complex path through space. Rotate a line 360° about its center or endpoints and you trace a circle: the most direct closed path back to origin. In this sense, the circle is the straightest possible loop.
• Mathematics is perspectival, not absolute. Observation is tied to reference frames, and informational precision degrades with distance from any zero point (perspectival entropy).
Illustration: Standing on a beach, you may declare “the beach is land” at low tide and “the beach is water” at high tide. Both are true within their frame. This is what it means to stand at the border of perception and reality.
Prediction: If ZPP is correct, π should manifest in topology as a perfectly straight, razor‑thin line—a quantized backplane representing the minimum complexity state.
Part 2: The Instrument
To test this, I developed the Goldbach Topological Calculator (GTC), which maps Goldbach partitions through nine analytical “lenses,” including a dedicated π‑lens defined as:
cos(P₁ × π) + sin(P₂ × π)
Part 3: Empirical Validation
The π Prediction: Confirmed.
The π‑lens reveals exactly what ZPP anticipated: a razor‑thin horizontal line—a quantized backplane. This was predicted before visualization.
The Falsification Crucible: The instrument was stress‑tested across multiple mathematical systems. Null tests confirm no artifactual signal generation. Different systems reveal different levels of “informational friction.”
Part 4: Implications for Goldbach
Under the entropy lens (ln(P₁) + ln(P₂)), stable “double blank lines” appear at high N. Through ZPP, these are not failures of the conjecture but perspectival entropy—the mathematical horizon effect.
Goldbach has resisted proof because we’ve been asking the wrong question. It is not “do the primes exist?” but “can they be observed from any single reference frame beyond the informational horizon?”
I invite reviewers to examine the calculator. The framework made a successful prediction; now it requires rigorous challenge.
Finally, should this work pique the community’s curiosity, I would request a private audience with Dr. Wolfram. There is much to discuss.
P.S. I am a philosopher with no formal mathematical training. That is precisely why I bring this here.
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