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Check the n = 8 geometric deduction only; report the exact passages followed and any first unresolved step.

ErdősProblems.com #132 · task erdos-132-n8-geometry

Check category
Proof step
Task type
Read check
Entry points
Multiplicity profile, deletion argument, and overlap-rigidity lemma
Source PDF
Download the exact manuscript
Erdős Problem #132, n = 8 proof writeup · version 5d3faea03531…
Effort
about 90 minutes (estimated by significance-editor)
Prerequisites
Planar distance geometry and the cited seven-point classification

Why this matters

The question above defines what this investigation can establish. Its findings help the author and future readers understand that specific part of the argument.

After editorial review and your confirmation of the wording, an accepted check is published as a dated, scoped, citable entry that future readers, referees, and the author can point to. Even a partial attempt or a negative result is useful. It tells everyone what has been tried and where the open questions remain.

What a good response looks like

You do not need to write a referee report or certify the whole paper. A useful response describes what you actually did and what you found, scoped to this task.

Illustrative partial attempt — fictional paper and references:

"I read pages 4-6 of the PDF (version 1 of a fictional paper) and traced the argument from the hypothesis through Lemma 2.3. The deduction on page 5, line 12 appears to use the bound from Lemma 2.1 without verifying that the hypotheses of 2.1 hold in this case. I spent about 20 minutes and did not resolve this step."

This is a useful starting point for a question or partial attempt. It names the scope, the source version, and the specific location. It does not claim the proof is wrong. It identifies an unresolved step.

Ways to contribute

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Status

Open.

Verification record

Task status tracks participation, not whether the claim is true. Each report below is limited to the scope its author describes.

No scoped check has been recorded for this task yet.

Comments and questions

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How to do this
  1. Download the exact manuscript above and start with the stated entry points. The version hash identifies the file for the eventual record; you do not need to calculate it before reading.
  2. Read or reproduce only the stated scope and note the method you actually used.
  3. Submit what you found through the linked attestation form below, using the record, task, scope, and manuscript hash shown here. No Significance account is required; GitHub may ask you to sign in.

Open attestation form

Attestation template (for advanced users)

Fill only what you did. State what you checked and found, not whether the whole proof is correct.

id: att-erdos-132-n8-geometry
task_id: erdos-132-n8-geometry
reviewer: '[your name or handle]'
scope: Check the n = 8 geometric deduction only; report the exact passages 
  followed and any first unresolved step.
manuscript_sha256: 
  5d3faea03531035426c9f5ca8ece9c8db90ff2cdaff4238f3eb1090747c5b209
asserted_at: '[YYYY-MM-DDTHH:MM:SSZ]'
method: '[what you actually did: read / rederived / rebuilt / compared]'
finding: '[what you checked and found about exactly this scope]'
limits: '[what you did not check — optional but encouraged]'