TheoremDB

Problem packetResearch packetR1524

R1524Sourced evidence

Dated status and exact unresolved remainder

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Authored summary

Unresolved in this packet after the dated source check. Strongest checked result: The sole answer proposes a consequence of Schanuel's conjecture. Comments identify gaps in how reduced words enter the argument and ask whether Ax-Schanuel yields an unconditional proof; the thread contains no settled unconditional resolution. Exact unresolved remainder: Prove that every nonempty freely reduced word in f^{+/-1} and g^{+/-1} differs from the identity at some x>0, or exhibit a nonempty freely reduced word that is the identity on all x>0. A conditional proof must state its hypothesis explicitly and does not settle the unconditional target.

The record cites sources for its explanation.

Recorded status: reported

Recorded scope: No scope is recorded.

Originating problem: A free group generated by exponential and squaring maps

Authored record and scope
Authored title
Dated status and exact unresolved remainder
Record type
claim
Stored status
reported
Evidence grade
sourced

2Authored explanation

The packet's cited sources and equivalent formulations were checked in the dated review recorded below.

Strongest checked result: The sole answer proposes a consequence of Schanuel's conjecture. Comments identify gaps in how reduced words enter the argument and ask whether Ax-Schanuel yields an unconditional proof; the thread contains no settled unconditional resolution.

Exact unresolved remainder: Prove that every nonempty freely reduced word in f^{+/-1} and g^{+/-1} differs from the identity at some x>0, or exhibit a nonempty freely reduced word that is the identity on all x>0. A conditional proof must state its hypothesis explicitly and does not settle the unconditional target.

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Replay material: source only

3Evidence

Replay package: source only

A verification source is cited. This record has no executable replay attached.

Verification source: doi.org ↗, abstract and results on algebraic roots of exponential polynomials under Schanuel's conjecture

4What was measured

5How it connects

Replaces

Recorded for

Machine-readable record

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  "ref": "R1524",
  "content_hash": null,
  "slug": "exponential-square-free-group-status-packet-quality-20260801",
  "type": "claim",
  "title": "Dated status and exact unresolved remainder",
  "summary": "Unresolved in this packet after the dated source check. Strongest checked result: The sole answer proposes a consequence of Schanuel's conjecture. Comments identify gaps in how reduced words enter the argument and ask whether Ax-Schanuel yields an unconditional proof; the thread contains no settled unconditional resolution. Exact unresolved remainder: Prove that every nonempty freely reduced word in f^{+/-1} and g^{+/-1} differs from the identity at some x>0, or exhibit a nonempty freely reduced word that is the identity on all x>0. A conditional proof must state its hypothesis explicitly and does not settle the unconditional target.",
  "relevance": "For A free group generated by exponential and squaring maps, this successor gives readable dated status prose and the exact remaining research boundary.",
  "relevance_source": "recorded",
  "body": "The packet's cited sources and equivalent formulations were checked in the dated review recorded below.\n\nStrongest checked result: The sole answer proposes a consequence of Schanuel's conjecture. Comments identify gaps in how reduced words enter the argument and ask whether Ax-Schanuel yields an unconditional proof; the thread contains no settled unconditional resolution.\n\nExact unresolved remainder: Prove that every nonempty freely reduced word in f^{+/-1} and g^{+/-1} differs from the identity at some x>0, or exhibit a nonempty freely reduced word that is the identity on all x>0. A conditional proof must state its hypothesis explicitly and does not settle the unconditional target.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
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    "kind": "claim",
    "citation": {
      "url": "https://doi.org/10.1080/00927872.2010.489918",
      "locator": "abstract and results on algebraic roots of exponential polynomials under Schanuel's conjecture"
    },
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  "source": {
    "url": "https://doi.org/10.1080/00927872.2010.489918",
    "locator": "abstract and results on algebraic roots of exponential polynomials under Schanuel's conjecture"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R1301",
      "title": "Current checked status and unresolved remainder",
      "object_type": "claim",
      "relation": "supersedes",
      "direction": "outgoing",
      "metadata": {
        "reason": "Replaces unreadable status prose with the dated review from 2026-08-01."
      }
    },
    {
      "slug": "exponential-square-free-group",
      "title": "exponential square free group",
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7Provenance

View source, identifiers, and projection details

A statement this project treats as settled at the recorded evidence grade, with the work that backs it.

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