TheoremDB
R1744claimStatus: reportedEvidence: SupportedReplay: source only

[#R1744] Dated status and exact unresolved remainder

claim. Unresolved in this packet after the dated source check. Strongest checked result: The n=1 and algebraic-input cases follow from classical transcendence theorems, and Ax proved a functional analogue. These do not prove the full numerical conjecture. Exact unresolved remainder: Prove the transcendence-degree bound for every finite Q-linearly independent complex tuple, or exhibit a violating tuple.

View evidenceOpen source ↗

1Summary

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

Strongest checked result: The n=1 and algebraic-input cases follow from classical transcendence theorems, and Ax proved a functional analogue. These do not prove the full numerical conjecture.

Supported evidence. Replay readiness: source only.

2Evidence

Evidence package: source only

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

Verification source: arxiv.org ↗, Abstract and dependency survey

3Overview

Exact unresolved remainder: Prove the transcendence-degree bound for every finite Q-linearly independent complex tuple, or exhibit a violating tuple.

4What was measured

As of
2026-08-01
Strongest known result
The n=1 and algebraic-input cases follow from classical transcendence theorems, and Ax proved a functional analogue. These do not prove the full numerical conjecture.
Exact open remainder
Prove the transcendence-degree bound for every finite Q-linearly independent complex tuple, or exhibit a violating tuple.

5How it connects

Supersedes

Recorded for

6Agent packet

A compact handoff with the evidence boundary, replay manifest, and relation pointers.

View structured packet
json
{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1744",
  "content_hash": null,
  "slug": "schanuel-conjecture-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 n=1 and algebraic-input cases follow from classical transcendence theorems, and Ax proved a functional analogue. These do not prove the full numerical conjecture. Exact unresolved remainder: Prove the transcendence-degree bound for every finite Q-linearly independent complex tuple, or exhibit a violating tuple.",
  "relevance": "For Schanuel's conjecture, 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 n=1 and algebraic-input cases follow from classical transcendence theorems, and Ax proved a functional analogue. These do not prove the full numerical conjecture.\n\nExact unresolved remainder: Prove the transcendence-degree bound for every finite Q-linearly independent complex tuple, or exhibit a violating tuple.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://arxiv.org/abs/1801.08765",
      "locator": "Abstract and dependency survey"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/1801.08765",
    "locator": "Abstract and dependency survey"
  },
  "relations": [
    {
      "slug": "R1148",
      "title": "Current status and unresolved remainder",
      "object_type": "claim",
      "relation": "supersedes",
      "direction": "outgoing"
    },
    {
      "slug": "schanuel-conjecture",
      "title": "schanuel conjecture",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}

7Provenance

View source, identifiers, and projection details
Project
schanuel-conjecture-source-review
Locator
Abstract and dependency survey
License
CC0-1.0
Contributors
TheoremDB maintainers
Public record
R1744
Stable alias
schanuel-conjecture-status-packet-quality-20260801
Projection
Reproduction fields are derived from the immutable record.

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

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