Corpus theorem canonical 2026-05-27T20:53:50+00:00
Corpus v3 · Theorem cid001411THM0115canonicalv1

Flat Connection Existence

The additive connection Γ_k(x,v) = (x+v) mod M_k is flat: parallel transport around any closed loop returns to the starting point. Verified computationally at stages 1-2.

Payload

Flat Connection Existence

The additive connection Γ_k(x,v) = (x+v) mod M_k is flat: parallel transport around any closed loop returns to the starting point. Verified computationally at stages 1-2.

Flat Connection Existence

Summary

The additive connection Γ_k(x,v) = (x+v) mod M_k is flat: parallel transport around any closed loop returns to the starting point. Verified computationally at stages 1-2.

Statement

No manuscript statement was extracted in this pilot run.

Proof / Justification

No immediate manuscript proof block was extracted in this pilot run.

Source Context

  • Registry source: book-02.jsonl line 197
  • Manuscript source: not matched

Lean / Formalization Notes

  • Formalization: formalized
  • Module: TauLib.BookII.Closure.Connection
  • Name: flat_connection_flat_2

Dependencies

  • Canonical: II.D78, II.D62

Generated by later projection phases.

Generated by later projection phases.

Revision Notes

  • 2026-04-24: Initial pilot migration.

Identifiers

  • Corpus ID cid001411
  • Primary alias THM0115
  • Type Theorem
  • Status canonical
  • Visibility public
  • Version v1

Aliases & legacy IDs

II.T50flat-connection-existencethm:flat-connection

Release lines

corpus_v3_workingcorpus_v2

Relations

Formalized by (1)

Appears in (1)

Downstream uses (computed) (2)

Items in the corpus that reference this one via load-bearing relations. Computed from the full corpus-v3 graph at build time.

Sources

  • Monograph cid000001Book II, Part 10, Chapter 55 (Wave M4)

Version & History

  • v1 · 2026-05-10 imported from v2 registry
  • v1 · 2026-05-10 wired formalized by in wave 5

Status disclaimer

A Corpus Item page reports the program's current internal record for this item. It does not imply external verification, scientific consensus, or final proof unless explicitly stated. Read it together with its dependencies, formalization status, and the program's overall stance.

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