Corpus v3 · Proof cid000022PRF0001canonicalv1

Proof of Master Constant Calibration

Semi-formal Corpus-addressed proof of the master constant calibration theorem (THM0001). Combines earned boundary constants (DEF0001), lobe-swap invariance (LEM0001), and refinement-pressure uniqueness (PRP0001) into the calibration crossing identity.

Payload

We prove the master constant calibration by combining the earned constants DEF0001, lobe-swap invariance LEM0001, and refinement-pressure uniqueness PRP0001.

By the lobe-swap invariance of the crossing condition (LEM0001) and the refinement-pressure uniqueness proposition (PRP0001), the calibration crossing fixed by earned boundary constants (DEF0001) is the unique value ι_τ = 2_τ / (π_τ + e_τ), as claimed by THM0001.

Proof

mode: semi_formalstatus: completeformality: prose_addressedversion-pinning: pinned

Proof steps

Earned constants.
The boundary constants used in the construction are available by DEF0001 — the lobe-swap closure on the τ-domain produces a non-empty set of earned constants.

Uses:prrp://def0001@v1 (uses definition)
Lobe-swap invariance fixes the crossing.
Apply LEM0001: the crossing condition determined by an earned constant b equals the crossing condition determined by σ_lobe(b). The crossing is therefore invariant under lobe-swap.

Uses:prrp://lem0001@v1 (uses lemma)
Uniqueness under refinement pressure.
Apply PRP0001: the crossing fixed by DEF0001 and LEM0001 is unique under refinement-pressure stability on B_τ. There is exactly one calibration crossing.

Uses:prrp://prp0001@v1 (uses theorem)
Conclude master constant identity.
Combining steps s1-s3, the unique calibration crossing fixed by earned boundary constants and lobe-swap invariance is

ι_τ = 2_τ / (π_τ + e_τ).

This establishes THM0001.

Formalization

lean_axiom_freesorries: 0project axioms: 0

ModuleTauLib.Geometry.CentralTheorem.Calibration
Declarationiota_tau_calibration

Identifiers

Corpus ID cid000022
Primary alias PRF0001
Type Proof
Status canonical
Visibility public
Version v1

Aliases & legacy IDs

PRF0042proof-iota-calibration

Release lines

corpus_v3_working

Relations

Upstream dependencies (3)

cid000007cid000008cid000009

Formalized by (1)

cid000020

Downstream uses (computed) (1)

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

REL0001release packet

Version & History

v1 · 2026-05-10 initial corpus item seed

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.