Computational Audit of the Recursive Peircean Reconstruction

Audit Boundary

The companion computational audit exhaustively checks large finite families of models and searches for counterexamples to the fixed finite claims. It is corroboration and regression testing, not a substitute for the general proofs in the manuscript.

Open the audit PDF or download the reproducibility bundle.

Finite Model Encoded On This Site

These are the exact finite structures checked by the companion audit.

• 3roles
• 4headings
• 12cells

• Roles: 3, with Presentation, Discrimination, and Mediated Integration denoted by ⟨1⟩, ⟨2⟩, and ⟨3⟩, respectively.
• Headings: 4, with Quality, Quantity, Modality, and Relation encoded as 00, 10, 01, and 11, respectively.
• Cells: 12, exactly one for every role-heading pair.
• Reversal: τ(00)=00, τ(10)=01, τ(01)=10, τ(11)=11.
• Orbit sizes: 1:2:1 for {00}, {10, 01}, and {11}, respectively.

Terms Used Here

Boundary

The character of a determination at its input or output: closed when no free contextual parameter remains, indexed when an explicit contextual parameter remains.

Reversal

The operation that exchanges the ordered input and output characters of a heading profile.

Reversal class

All profiles connected by that exchange: {00} · {10, 01} · {11}.

Quotient

The coarser three-part classification obtained by treating profiles in the same reversal class as equivalent, forgetting orientation while retaining the number of indexed positions.

Quantity Correspondence

• Plurality / Particular: ${\exists }_{C}P={\bigvee }_{x\in C}P(x)$, Particular scope presents open support without designating which witness supplies it.
• Unity / Singular: ${\mathrm{ev}}_a(P)=P(a)$, Singular judgment designates this member of the manifold rather than leaving the witness open or ranging exhaustively.
• Totality / Universal: ${\forall }_{C}P={\bigwedge }_{x\in C}P(x)$, Universal scope integrates every coordinate under one exhaustive condition.

Artifact Integrity

The public manifest declares 6 hashed artifacts for Kant's Table as a Recursive Peircean Product, v4.

• Paper (v4 PDF)

  Current manuscript.

  368 KB · SHA-256 e594365d0a9b60d5a2c32c741d07554a1b364cd3bd94480d93e73e653c36ef86

  available
• LaTeX source (v4)

  Source bundle for the current manuscript.

  40 KB · SHA-256 393de5a2cb01bc5d869d88cf4e1b3dda7742e7b423cf9a1d8a41a915424bb0c3

  available
• Computational audit

  Current companion audit.

  247 KB · SHA-256 1caa9aae4abb39680e41baa57f01427a93fb8d508a452df4df0e8af5ff76e7df

  available
• Audit source and reproducibility bundle

  Source and reproduction materials for the audit.

  702 KB · SHA-256 00852eb1582bda9e38960b9f9b3c828dbaf4f11d1a50e772f33e277109e127a9

  available
• BibTeX

  BibTeX citation record.

  368 bytes · SHA-256 9a019c7c5cb785274d62090c26e2a648511f0a6743760c6f2e9edb6c0ad61ac2

  available
• Artifact manifest

  Machine-readable artifact manifest.

  available
• Citation File Format

  Repository citation metadata.

  309 bytes · SHA-256 8a7afc959c6ceee81e9f75edd6958b008f4d6612f77c07cffccabbdbc657c43c

  available
• SHA-256 checksums

  Integrity checksums for the publication artifacts.

  available

What the Audit Does Not Establish

The mathematics does not by itself prove that Kant's table is this structure. The substantive philosophical burden remains in:

τ ∘ τ = id because 4 listed profiles return to themselves after two reversals.