Skip to main content

A registered result in its source context

Original ledger classification: Numerical (contraction bound) [E]/[C]

Recorded statement: SEAM FINITE RECOVERABILITY CODE (2026-06-16): the seam as a finite quantum-error-correction-style code with recovery rate (2/3)^6=64/729. Code dimension = dim S^+ = 16 = 2^(g_car-1); the gapped boundary transport T on the cusp-weight…

Statement, assumptions and sources

Paper context: Origin Theory

The exact identifier, original classification and full claim are available below.

The source wording and classification below are preserved as recorded. A paper link, shared script or authored topic relation does not upgrade the claim or report a new proof run. Read later reviewed findings separately.

Read the exact registered claim and its dependencies

QEC.SEAM.01

Original ledger classification: Numerical (contraction bound) [E]/[C]

Original claim text

SEAM FINITE RECOVERABILITY CODE (2026-06-16): the seam as a finite quantum-error-correction-style code with recovery rate (2/3)^6=64/729. Code dimension = dim S^+ = 16 = 2^(g_car-1); the gapped boundary transport T on the cusp-weight 3-space (deviation directions (1,-1,0) and the Nariai anchor (1,1,-2)) is symmetric, doubly stochastic (CPTP), with spectrum {1,(2/3)^6,(1/3)^6}; on the trace-zero deviation subspace ||T delta|| <= (2/3)^6 ||delta||, hence ||T^n delta|| <= (2/3)^{6n} ||delta|| (a Knill-Laflamme-type per-step recovery bound). A free ratio r != (2/3)^6 gives r^n (rate not generic); breaking mu4-equivariance destroys it. 'Finite recoverability code' FIRST, 'holographic code' SECOND.

Original classification detail

[E] code dim 16, transport spectrum {1,(2/3)^6,(1/3)^6}, recovery bound ||T^n delta||<=(2/3)^{6n}||delta||; holographic/Petz reading [C] gated on the Seam-Horizon theorem

Dependencies as recorded

SEAM.ATTRACT.01; SEAM.TRANSFER.01; HOR.PAGE.01

Open the original ledger source, row 311

Location recorded in the ledger

These document locations are recorded directly on the ledger row. They are document level navigation, rather than a newly inferred section citation.

Sections that explicitly cite this claim

A literal claim identifier is present in these paper sections. The section and its premises determine what the citation supports.

Navigation through a shared verification script

These sections cite a script associated with the claim. This is a source navigation join, rather than an explicit citation of the claim or a theorem equivalence.

All 40 linked sections

Registered verification modules

  • v221_seam_qecc.pyRegistered verification module · horizon
    Read the description recorded in the module registry

    The seam as a FINITE recoverability code (recovery rate (2/3)⁶=64/729). Code dimension dim S⁺=16=2^(g_car−1); the gapped transport T on the cusp-weight 3-space (deviations (1,−1,0) and the Nariai anchor (1,1,−2)) is symmetric, doubly stochastic (CPTP), spectrum {1,(2/3)⁶,(1/3)⁶}; on the trace-zero subspace ||T δ||≤(2/3)⁶||δ|| so ||Tⁿ δ||≤(2/3)^{6n}||δ|| (Knill-Laflamme-type bound); a free ratio breaks it. Holographic/Petz reading [C], gated on the Seam-Horizon theorem. Python-only (numerical contraction bound).

A registered module is a source reference. Its presence does not assert that the module was executed in this snapshot.

Search later reviewed research for this identifierRead the coverage boundaries