sample_object_count_split
plain-language theorem explainer
In the GWTC-3 ringdown HDF5 sample, the recorded group count plus dataset count equals the total HDF5 object count: 14 + 83 = 97. Anyone citing the one-member schema certificate or the bundled sample-schema statement uses this identity. The proof unfolds three numeric constants and closes by decidable arithmetic.
Claim. For the inspected GWTC-3 ringdown HDF5 sample member, the group count plus the dataset count equals the total HDF5 object count: $14 + 83 = 97$.
background
This module freezes a schema-level inspection of one real HDF5 posterior member from the GWTC-3 ringdown ZIP, obtained without downloading the full 1.44 GB archive. A companion script range-reads the ZIP central directory, selects the smallest .h5 member (rin/rin_S190727h_pyring_DS_1mode_10M.h5), inflates only that member, and records live h5py metadata.
Three natural-number constants capture the object inventory: total HDF5 objects (97), groups (14), and datasets (83). In HDF5, every named object is either a group or a dataset, so these three figures must add consistently. The module status is structural theorem: zero sorry, zero new RS-internal axioms; this is schema inspection only, not a posterior likelihood claim.
proof idea
Term-mode proof by unfolding the three definitions to the literals 14, 83, and 97, then decide on the closed natural-number equation. No external lemmas are required beyond definitional equality and decidable arithmetic on Nat.
why it matters
The identity is one field of the sample-schema certificate structure, which packages naming, size positivity, uncompressed-versus-compressed ordering, and this object-count split. It also appears as a conjunct in the one-statement HDF5 sample schema theorem that bundles member name, object split, posterior path, sample count positivity, and field count.
In the Recognition verification layer this is infrastructure, not a forcing-chain step: it pins that the live GWTC-3 ringdown sample the project cites has a coherent HDF5 inventory. Downstream consumers can treat the certificate as a single checked witness rather than re-deriving the arithmetic. It does not touch T0–T8, RCL, or mass-ladder physics; it closes a reproducibility hinge for gravitational-wave posterior schema claims.
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