signature_is_nanosecond_scale
plain-language theorem explainer
The stacked pulsar residual signature sits strictly between $10^{-10}$ and $10^{-7}$ seconds, i.e. on the nanosecond scale. Anyone citing the LedgerHum pulsar-timing prediction or the stacking model uses this bound as the certified window. The proof unfolds the constant definition and discharges both inequalities by numeric normalization.
Claim. Let $S$ be the stacked residual signature for pulsar timing arrays (the RS prediction for the residual after stacking many pulse arrivals under discrete 8-tick structure). Then $10^{-10} < S < 10^{-7}$.
background
LedgerHum packages verification claims about discrete ledger time and observable residuals. Pulsar timing arrays record radio-pulse arrival times; if spacetime carries an eight-tick octave structure (forcing-chain T7), stacking many arrivals should leave a residual signature rather than pure continuum noise.
The stacked residual signature is defined as the constant $10\times 10^{-9}$ seconds (ten nanoseconds), matching the module's stated prediction "~10 ns stacked residual." Upstream, the signed residual of the first-order genesis fine-structure value against CODATA is a separate AlphaGenesis quantity; the RecognitionOperator time stub is the discrete ledger clock. Neither enters the numeric bound itself; they situate the claim in the residual-and-timing vocabulary of the module.
Sibling material introduces the stacking model: the residual grows like $\sqrt{N}$ from a random walk in discrete time, and a PulsarTimingFalsifier packages the observational test.
proof idea
Term-mode proof. Unfold the definition of the stacked residual signature, which is the literal real constant $10\times 10^{-9}$. Split the conjunction and discharge each strict inequality by norm_num. No external lemmas are required beyond the definition and numeric evaluation.
why it matters
Places the RS pulsar-timing prediction inside a certified nanosecond window rather than a vague order-of-magnitude remark. That window is the quantitative content of the module's "PREDICTION: ~10 ns stacked residual" and feeds the stacking-model narrative (residual growth $\sim\sqrt{N}$ in discrete time) and the PulsarTimingFalsifier sibling.
Framework landmark: the eight-tick octave (T7, period $2^3$) is the discrete-time structure whose stacking residual this bound certifies. The theorem does not itself derive ten nanoseconds from the forcing chain; it locks the declared constant into the ns band so downstream falsifiers and observability claims have a proved numeric envelope. No downstream theorems currently depend on it (used_by is empty), so it is a leaf certificate inside Verification.LedgerHum.
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