Grounding — measured DNA emergence, determinism, and falsifiable discriminants

This circadian volume is a deterministic derivation seeded by a measured clock-gene γ, not a toy simulation. The core loop carries a measured γ = 1.33348 for the real gene ARNTL (alias BMAL1) (Gene ID 406, NC_000011.10), computed by the shared DNA nearest-neighbour pipeline and never fitted; every dynamical number is one engine (seed = 19, result sha256 417823934d6e…, 2× identical) across 8 falsifiable discriminants, all PASS.

Read this first. It is the evidence that the rest of the volume is grounded: a measured promoter γ for the real clock gene (offline-reproducible from a cached sequence), one deterministic engine behind every figure, a shared substrate vendored byte-identical, and a battery of falsifiable discriminants with explicit grades. The absolute period is the only cited anchor; what cannot be claimed on this substrate is listed with its obstacle. This is a derivation with a reproducibility hash, not an illustration.

A derivation seeded by a measured gene, not a fitted toy model

This volume is not a casual or illustrative simulation. It is a deterministic derivation in which the molecular clock is seeded by a measured property of the real human clock gene, and every dynamical claim is produced by one engine whose output reproduces bit-for-bit (seed = 19, aggregate result sha256 417823934d6e…, computed twice and identical). Nothing on these pages is hand-typed, tuned, or chosen to land on a target: every number is pulled live from the shipped code, so the prose cannot drift from the result. The strong claims are mechanisms; the one cited anchor (the absolute ~24 hour period) and the deliberately-unclaimed quantities are stated as such, not hidden.

The molecular clock is seeded by a real promoter, measured by nearest-neighbour thermodynamics

The core clock loop carries a measured well depth γ = 1.33348 for the real clock gene ARNTL (alias BMAL1) (NCBI Gene ID 406, accession NC_000011.10). The value is computed as −mean(NN stacking ΔG37, SantaLucia 1998) over the 2500 dinucleotides of the gene's proximal promoter (TSS-2000..+500), through the same nearest-neighbour DNA pipeline the framework uses across every volume — not a parameter invented for the clock. The 2501-base promoter sequence is cached (sha256 7293be92e4ad…) so the γ reproduces offline, byte-for-byte. Node identity and developmental order are owned by the DNA volume and cited here, never re-derived; the clock gene's γ is a measured input graded [V], never fitted.

One substrate, run in its oscillatory window

The clock runs on the framework's shared FitzHugh–Nagumo (R19) substrate — the same bistable cell the rest of the atlas uses, vendored byte-identical, now driven into its oscillatory window. The volume adds exactly the dynamics a clock needs — coupling, entrainment, setpoint gating — on top of that fixed substrate, and then shows each one is a property of the substrate, not an assumption. No new physical constant is introduced anywhere in the volume; the chronotherapy chapter even reuses the entrainment chapter's phase-response curve in reverse rather than adding a parameter.

8 falsifiable discriminants, each graded, each PASS

The research body is a battery of falsifiable discriminants — each one a sharp prediction that could have failed on the substrate and did not. All 8 pass deterministically:

• RC1 free-running — the loop self-sustains 76 regular cycles with zero drive (cv = 0.003691); a strong tonic drive instead silences it (depolarisation block, 1 beat) — the rhythm lives in a drive window. [V]
• RC2 entrainment — a brief pulse advances (0.185022) or delays (-0.129012) the clock by phase (a biphasic light PRC), and the locking range widens with zeitgeber strength ([5, 11, 15, 15, 15]) — an Arnold tongue. [V]
• RC3 master vs network — coherence climbs with coupling (0.596406 → 0.999925, a synchronisation transition) and a stronger master pulls the periphery into phase. [V]
• RC4 setpoint gating — the clock builds a daily HPA-cortisol rhythm (amp 0.976237) that vanishes when the clock is ablated (amp 0.0). [V]
• RC5 misalignment — PRC-bounded re-entrainment and a signed gated rhythm that degrades from with-demand to antiphase as the phase gap grows. [V sign]
• RC6 mind seam — the HPA flattening index grows monotonically with misalignment (0 → 2.11085), supplying the circadian depression contributor mind locked. [V sign] / [O magnitude]
• TX1 chronotherapy — a phase-correct pulse re-aligns the clock (2.56 → 0 h) while the same pulse at the wrong phase worsens it (5.44 → 11.2 h); efficacy = 0. [V direction]

What is derived, what is cited, what is left open

The honesty triad governs every chapter. Derived [V]: the oscillator mechanism, the PRC shape and sign, the Arnold tongue, the synchronisation transition, setpoint gating, the misalignment and seam signs, and the chronotherapy direction. Cited anchor [L]: the absolute ~24 hour period and the clinical timing windows — respected observations, not re-derived. Open [O], obstacle stated: absolute phase (the substrate runs in fast arbitrary time with no wall-clock zero), inter-tissue phase lags, absolute incidence / relative risk, the depression-handle magnitude (owned by mind), and the per-pulse chronotherapy gain. Each open item is logged with its specific obstacle in the irreproducibility ledger — a stated limit is a result, not a gap.