diff --git a/docs/concepts/GAMMA_RADIX_METAPROBE.md b/docs/concepts/GAMMA_RADIX_METAPROBE.md new file mode 100644 index 00000000..357ebc08 --- /dev/null +++ b/docs/concepts/GAMMA_RADIX_METAPROBE.md @@ -0,0 +1,218 @@ +# Gamma Radix MetaProbe + +Date: 2026-05-19 +Status: BEAUTIFUL_PROVISIONAL + +## One-line definition + +Gamma Radix MetaProbe is a symbolic, receipt-bearing pulse-tracing architecture that uses gamma-length transmission as a radix metaphor for ultra-fine address/probe space, while keeping the implementation in software-accessible manifolds, WebGPU/PIST surfaces, DSP chunks, and FAMM/NUVMAP witness routing. + +This is **not** a claim that ordinary software can dereference literal gamma-wavelength physical memory cells. It is a virtual chart/probe encoding model: gamma-scale coordinates are lawful names, not guaranteed physical addresses. + +## Core idea + +Instead of treating ray tracing as RGB light transport through fixed geometry, treat tracing as packet propagation through admissible manifolds: + +```text +pulse transport -> attenuation / delay / scatter / residual -> inferred geometry/state +``` + +The gamma pulse is the conceptual radix carrier. Each pulse branch is sorted by energy, direction, time, chirality, interaction kernel, spectral mode, density response, and residual scar. + +## Packet primitive + +The packet aligns with the existing compactified packet primitive: + +```text +Gamma_i = gamma_i ⊗ chi_i ⊗ kappa_i ⊗ tau_i ⊗ U_i Lambda_i a_i ⊗ theta_i ⊗ epsilon_i +``` + +Where: + +- `gamma_i` = energy-density pulse / symbolic gamma carrier +- `chi_i` = chirality, braid orientation, or handedness witness +- `kappa_i` = material / interaction / scattering kernel +- `tau_i` = delay shell or time-of-flight term +- `U_i Lambda_i a_i` = spectral/eigen decomposition payload +- `theta_i` = manifold routing angle / projection coordinate +- `epsilon_i` = residual scar / admissibility failure witness + +## Radix basis + +The radix is not base-2 or base-10. It is a multi-axis pulse-state basis: + +```text +R_Gamma = { E, theta, phi, t, chi, kappa, rho, sigma, epsilon } +``` + +Interpretation: + +| Digit | Meaning | +|---|---| +| `E` | energy bin / symbolic frequency band | +| `theta, phi` | angular route / projection direction | +| `t` | pulse arrival time / time-of-flight | +| `chi` | chirality / braid handedness | +| `kappa` | interaction kernel | +| `rho` | density-field response | +| `sigma` | spectral mode / surface state | +| `epsilon` | residual scar / admissibility failure | + +## Relation to existing stack + +### NUVMAP + +NUVMAP becomes the virtual address projection layer: + +```text +N = (x, y, z, t, E, chi, sigma, rho, epsilon) +``` + +This gives the system an ultra-dense symbolic coordinate space without claiming literal physical storage density. + +### FAMM + +FAMM routes each pulse by field, shear, spectral, and residual state: + +```text +Route_Gamma = FAMM(rho, G, C, epsilon) +G = A^T A +C = U Lambda U^T +``` + +Each branch is lawful only if its residual remains below the active boundary condition. + +### BraidStorm + +A single pulse becomes a strand; many pulses become a braidstorm: + +```text +B_Gamma = { Gamma_1, Gamma_2, ..., Gamma_n } +``` + +The useful information comes from crossings, timing shear, chirality mismatch, interference, and closure receipts. + +### PIST / WebGPU blitter surface + +The practical implementation does not require gamma radiation. The gamma pulse can be projected as: + +- Fourier packets +- DSP chunks +- audio-domain probes +- hexcode spectral packets +- WebGPU buffer transitions +- PIST-like surface dispatches + +Each WebGPU dispatch is a bounded surface transition: + +```text +PIST_GPU : Gamma_i -> Gamma_{i+1} +``` + +The GPU surface records residual/scar/witness output for each lawful or failed transition. + +### MetaProbe / WaveProbe + +Gamma Radix MetaProbe fits the pure L3 MetaProbe layer: + +- non-settling +- probe-only +- low-impact +- cheap virtual execution +- exports only when a separate settlement / receipt boundary is invoked + +It can be used to sample route quality, detect local manifold stress, or test compression/reconstruction hypotheses without committing every intermediate state. + +## Where the savings show up + +The savings are **not** from creating literal gamma-scale software memory. They appear by replacing expensive committed computation with cheaper probe computation. + +### 1. Settlement avoidance + +Most branches never need to become final committed state. MetaProbe can run symbolic probes, discard failed branches, and only export winners. + +Savings axis: + +```text +full execution + storage + commit + -> probe + witness + selective export +``` + +### 2. Sparse residual transmission + +Instead of transmitting full state, transmit: + +```text +generator + route witness + residual repair +``` + +This is the same savings pattern as GCCL-Rep / nibble-delta witness substrate: sparse manifold telemetry can be much smaller than raw state replay. + +### 3. WebGPU/edge/free-tier computation + +For browser/WebGPU or free-tier worker contexts, the blitter surface can run bounded, low-duty symbolic probes. The value comes from using available local/edge GPU cycles for spectral transforms instead of renting continuous server compute. + +Constraint: this must stay within provider terms and rate limits. The architecture is legitimate only when request caps, duty cycles, and fair-use boundaries are respected. + +### 4. Cacheable probe fields + +Radix branches that repeat can be memoized as route receipts: + +```text +same packet class + same boundary condition -> reuse prior branch witness +``` + +This reduces repeated exploration of the same local manifold basin. + +### 5. Compression-native reconstruction + +The tracer is useful when output can be reconstructed from a compact law + residual, not when every pixel/sample/state must be explicitly stored. + +Savings axis: + +```text +raw samples -> lawful reconstruction core + residual pullback +``` + +### 6. Compute triage + +The gamma radix is a sorting/routing device. It tells the system where expensive compute is worth spending: + +- low residual: accept / cache / compress +- medium residual: refine locally +- high residual: route to FAMM scar / reject / quarantine +- impossible: NaN boundary / no commit + +## Boundary condition + +This concept is useful only if it remains honest about the physical/software boundary: + +- software can name gamma-scale coordinates +- software cannot dereference them as physical RAM +- WebGPU can simulate/probe the radix surface +- FAMM/NUVMAP can route symbolic witnesses +- exactness must be handled through residual repair and receipts + +## Minimal implementation target + +A first prototype can be purely software: + +1. Define `GammaPacket` with fields for energy bin, direction, time, chirality, spectral mode, and residual. +2. Implement radix branching over packet fields. +3. Run branches over a WebGPU or CPU spectral kernel. +4. Emit route receipts and residual scars. +5. Compare cost against naive full-state evaluation. + +## Claim status + +This should remain `BEAUTIFUL_PROVISIONAL` until there are benchmark receipts showing: + +- probe cost vs full execution cost +- residual size vs raw output size +- cache hit rate for repeated route witnesses +- WebGPU dispatch cost under real browser limits +- byte-exact reconstruction where required + +## Keeper phrase + +Gamma Radix MetaProbe: gamma-length coordinates as virtual probe radix, not physical RAM; savings appear when cheap pulse-branch probes replace committed computation, raw state transfer, and repeated full execution.