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Research-Stack/5-Applications/scripts/hutter_pist_decoder.c
Brandon Schneider 0709b298b3 Consolidate research stack updates
2026-05-05 21:09:48 -05:00

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/*
* PIST Extended Encoding — Minimal Self-Contained Decoder for Hutter Prize
*
* Compiles to a single binary that, when run, outputs enwik9 (1,000,000,000 bytes).
* The compressed data is embedded at the end of this executable.
*
* Build: gcc -O3 -o archive.exe hutter_pist_decoder.c -lm
* Run: ./archive.exe > enwik9
*
* Size budget:
* Current record L = 110,793,128 bytes
* Target S = S1 + S2 < L (where S2 = sizeof(archive.exe))
* 1% improvement = S < 109,685,207 bytes
*
* Architecture:
* - O(1) coordinate computation per byte position (no search)
* - 8-opcode register machine with manifold addressing
* - Bootstrap basis embedded in binary header
* - Program stream embedded after code section
*
* Mathematical foundation — Frozen-In Coordinate Invariance
* (Asenjo, Comisso & Winkler, PRL 2026, DOI: 10.1103/6c4q-kx6f)
*
* The decoder relies on the same principle as frozen-in gravitational fields:
* under an ideal "Ohm-type" condition, field structures remain preserved
* as the system evolves. Here, the "field" is the composite address structure,
* and "evolution" is the sequential decode operation.
*
* Eq 1 (PIST shell decomposition): n = k^2 + t
* Eq 2 (Mass function): m(k,t) = t(2k+1-t) [t < 2k+1-t]
* Eq 3 (Mirror): mirror(n) = k^2 + (2k+1-t)
* Eq 4 (Tree address): path_i(n) = floor(n / 20^i) mod 20
* Eq 5 (Surface coords): x = 1 + (n mod 255), y = 1/x
* Eq 6 (Torus angles): theta = n*Phi mod 2pi
* phi = n*Phi^2 mod 2pi
* psi = n*Phi^3 mod 2pi
* Eq 7 (Frozen-in prediction): p(n) = basis[n%B] XOR keystream(n)
* XOR (n mod 256)
* XOR mirror(n)
* Eq 8 (Decode): output = p(n) XOR residual(n)
*
* The composite address is a topological invariant: it depends only on n,
* not on data. Like gravitational helicity H_g = integral(A_g . B_g dV),
* the coordinate structure is conserved under encode/decode dynamics.
*/
#include <stdio.h>
#include <stdlib.h>
#include <stdint.h>
#include <string.h>
#include <math.h>
/* ─── Constants ─── */
#define ENWIK9_SIZE 1000000000ULL
#define PHI 1.618033988749895
#define TWO_PI 6.283185307179586
#define TREE_DEPTH 3
#define TREE_BRANCHES 20
#define BASIS_SIZE 16
#define STACK_SIZE 256
#define BOOTSTRAP_SIZE 16
/* ─── PIST Coordinate Primitives ─── */
static inline uint32_t isqrt(uint32_t n) {
uint32_t x = n, y = (x + 1) >> 1;
while (y < x) { x = y; y = (x + n / x) >> 1; }
return x;
}
static inline void pist_encode(uint32_t n, uint32_t *k, uint32_t *t) {
*k = isqrt(n);
*t = n - (*k) * (*k);
}
static inline uint32_t pist_mass(uint32_t k, uint32_t t) {
if (k == 0) return 0;
uint32_t m = 2 * k + 1 - t;
uint32_t tf = t < m ? t : m;
return tf * (2 * k + 1 - tf);
}
static inline uint32_t pist_mirror(uint32_t n) {
uint32_t k = isqrt(n);
uint32_t t = n - k * k;
if (k == 0) return 0;
return k * k + (2 * k + 1 - t);
}
/* ─── Tree Address (Base-20 Recursive Traversal) ─── */
static inline void tree_address(uint32_t n, uint32_t path[TREE_DEPTH]) {
for (int i = 0; i < TREE_DEPTH; i++) {
path[i] = n % TREE_BRANCHES;
n /= TREE_BRANCHES;
}
}
/* ─── Surface Coordinates (y = 1/x) ─── */
static inline void surface_coord(uint32_t n, double *x, double *y, double *theta) {
*x = 1.0 + (double)(n % 255);
*y = 1.0 / *x;
*theta = fmod((double)n * PHI, TWO_PI);
}
/* ─── Toroidal Angles (Φ-Irrational Rotation) ─── */
static inline void torus_angles(uint32_t n, double *theta, double *phi, double *psi) {
double nd = (double)n;
*theta = fmod(nd * PHI, TWO_PI);
*phi = fmod(nd * PHI * PHI, TWO_PI);
*psi = fmod(nd * PHI * PHI * PHI, TWO_PI);
}
/* ─── Composite Address ─── */
typedef struct {
uint32_t k, t;
uint32_t mass;
uint32_t mirror;
uint32_t tree[TREE_DEPTH];
double surf_x, surf_y, surf_theta;
double torus_theta, torus_phi, torus_psi;
} Address;
static inline void composite_address(uint32_t n, Address *addr) {
pist_encode(n, &addr->k, &addr->t);
addr->mass = pist_mass(addr->k, addr->t);
addr->mirror = pist_mirror(n);
tree_address(n, addr->tree);
surface_coord(n, &addr->surf_x, &addr->surf_y, &addr->surf_theta);
torus_angles(n, &addr->torus_theta, &addr->torus_phi, &addr->torus_psi);
}
/* ─── Register Machine State ─── */
typedef struct {
uint32_t pc; /* Program counter */
uint32_t sp; /* Stack pointer */
uint8_t acc; /* Accumulator */
uint8_t flags; /* Condition codes: bit0=halt, bit1=emit */
uint32_t entropy; /* Local information density */
uint32_t depth; /* Current PIST shell */
} State;
/* ─── Instruction Decode ─── */
#define OP_NOOP 0
#define OP_LOAD 1
#define OP_STORE 2
#define OP_ADD 3
#define OP_XOR 4
#define OP_BRANCH 5
#define OP_FUSE 6
#define OP_HALT 7
static inline uint8_t decode_opcode(uint8_t b) { return b & 0x07; }
static inline uint8_t decode_operand(uint8_t b){ return b >> 3; }
/* ─── Quasi-Periodic Keystream Modulation ─── */
static inline uint8_t keystream_value(uint32_t n) {
double t, p, s;
torus_angles(n, &t, &p, &s);
double mod = sin(t) + cos(p) + sin(s);
return (uint8_t)((mod + 3.0) * 42.5); /* Map [-3,3] to [0,255] */
}
/* ─── Basis Operations ─── */
static uint8_t basis[BASIS_SIZE]; /* Current prediction basis */
static uint8_t data_stack[STACK_SIZE]; /* Data stack for STORE/LOAD */
static inline uint8_t basis_predict(uint32_t n, uint8_t opcode, uint8_t operand) {
/* Simple prediction: rotate through basis by position */
return basis[n % BASIS_SIZE] ^ operand;
}
static inline void basis_fuse(uint8_t *parent_a, uint8_t *parent_b, int size) {
/* Set intersection + bilinear hybrid (placeholder) */
for (int i = 0; i < size && i < BASIS_SIZE; i++) {
basis[i] = (parent_a[i] + parent_b[i]) >> 1; /* mean operator */
}
}
/* ─── Execute Single Instruction ─── */
static inline void execute(uint8_t opcode, uint8_t operand, uint32_t pos, State *st) {
Address addr;
composite_address(pos, &addr);
switch (opcode) {
case OP_NOOP:
break;
case OP_LOAD:
/* Read from basis vector at coordinate-derived index */
st->acc = basis[addr.mass % BASIS_SIZE] ^ operand;
break;
case OP_STORE:
/* Push to data stack */
if (st->sp < STACK_SIZE) {
data_stack[st->sp++] = st->acc;
}
break;
case OP_ADD:
/* Add weighted coordinate value */
st->acc = (st->acc + (uint8_t)(addr.mass % 256) + operand) & 0xFF;
break;
case OP_XOR:
/* XOR with mirror prediction */
st->acc ^= (uint8_t)(addr.mirror % 256) ^ operand;
break;
case OP_BRANCH:
/* Conditional skip based on mass threshold */
if (addr.mass < (addr.k * (addr.k + 1))) {
st->flags |= 0x02; /* Set skip flag */
}
break;
case OP_FUSE:
/* Placeholder: would fuse with parent basis */
/* In full implementation: decode parent basis from stream */
st->acc = st->acc ^ operand;
break;
case OP_HALT:
st->flags |= 0x01; /* Set halt flag */
break;
}
st->depth = addr.k;
st->entropy = addr.mass;
}
/* ─── Main Decoder Loop ─── */
/*
* The compressed stream format embedded after the code section:
* [BOOTSTRAP: 16 bytes basis] [PROGRAM: variable-length byte sequence]
*
* The decoder reads itself to locate the embedded data.
*/
static const char *self_path = NULL;
static void set_self_path(const char *argv0) {
self_path = argv0;
}
static uint8_t *read_embedded_stream(size_t *out_len) {
FILE *self = NULL;
/* Try argv[0] first */
if (self_path) {
self = fopen(self_path, "rb");
}
/* Fallback to common names */
const char *fallbacks[] = {"archive9.exe", "archive.exe", "./archive9.exe", "./archive.exe", NULL};
for (int i = 0; !self && fallbacks[i]; i++) {
self = fopen(fallbacks[i], "rb");
}
if (!self) {
fprintf(stderr, "Error: cannot open self (tried %s and fallbacks)\n",
self_path ? self_path : "(none)");
exit(1);
}
fseek(self, 0, SEEK_END);
size_t total_size = ftell(self);
/*
* Find marker that separates code from data.
* In practice, the build process appends compressed data after compilation.
* For now, we use a simple marker at the end.
*/
uint8_t marker[8] = {0xDE, 0xAD, 0xBE, 0xEF, 0x50, 0x49, 0x53, 0x54}; /* "PIST" */
/* Search backwards for marker */
size_t data_start = 0;
uint8_t buf[8];
for (size_t i = total_size - 8; i > 0; i--) {
fseek(self, i, SEEK_SET);
if (fread(buf, 1, 8, self) == 8) {
if (memcmp(buf, marker, 8) == 0) {
data_start = i + 8;
break;
}
}
}
if (data_start == 0) {
fprintf(stderr, "Error: embedded data marker not found\n");
fclose(self);
exit(1);
}
size_t data_len = total_size - data_start;
uint8_t *data = malloc(data_len);
if (!data) {
fprintf(stderr, "Error: malloc failed\n");
exit(1);
}
fseek(self, data_start, SEEK_SET);
fread(data, 1, data_len, self);
fclose(self);
*out_len = data_len;
return data;
}
/* ─── Prediction Model ───
* For roundtrip testing, the simplest model is:
* prediction(n) = basis[n % BASIS_SIZE] ^ keystream_value(n) ^ (n & 0xFF)
* output(n) = prediction(n) ^ residual(n)
* where residual(n) is the byte from the compressed stream.
*
* The compressor finds residuals such that output equals the original data.
* This is trivial: residual = data XOR prediction.
*
* Compression ratio depends on prediction accuracy.
* If prediction matches data, residual = 0 (runs of zeros compress well).
*/
static inline uint8_t predict(uint32_t n) {
uint8_t b = basis[n % BASIS_SIZE];
b ^= keystream_value(n);
b ^= (n & 0xFF);
b ^= (uint8_t)(pist_mirror(n) % 256);
return b;
}
/* ─── AngrySphinx Gear Reduction & FAMM Scar Tracking ───
*
* Gear Law: C_out = G_AS * C_in + C_semantic + C_reality + C_constructive + C_cringe
*
* FAMM-coupled gear ratio:
* G_AS(t) = 1 + alpha*L_FAMM(t) + beta*R_repeat(t) + gamma*U_unknown(t) + delta*H_route(t)
*
* Where:
* L_FAMM = torsional stress^2 + interlock energy + phase delta
* R = repeated hostile route count
* U = unknown-route uncertainty (1 if no scars, else 0)
* H_route = frozen-route helicity / connectivity penalty
*
* In the decoder context, FAMM scars act as negative context:
* - Failed predictions are recorded as route scars
* - Future basis selection avoids scarred prediction paths
* - Gear ratio increases with accumulated hostile engagement
*/
#define FAMM_MAX_SCARS 256
#define FAMM_HASH_MOD 251
typedef struct {
uint32_t route_hash;
uint8_t outcome; /* 0=success, 1=failure, 2=trap, 3=partial */
uint16_t effort; /* scaled effort value */
} FAMMScar;
static FAMMScar famm_scars[FAMM_MAX_SCARS];
static uint16_t famm_scar_count = 0;
static inline uint32_t route_hash(uint32_t n, uint8_t opcode) {
/* Simple route signature: position + opcode mix */
return ((n * 2654435761u) ^ (opcode * 0x9E3779B9)) % FAMM_HASH_MOD;
}
static inline void famm_record_scar(uint32_t n, uint8_t opcode, uint8_t outcome, uint16_t effort) {
if (famm_scar_count >= FAMM_MAX_SCARS) {
/* FIFO eviction: shift scars down */
memmove(&famm_scars[0], &famm_scars[1], sizeof(FAMMScar) * (FAMM_MAX_SCARS - 1));
famm_scar_count = FAMM_MAX_SCARS - 1;
}
famm_scars[famm_scar_count].route_hash = route_hash(n, opcode);
famm_scars[famm_scar_count].outcome = outcome;
famm_scars[famm_scar_count].effort = effort;
famm_scar_count++;
}
static inline uint16_t famm_hostile_route_count(void) {
uint16_t count = 0;
for (uint16_t i = 0; i < famm_scar_count; i++) {
if (famm_scars[i].outcome >= 1) count++;
}
return count;
}
static inline uint16_t famm_repeated_hostile_count(uint32_t n, uint8_t opcode) {
uint32_t h = route_hash(n, opcode);
uint16_t count = 0;
for (uint16_t i = 0; i < famm_scar_count; i++) {
if (famm_scars[i].route_hash == h && famm_scars[i].outcome >= 1)
count++;
}
return count;
}
static inline float famm_load(void) {
/* L_FAMM = Sigma^2 + I_lock + Delta_phi (simplified) */
float torsion = 0.0f;
float interlock = 0.0f;
for (uint16_t i = 0; i < famm_scar_count; i++) {
torsion += famm_scars[i].effort * 0.1f;
if (famm_scars[i].outcome == 2) interlock += 1.0f;
}
float phase_delta = famm_scar_count > 0 ? 1.0f : 0.0f;
return torsion * torsion + interlock + phase_delta;
}
static inline float gear_ratio(uint32_t n, uint8_t opcode) {
/* G_AS = 1 + alpha*L_FAMM + beta*R_repeat + gamma*U_unknown */
float alpha = 0.5f;
float beta = 1.0f;
float gamma = 2.0f;
float L_famm = famm_load();
uint16_t R_repeat = famm_repeated_hostile_count(n, opcode);
float U_unknown = (famm_scar_count == 0) ? 1.0f : 0.0f;
return 1.0f + alpha * L_famm + beta * (float)R_repeat + gamma * U_unknown;
}
/* ─── Gear-Reduced Prediction ───
*
* Standard prediction is a commuting composition of basis, keystream,
* position, and mirror terms. The gear-reduced version introduces
* noncommuting composition: the FAMM-scar-modified gear ratio feeds
* back into the prediction operator sequence.
*
* Noncommuting trisqueezing analog:
* p(n) = A(B(A(n))) where A = basis-layer, B = gear-modulated layer
*/
static inline uint8_t predict_layer_a(uint32_t n) {
return basis[n % BASIS_SIZE] ^ (n & 0xFF);
}
static inline uint8_t predict_layer_b(uint32_t n, uint8_t opcode) {
float G = gear_ratio(n, opcode);
uint8_t gear_mod = (uint8_t)((uint32_t)(G * 16.0f) & 0xFF);
return keystream_value(n) ^ gear_mod ^ (uint8_t)(pist_mirror(n) % 256);
}
static inline uint8_t predict_gear_reduced(uint32_t n, uint8_t opcode) {
/* Noncommuting composition: A then B then A (trisqueezing analog) */
uint8_t a1 = predict_layer_a(n);
uint8_t b = predict_layer_b(n, opcode);
uint8_t a2 = predict_layer_a(n ^ b); /* B modifies the input to A */
return a1 ^ b ^ a2;
}
int main(int argc, char *argv[]) {
if (argc > 0) {
set_self_path(argv[0]);
}
size_t stream_len;
uint8_t *stream = read_embedded_stream(&stream_len);
if (stream_len < BOOTSTRAP_SIZE) {
fprintf(stderr, "Error: stream too short\n");
free(stream);
return 1;
}
/* Initialize bootstrap basis */
memcpy(basis, stream, BOOTSTRAP_SIZE);
/* Output buffer for batching (reduces syscalls) */
uint8_t outbuf[65536];
size_t outpos = 0;
/* Decode: one output byte per residual byte */
uint32_t n = 0;
for (size_t i = BOOTSTRAP_SIZE; i < stream_len; i++, n++) {
uint8_t residual = stream[i];
uint8_t p = predict(n);
uint8_t out = p ^ residual;
outbuf[outpos++] = out;
if (outpos >= sizeof(outbuf)) {
fwrite(outbuf, 1, outpos, stdout);
outpos = 0;
}
}
/* Flush remaining output */
if (outpos > 0) {
fwrite(outbuf, 1, outpos, stdout);
}
free(stream);
return 0;
}
/* ─── Build Instructions ───
*
* 1. Compile decoder:
* gcc -O3 -s -fno-stack-protector -fomit-frame-pointer \
* -o archive.exe hutter_pist_decoder.c -lm
*
* 2. Strip symbols:
* strip --strip-all archive.exe
*
* 3. Embed compressed data:
* cat archive.exe compressed_stream.bin > archive_tmp.exe
* mv archive_tmp.exe archive.exe
* chmod +x archive.exe
*
* 4. Verify:
* ./archive.exe | cmp - enwik9
*
* Size targets:
* Current record L = 110,793,128 bytes
* Decompressor binary ~8-15KB (with -O3 -s)
* Compressed data budget ~109MB for 1% prize
*/
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