0D Genus Layer: Absorbing Infinities

0D Genus Layer

Zero-width layer at genus-0 absorbing all infinities from physics equations (Hawking-Ellis, Vaidya, EFE)

Gabriel's Horn Model

Finite volume (π) + infinite surface area; tip as x→∞ IS the 0D genus layer geometry

Menger-Horn Pipeline

16D→0D dimensional descent like Gabriel's Horn with shrinking cross-section

Torricelli Paradox Reframed

You can fill coverage domain (finite) but cannot paint its boundary (infinite); 0D layer absorbs painting

Summary: Resolves infinity requirements from physics equations by embedding them into zero-width 0D genus layer, modeled by Gabriel's Horn tip geometry.


Prime Gap Entropy Collapse DeepSeek v3.2 Review

Prime Gap Entropy Collapse Detector

Sliding-window detector using braid crossing count, Hurst exponent (σ_q), and correlation dimension (D₂) on prime gaps to identify entropy-collapse motifs.

K=7 Braid Threshold

Original non-selective threshold with 94.57% FPR under random-permutation null. Identified as artifact source.

K=21 Corrected Threshold

Calibrated threshold yielding ~5% FPR under random-permutation null. Strict >21 gives 3.05% FPR; inclusive >=21 gives 5.43%.

Fusion Rule

Triple condition: braid(t→t+1) AND sigma_q(window t+1) AND D_q(window t+1) targeting turbulent transition into collapsed arrival window.

Random-Permutation Null

Statistical null model assuming distinct values and uniform marginals; inappropriate for prime gaps due to ties and local dependence.

Sidon Label

Address from a set where all pairwise sums are distinct; powers of 2 are canonical Sidon set for 8 strands.

Summary: DeepSeek v3.2 review validates the prime-gap entropy-collapse detector arithmetic, identifies K=7 as non-selective (94.57% FPR), confirms K=21 as defensible at ~5% FPR, and catalogs 6 failure modes including tied ranks and overlapping windows.


Prime Gap Entropy Collapse DeepSeek v4-Flash Continuation

Canonical Spec Patches

10 explicit warnings and clarifications to add to the canonical spec covering heuristic thresholds, window features, prime-gap null mismatch, multiple testing, and reproducibility.

Parameter Sensitivity

Results depend on window size (n=8), step size (1), and feature thresholds; small changes can eliminate or create signals.

Edge Effects

First and last n-1 windows have incomplete neighbors for the fusion rule; must be excluded or treated separately.

Summary: Continuation of DeepSeek review providing 10 canonical spec patches including warnings about heuristic thresholds, window features, prime-gap null mismatch, multiple testing, and reproducibility requirements.


Adversarial Review: Semantics Lean Codebase

QFactor Double-Scaling Bug

ofNat 65536 creates Q16_16 with raw integer 65536*65536=4294967296 which saturates to q16MaxRaw, producing garbage results in calculateQFactor.

sub_eq_add_neg Overflow

Admitted theorem that is false when b.toInt = q16MinRaw because neg q16MinRaw overflows to q16MaxRaw, off by 1.

abs_mul_le False Theorem

Admitted theorem with documented counterexamples; downstream modules can derive False from it.

ofFloat in Compute Paths

942 occurrences of ofFloat in compute paths violating AGENTS.md mandate; undermines fixed-point determinism guarantee.

Division by Zero Asymmetry

Q16_16 division by zero returns infinity (maxVal) while Int division by zero is silent no-op; creates divergent behavior.

Tautological Eigensolid Convergence

eigensolid_convergence proof is h_eig — hypothesis IS the conclusion; provides no actual convergence guarantee.

ACI Preservation Theorem

Central safety theorem of SSMS admitted with dependencies on known-false lemmas sub_eq_add_neg and abs_triangle.

Sidon Slack Underflow

UInt32 subtraction wraps around if slot > 128; no precondition ensures slot ≤ 128 in BraidEigensolid.lean.

AVMIsa Missing Primitives

Prim.addSatQ16 and Prim.subSatQ16 declared but not implemented in evalPrim; always return typeMismatch error.

Q16_16 Constants via ofFloat

pi, e, ln2, sqrt2 defined via ofFloat introducing 1 LSB error; should use ofRatio with rational approximations.

Summary: Comprehensive adversarial review of Semantics Lean codebase finding 7 CRITICAL, 12 HIGH, 18 MEDIUM, 9 LOW issues including false admitted theorems, 942 ofFloat violations, tautological convergence proof, and systemic Q16_16 compliance failures.


Full Adversarial Review — Research Stack

Verilog Q16_16 Multiply Bug

a_reg * b_reg produces Q32.0 not Q16.16; missing >>16 shift means every hardware computation through the central ALU is off by 2^16.

WGSL Data Races

Pervasive non-atomic += on shared storage buffers from multiple workgroups; all GPU compute results are non-deterministic.

Rust Double-Free

Arc::from_raw on pointer from Arc::as_ptr steals reference count; exploitable memory corruption in thermodynamic.rs.

Shell Injection

format!("command -v {command}") passes unsanitized input to sh -lc; arbitrary command execution in tools/src/lib.rs.

Hardcoded Credentials

30+ files contain plaintext passwords, OAuth secrets, and API keys committed to git.

SHA-256 Padding Bug

Only 62 bits assigned instead of 64-bit big-endian bit count in cff_accelerator.v; all hardware hashes incorrect.

Remote Code Execution Vectors

11 RCE vectors across Python (pickle.load, eval, torch.load, trust_remote_code), Rust (shell injection), and Shell (root password in process list).

Credential Exposure

8 credential exposure sites including production RDS hostname, internal Tailscale IPs, decrypted credentials printed to stdout, and bearer tokens over HTTP.

Summary: Full-codebase adversarial review scanning ~35,000 source files finding 248 issues (51 CRITICAL, 76 HIGH, 80 MEDIUM, 41 LOW) across Lean, Verilog, WGSL, Rust, Python, TypeScript, and Shell with 11 RCE vectors, 8 credential exposures, and systemic AGENTS.md compliance violations.


QC Report — Physics/ Code Structure & Efficiency

absDiff Duplication

absDiff function duplicated 4x across DESIInvariant, H0ValveTest, ValveTestSuite, ClusterBHAnchors; should be in Shared.lean.

scale = 65536 Duplication

scale constant duplicated 6x; should be single shared definition.

Dead Code

Dead q16_div in DESIModelProjection, dead DESIParam in DESIInvariant, dead ModelParams/Residual/Verdict structures.

Naming Convention Audit

rD → rd field naming, SCALE vs scale casing inconsistency, Q16.16 arithmetic inconsistency between files.

Summary: QC report finding 4 high-priority structural issues (duplication + dead code), 5 medium-priority (dead structures, consolidation), and 5 low-priority (consistency, naming) across 8 Physics/ files, all building cleanly with 3529 jobs.


Claim Cross-Reference Report: Attack CSVs vs. Research Stack Repo

Claim Cross-Reference Methodology

Direct grep search across repo followed by file content inspection; classification: DEFENDED, ORPHANED, RENAMED, UNEXPECTED_CONNECTION.

Epistemic Tag Self-Correction

Repo uses PRIOR ART, PROJECT DATA, INFERENCE, SPECULATIVE tags to self-label claim strength; attack misses this self-correction mechanism.

Sidon Addressing Novelty

Attack confirms Sidon addressing as genuinely novel; implemented in Rust + Python + Lean.

Attack reads user-requested analogies and thought experiments as scientific claims; assistant consistently warned against literal interpretation.

Honesty Audit

Repo's boundary statements and epistemic tags are more precise than attack's blunt verdicts; repo is self-critical about its own claims.

Orphaned Claims

RFS-16096, hydrogen closure η_H=τ/α, and 'Underverse' have zero repo evidence.

Summary: Cross-references attack CSVs against repo evidence across number theory, math physics, fractal topology, and framework domains; finds attack is directionally correct but systematically mischaracterizes conversational genre as scientific claims, missing the repo's self-correction mechanisms.


Theorem Jiggle DAG

Theorem Jiggle

Placeholder or vacuous theorem proving trivial statements; fixed by replacing with honest comments or real consistency checks.

get! Without isSome Guard

Unsafe array access .get! without companion .isSome theorem; fixed by adding intermittency_midpoint_some companion theorem.

Heuristic Constants

Moody chart slopes, calibrated w0, wa with no SM derivation — acknowledged as heuristic but acceptable for engineering bridge.

Summary: Audited 82 theorems across Physics/ files, fixed 3 jiggles (placeholder theorems, vacuous bounds, missing guards), acknowledged 10 known jiggles as acceptable heuristics, with 69 clean theorems (84%) and 3529-job zero-error build.


RG Flow Assumption DAG

SM Beta Functions

Standard 1-loop RGEs for SM couplings validated by LEP, LHC, g-2 to 10^-12; Generation 1 — SOLID.

omega = |β|/|g|

Well-defined dimensionless number at EW scale (0.05775); calling it 'torsion' is a metaphysical leap with no geometric justification.

alpha = max|β|/(4π)

Invented relation with no Lagrangian term; 1-loop formula gives 10% error, 2-loop correction retrofitted to match α=1/137.036.

w0 Projection Formula

Heuristic projection with no QFT derivation; uses ΛCDM best-fit values to predict deviation from ΛCDM — circular.

wa from SM Running

SM gives wa≈-0.06 from Higgs running; DESI observes wa=-0.59±0.25. Factor 10 gap — most interesting tension.

CMB from omega

Q≈ω·α/π predicts CMB fluctuation amplitude 13× above measured; handwaved as Saha approximation error.

Summary: Traces 7 generations of RG flow assumptions; Gens 1-2 pass inspection (SM beta functions solid, omega defined but mislabeled), Gens 3-7 are invented/heuristic/broken; recommends deleting CMBTorsion.lean and TorsionWall.lean unless alpha formula gets proper derivation.


QC Fix DAG — Missing Witnesses

Missing Witness Fix

Added #eval witnesses and annotations to 10 files that lacked computational verification for their definitions.

Summary: Added missing #eval witnesses and annotations to 10 Physics/ files; lake build passes.


QC Fix DAG — Unused Imports Removal

Unused Import Removal

Removed redundant imports from 6 files; kept imports that are directly used. Verified by 3530-job lake build.

Summary: Removed unused imports from 6 Physics/ files while preserving all directly-used imports; 3530-job build passes.


QC Naming Round 2 Fix DAG

Naming Convention Enforcement

Completed 20 renames across 4 files converting snake_case to camelCase per AGENTS.md §2 naming conventions.

Hermite Spline Constants

RE_LAMINAR→reLaminar, RE_TURBULENT→reTurbulent, Y0→y0, Y1→y1, H_M0→hM0, H_M1→hM1 in UniversalBridge.lean.

Summary: Completed 20 renames across 4 files converting snake_case to camelCase; verified cross-file references, 3530-job build passes.


QC Fix DAG — Naming Convention Fixes

LawfulInteraction Rename

Renamed to lawfulInteraction across Conservation.lean, Interaction.lean, Tests.lean (3 files).

FaithfulMeasurement Rename

Renamed to faithfulMeasurement in Projection.lean and Tests.lean (2 files).

Q16 Constant Naming

Renamed G_const→gConst, c_const→cConst, hbar_const→hbarConst, kB_const→kBConst in StringStarConstants.lean.

Summary: Renamed 40+ symbols from snake_case to camelCase across 9 files; all cross-references updated; 3530-job build passes.


QC Fix DAG — L13/L14: DESIInvariant Naming & Precision

rD→rd Field Rename

Renamed DESIObservation.rD to rd for camelCase consistency.

rdDr1/rdDr2 Precision Fix

Changed rdDr1 from 147 to 14709 and rdDr2 from 147 to 14718 (×100) for sub-Mpc precision.

Summary: Renamed rD→rd field and increased BAO sound horizon precision to ×100 (147→14709/14718) in DESIInvariant.lean; 3530-job build passes.


QC Fix DAG — L10: h00/h01 Helper Factoring

hermiteSharedTerms Helper

Private helper factoring shared Q16.16 arithmetic (t2, t3, term3, term2) from h00 and h01 basis functions.

Summary: Factored shared Q16.16 arithmetic into hermiteSharedTerms helper, reducing duplication in h00/h01 basis functions; 3530-job build passes.


QC Flagger Build DAG — Automated Inspection Tool

Automated 5-point inspection tool for Lean files: structural health, naming conventions, Q16_16 compliance, proof quality, dependency analysis.

QC Flagger Protocol

5-point inspection: structural health (sorry/axiom count), naming (camelCase check), Q16_16 compliance (Float detection), proof quality (companion theorems), dependency analysis (unused imports).

Summary: Built lean_qc_flagger.py automated 5-point inspection tool covering structural health, naming, Q16_16 compliance, proof quality, and dependencies; tested on 20 Physics/ files with 227 issues found (0 ERROR).


QC Fix DAG — F01: 7 sorry Theorems

F01 Q16_16 FixedPoint Theorems

7 theorems examined: 6 PASS (add_total, mul_total, div_total, round_valid, mul_no_overflow, E_0_bounds), 1 FAIL (convergence_to_fixed_point requires Banach fixed-point theorem).

convergence_to_fixed_point Quarantine

Theorem quarantined because it requires Banach fixed-point theorem not available in Mathlib.

Summary: Examined 7 sorry theorems in F01_Q16_16_FixedPoint.lean; proved 6 via exact/simp tactics, quarantined convergence_to_fixed_point as it requires Banach fixed-point theorem; 3530-job build passes.


QC Consolidated Fix DAG

Consolidated QC DAG

Mermaid DAG aggregating all QC fixes: L10 (helper factoring), L13/L14 (naming/precision), F01 (sorry proofs), flagger tool.

QC Resolution Rate

13 of 14 original QC issues resolved, 1 quarantined (convergence_to_fixed_point).

Summary: Consolidated DAG of all QC fixes: 9 issues fixed, 1 quarantined, 1 new tooling (lean_qc_flagger.py); 3530-job zero-error build.


Prime Gap Entropy-Collapse Rerun Receipt — K=21

K=21 Rerun

Rerun of prime-gap detector with corrected strict threshold crossing_count>21; 38 strict fires across 999,991 windows in first 1M primes.

Braid-Tail-Only Counts

Counts using only the braid component without sigma_q/D2 filter; shows braid component alone fires much more frequently.

Strict Fire Examples

First 5 strict fires at t=51541,71717,88616,117020,136640 with crossing counts 22-23 and alternating small/large gap motifs.

Summary: Reruns prime-gap entropy-collapse detector with corrected K=21 threshold; original K=7 signal (86,565 fires) reduces to 38 strict fires (0.0038%), confirming the original was an artifact of non-selective threshold.


Full-Stack Assumption DAG

Full-Stack Audit

78 files audited, ~280 assumptions identified across Physics/Lean, Infrastructure/Shim, and 5-Applications.

Assumption Severity Grades

Green (solid proofs), Yellow (structurally correct but claims not proven), Red (0 theorems, claims in comments only).

Physics Module Grades

PIST.lean Green (17+ real proofs), BraidedFieldPaths Yellow, BraidCross/Law19_VoidScar/BoundaryEigenFire/HyperEigenSpectrum/FAMM/BraidBracket/BraidStrand/BraidField/NBody Red.

Infrastructure Heuristic Assumptions

190+ heuristic assumptions across ~22 receipt generators; dominant failure mode: metaphors written as equations.

PIST Compression

PIST 'compression' is coordinate remapping, not compression; multiple scripts import shock physics as metaphor.

Summary: Full-stack audit of 78 files finding ~280 assumptions; PIST.lean is Green (17+ real proofs), 10+ modules are Red (0 theorems, claims in comments only), Infrastructure has 190+ heuristic assumptions, and NBody.lean has a broken theorem referencing nonexistent lemma.


Deterministic Build Receipt

DESI DR2 Constants

Hardcoded Int literals for w₀=-58327, w_a=-31457, w₀(ΛCDM)=-65536, H₀=6826, Ω_m=19312, σ₈=52953, r_d=147; zero Float.

native_decide Theorems

17 theorems verified by native_decide: w0_above_LCDM, wa_below_LCDM, w0_in_3sigma, wa_in_3sigma, omegam_in_3sigma, model_w0_direction_aligns, model_wa_direction_aligns, residual bounds.

Determinism Guarantee

Every value is a hardcoded Int literal, verified by native_decide (compile-time deterministic), verified by #eval (same result every build), within Lean namespace (no global mutable state).

Adjacent Coprime Classification

30 theorems verified by native_decide for Fibonacci, Bad, Ex3, Bad2, Ex5 examples with pairwise gcd checks.

Summary: Deterministic build receipt with 3529 jobs, 0 errors; all values are hardcoded Int literals verified by native_decide and #eval; 17 theorems in DESI modules, 30 in AdjacentCoprimeClassification; zero Float arithmetic.


DESI Model Projection Receipt

DESI DR2 Observational Invariants

w₀=-0.89, w_a=-0.48, Ω_m=0.2947, σ₈=0.808, H₀=68.26, r_d=147 Mpc with Q16_16 encodings.

16D Menger/Koch/Gabriel-Horn Fiber Model

Model projected onto DESI DR2 observables; w₀ calibrated (not predicted), w_a/Ω_m/σ₈ are structural predictions.

Boundary Statement

Explicit statement: NOT a cosmological model, NOT a replacement for ΛCDM; IS a receipt that Menger/Koch/Gabriel-Horn geometry reproduces direction and sign of observed dark-energy deviation.

Verified Geometry Constants

Menger d_H=2.7268, Koch D_K=1.2619, divergence base=1.8, horn volume=finite, horn surface α=0.007, torsion β=0.003; all proven in Lean.

w_a Tension

Model predicts -0.55, DESI observes -0.48; within 1σ but model central value more negative; worth tracking as precision improves.

Summary: DESI model projection receipt documenting 17 native_decide theorems comparing 16D Menger/Koch/Gabriel-Horn fiber model against DESI DR2; all observables consistent within 1σ; w₀ calibrated not predicted; explicit boundary statement that this is NOT a cosmological model.


Research Stack Receipt: Persistent Codebase Memory

FAMM-Based Codebase Memory

Rust crate implementing persistent codebase memory with DualMapMemory (ahead/behind maps), DomainBank (1000-cell FAMM bank), and scar differentials.

CodeDomain

7 domains (0-Core through 6-Docs) for organizing codebase artifacts.

CodeCell

Artifact with path, type, data, delay (staleness), delay_mass (uncertainty), version_hash.

DualMapMemory

ahead (speculative) + behind (committed) + per-domain scar differentials; commit_if_admissible checks |Delta| <= epsilon.

MemoryAccessReceipt

Receipt emitted by observe/commit operations for auditability.

Summary: Built FAMM-based persistent codebase memory Rust crate with 7 CodeDomains, 1000-cell DomainBank, DualMapMemory with scar differentials; 6 tests pass; 3 Lean modules quarantined due to naming collisions.


M4 Receipt — Rydberg 1/n Experimental Test Pre-Registration

Rydberg 1/n Prediction

Fractional frequency shift Δν/ν of rotational transitions in high-n circular Rydberg states scales as 1/n with coefficient C=7/27≈0.259.

Pre-Registration Lock

Prediction coefficient C=7/27 and test states [40..100] fixed on 2026-05-22; not subject to post-hoc modification.

Falsification Criteria

If |Δν/ν(n) - C/n| > 2σ for ≥3 distinct n values in [40,100], prediction falsified; if ≥5 of 7 test states consistent, provisionally confirmed.

RydbergExperimentalTest Module

Lean module with predictedFracShift, uncertainty envelopes, fracShiftConsistent, testStates, minConsistentStates, falsificationThreshold, PreRegistration structure, 4 theorems + 7 #eval! witnesses.

Summary: Pre-registered experimental test predicting Δν/ν = (7/27)/n for high-n Rydberg states; formalized in Lean with honest uncertainty envelopes, falsification criteria, and 7 test states; awaiting ETH Zürich experimental data.


M3 Receipt — Honest Uncertainty Bounds Fix

PredictedValue Structure

Structure with central/lower/upper/sigma fields for honest uncertainty envelopes; replaces exact-match claims.

Exact-Match Replacement

Replaced 6 '0.00% error' exact-match theorems with honest uncertainty envelopes using residualBounded and percentResidual.

Calibration vs Prediction

w₀ is calibrated (set equal to DESI central value), not predicted; residual bounded at 0σ by design.

Fine Structure Constant Honest Bound

Changed from residual=0 to residual≤66 (Q16_16 resolution); residual≈1.7×10⁻⁶ well within fixed-point truncation.

Summary: Replaced 6 exact-match '0.00% error' claims with honest uncertainty envelopes using PredictedValue structure; clarified w₀ calibration vs prediction; fine-structure constant residual bounded at Q16_16 resolution.


Credential Server & PQ SSH Recovery Receipt

Credential Server

HTTP API at 172.245.19.182:8444 serving credentials for 8 providers (deepseek, quandela, wolfram_alpha, gemini, ollama, venice, bedrock, linear).

Post-Quantum SSH

OpenSSH 10.0p2 with ML-KEM + X25519 hybrid KEX (mlkem768x25519-sha256); Ed25519 host keys; legacy DSA/SSHv1 removed.

Credential Provider

Client-side module querying microVM for credentials; resolution chain: rds → remote → config_file → env.

Credential Recovery

Recovery steps: extract keys from Research-Stack-Archive-2026-05-12.tar, run recover_credential_server.sh, verify /status endpoint.

Summary: Documents credential server deployment on RackNerd microVM with 8 provider backends, post-quantum SSH (ML-KEM+X25519 hybrid), and recovery procedure from Research-Stack-Archive.


RDS Substrate Provisioning Receipt

RDS Substrate

PostgreSQL 17.7 on aarch64 at database-1-instance-1.cghu8yqogqwo.us-east-1.rds.amazonaws.com:5432; IAM auth, SSL required.

Provisioned Schemas

4 schemas (credential_store, topology, knowledge, ingestion) with 9 tables covering encrypted credentials, node topology, pgvector embeddings, and job queue.

pgvector Knowledge Storage

HNSW-indexed pgvector(1536) embeddings table for document chunk vectors.

Credential Ingestion

6 providers (bedrock, deepseek, ollama, quandela, venice, wolfram_alpha) ingested with classification levels and node assignments.

Summary: Provisioned PostgreSQL 17.7 RDS as central data substrate with 4 schemas (credential_store, topology, knowledge, ingestion), pgvector HNSW embeddings, and 6 ingested credential providers.


Credential Provider Deployment Receipt

apiProvider Service

New ServiceKind added to TopologyNode.lean with [.network] hardware requirements and 1 Q16_16 cost per tick.

Source Credential Extraction

6 API keys extracted from Research-Stack-Archive-2026-05-12.tar: DeepSeek, Quandela, Wolfram Alpha, Gemini, Ollama, Venice.

Credential Provider Module

Python module credential_provider.py with resolve_credential(provider) interface; resolution chain: rds → remote → config_file → env.

Summary: Deployed apiProvider service to microVM topology; extracted 6 API keys from archive; created credential_provider.py with multi-source resolution chain; Lean verification blocked by pre-existing FixedPoint.lean failures.


E2E Master Receipt — End-to-End Trace for E = mc²

E2E Master Trace

8-step end-to-end pipeline processing E=mc² from raw LaTeX through EquationShape, spectral profile, Sidon address, chaos game, Finsler metric, QUBO, QAOA, Hachimoji state, to SHA-256 receipt.

EquationShape Parsing

Structural signature ⟨n_vars=3, n_ops=2, max_depth=1, n_quantifiers=0, n_relations=1⟩ for E=mc²; proven by rfl.

Sidon Address

8-element Sidon address [4,16,16,1,16,1,16,8] as spectral fingerprint; proven valid by simp.

Chaos Game Basin Convergence

Deterministic Sidon-guided chaos game converging to q_braid basin in 1390 steps; IFS contraction α=0.5.

Finsler Metric Construction

F = α(Fisher) + β(torsion drift) Randers metric; α=0.4167 base cost, β=0.1500 drift strength.

QUBO Encoding

8 binary variables, 36 couplings encoding Finsler path cost as quadratic unconstrained binary optimization.

QAOA Circuit

p=2 depth, 8 qubits, approximation ratio >0.95; bitstring [1,0,0,0,0,0,0,0] selecting Φ state.

Hachimoji State Φ

beautifulTopologicalFolding regime, phase 0°, forward direction, ambidextrous chirality; proven by rfl.

Merkle Receipt Hash

SHA-256 hash of canonical JSON (sorted keys, no whitespace) of all 8 step witnesses; any change invalidates receipt.

Summary: Complete 8-step E2E trace for E=mc²: 3 steps PROVEN (shape, Sidon, Hachimoji), 3 COMPUTED (chaos game, QAOA, hash), 2 STATED with sorry (Finsler, QUBO); 15 top-level theorems, receipt SHA-256 committed.


Master Receipt: Chentsov-Hachimoji Library Integration

Chentsov's Uniqueness Theorem

Fisher information metric is the unique Riemannian metric on the 8-state Hachimoji probability simplex; proven with zero sorry in ChentsovFinite.lean.

HachimojiCodec Pipeline

5-stage deterministic pipeline: Parse → Classify → Receipt → Admit → Emit; converts equations to certified emit stamps.

Fisher-Metric Classification

Equations classified by Fisher-metric distance on the Chentsov-unique simplex; thresholds forced by the metric, not hand-tuned.

Triple RRC Admission

Three gates: typeAdmissible (structural type match), projectionAdmissible (Fisher distance in region), mergeAdmissible (both pass).

Hachimoji States

8 states: ADMIT(A), TRACE(T), GROUND(G), CHALLENGE(C), BIND(B), SEARCH(S), PROOF(P), ZERO(Z) with Fisher distance ranges.

Deterministic Classification

No randomness, no ML, no external state; same equation always produces same state, receipt, and stamp.

Summary: Integrates Chentsov's uniqueness theorem (Fisher metric is unique on Δ⁷, proven zero sorry) with HachimojiCodec 5-stage pipeline; 12/12 test equations pass; 7/12 admitted via triple RRC gating; receipt hash committed.


Hachimoji Codec — Library Receipt

EquationShape

5-field structure: n_vars, n_ops, max_depth, n_quantifiers, n_relations extracted from equation text.

HachimojiState

8 Greek states (Φ, Λ, Ρ, Κ, Ω, Σ, Π, Ζ) with conditions based on structural features.

LogogramReceipt

Receipt with regime (beautifulTopologicalFolding/tornManifoldRegime/horribleManifoldTearing) and 5 witness booleans.

Admission Gates

typeAdmissible, projectionAdmissible (payloadBound ∨ (tearBoundary ∧ ¬detachedMass)), mergeAdmissible (¬residualLane).

Regime Table

Maps each Hachimoji state to regime and 5 boolean witness flags determining admission outcome.

Summary: Hachimoji codec receipt documenting 5-stage pipeline (Parse→Classify→Receipt→Admit→Emit), 8 Hachimoji states with regime tables, 3 admission gates, 6/6 tests passing, and full determinism guarantee.


Conceptual Upgrade Receipt — Operator-Theoretic Hachimoji Codec V2

4-dimensional state descriptor: Phase × Chirality × Direction × Regime; 144 possible 4-tuples, only 8 canonical states satisfy all invariants.

Consistency Invariant

6 rules encoding structural coherence: Phase-Direction, Axis-Chirality, Beautiful Phase Range, Horrible Phase Range, Left Chirality-Direction, Regime Half-Plane.

consistency_error_bound Theorem

¬consistencyInvariant(s) → admission(s, shape) = QUARANTINE; deterministic structural guarantee replacing statistical reasoning.

Counterexample Detection

Detects old pipeline E∘S failure modes: DEGENERATE_PROJECTION, EMPTY_EIGENSPACE, NO_SPECTRAL_STRUCTURE, SAMPLING_NON_TERMINATION, BASE_RATE_LEAKAGE.

Base-Rate Leakage

Old spectral pipeline appeared to work because Fiedler vector is near center of eigenspace distribution; any estimator returning mean gets ~92.5% purity for free.

Operator-Theoretic Shift

From statistical reasoning ('92.5% purity') to structural reasoning ('4-tuple satisfies all 6 invariants'); no sampling, no randomness.

Summary: Upgrades Hachimoji codec from 1D regime classifier to 4D state descriptor with 6-rule consistency invariant, counterexample detection for old pipeline failure modes, and theorem-backed deterministic structural guarantee; 17/17 + 14/14 + 10/10 tests pass.


BIND Optimization Receipt v2.0

Bind Semigroup Cocycle

Reformulated BindAssociative as semigroup cocycle condition: f(ab,c)+f(a,b) = f(a,bc)+f(b,c); well-typed, mathematically meaningful, general for any A and M.

Five Bind Axioms

Associativity (cocycle), Identity (monoid), Metric Monotonicity, Triangle Inequality, Torsion Awareness; all as Lean classes extending Associative.

T1 SIM Reduces to Fisher-Rao

When τ=0, torsion tensor vanishes, Fisher metric is unique monotone metric by Chentsov's theorem, SIM flow reduces to Fisher-Rao natural gradient flow.

S1-S4 Specializations

S1_FisherRaoBind (τ=0, commutative), S2_AlcubierreBind (τ=warp), S3_MOIM_Bind (empirical), S4_MetabolicBind (evolving, genus-3).

Fisher information matrix is symmetric by commutativity of real multiplication; proven by rw [mul_comm].

Vacuous Theorem Elimination

Replaced 4 True:=by trivial theorems (T1-T4) with proper mathematical statements with sorry and detailed proof sketches.

Summary: Rewrites bind axiomatization from broken ill-typed associativity to semigroup cocycle condition; eliminates 4 vacuous True:=by trivial theorems with proper statements; adds S1-S4 specializations; 4 proven theorems, 10 sorry with proof sketches.


Closed Trace Receipt — End-to-End Integration

Closed Trace v1

6-step end-to-end trace for E=mc²: EquationShape → 5D Manifold → Sidon Address → Chaos Game → Bind Cost → Merkle Hash; 9 proven, 3 stated.

5D Manifold Projection

complexity=0.667, abstraction=0.0, verification=1.0, cross_domain=0.5, utility=0.42 for E=mc²; proven by rfl.

Bind Cost (Fisher-Rao)

bind_cost≈1.208 using Fisher-Rao distance with BindTriangleInequality axiom; stated with sorry.

Merkle Tree Hash Chain

SHA-256 receipt hash computed from all 5 witness hashes; singleton root equals element, mixing is non-commutative.

Summary: First closed end-to-end trace for E=mc² through 6 components; 9 theorems proven, 3 stated with sorry; demonstrates all optimized components wire together from equation text to cryptographic receipt.


Sidon-Chaos Optimization Receipt

Sidon Chaos Addresses

8-element Sidon set {1,2,4,8,16,32,64,128} for strand labeling; proven Sidon by native_decide.

MAIN THEOREM: Two trajectories with same total address and length≤2 have same unordered strand pairs; proven via Sidon property of powers of 2.

Basin assignment is unique for short trajectories; same address implies same trajectory (up to permutation).

All 36 unordered pairwise sums are distinct, achieving theoretical Sidon maximum; proven by native_decide.

E8-to-8-Strand Bridge

240 E8 roots → 120 positive roots → 8 simple roots; each αᵢ maps to strand i with Sidon address 2ⁱ; Coxeter number h=30 connects to Singer modulus 31=5²+5+1.

Deterministic Sidon-Guided Chaos Game

LCG seeding from equation hash, strand selection via sidon_address(hash%8), convergence detection by energy ratio variance <0.01.

Core function: hash → (Sidon addr, E8 coeff) triple-step embedding; proven valid, deterministic, and injective on addresses.

Summary: Optimizes Sidon-chaos pipeline with 10 proven theorems including chaos_trajectory_no_collision, E8-to-8-strand bridge (Coxeter number connects to Singer modulus), and deterministic convergence; 3 conjectural/WIP theorems remain.


Spectral Optimization Receipt

EquationShape Parser

Replaced meaningless omega proofs with prove_shape function computing actual parse; rfl proves parsing equals claimed structure at compile time.

5D Manifold Coordinates

Replaced hash-based golden-ratio noise with actual equation properties: complexity=operator density, abstraction=quantifier depth, verification=proof status, cross_domain=cross-refs, utility=search frequency.

Proper Merkle Tree

Replaced commutative addition-based subtree fold with mixHash using 33-bit rotation, 17-bit rotation, and odd constant multiplication; non-commutative and non-associative.

Spectral-to-Sidon Bridge

spectral_to_sidon_address maps 8D spectral profile to Sidon address via magnitude thresholds; B2 Sidon property guarantees unique addressing.

Sidon Address Validity

sidon_address_valid theorem proven; all pairwise sums distinct; chaos game IFS contraction ensures convergence to unique fixed point.

Summary: Rewrites 3 core files fixing 4 critical issues: meaningless binned formalizations replaced with real EquationShape parser, hash-based manifold replaced with equation properties, broken Merkle tree replaced with proper non-commutative mixHash, and spectral-to-Sidon bridge added.


Research Stack Infrastructure

Tailscale Mesh Network

5-node mesh: nixos (control plane), qfox-1 (GPU RTX 4070), 361395-1 (edge/funnel), racknerd (edge worker), steamdeck (worker).

k3s Cluster

v1.35.4+k3s1 with Flannel CNI, Traefik ingress; namespaces: services, media, mail, monitoring, edge, ai-models, research.

Tang Nano 9K FPGA

Gowin GW1NR-LV9 with Blitter6502OISC SUBLEQ CPU, Q16 LUT Core, Voltage Controller, Scale Space BRAM, HiGHS Pivot; 195.92 MHz achieved.

Video-as-Compute

GPU detection and optimization routing for NVIDIA/AMD/CPU via vcn_compute_substrate.py; lossless YUV range correction; heterogeneous frame slicing.

Q16 LUT Core

Hardware fixed-point arithmetic unit: 8 ops (add, sub, mul, div, sqrt, abs, min, max), 2-stage pipeline, 74ns latency.

SUBLEQ CPU with 4K memory, UART; 2000 LUTs, ~500 FFs.

Lean 4 / Semantics

Lean 4.30.0-rc2 + Mathlib; 3572 jobs, 0 errors; 10,353 .lean files; key modules: FixedPoint, AdjugateMatrix, GoldenRatioSeparation, etc.

Caddy with Porkbun DNS-01

Wildcard TLS certificates via Porkbun DNS-01 challenge; domain researchstack.info.

Authentik OIDC

SSO authentication for web-facing endpoints; auth.researchstack.info.

Summary: Comprehensive infrastructure documentation covering Tailscale mesh (5 nodes), k3s cluster (7 namespaces), Tang Nano 9K FPGA (SUBLEQ CPU + Q16 LUT), GPU video-as-compute, Lean 4 Semantics (3572 jobs), and Caddy/Authentik TLS/SSO.


Disaster Recovery — Research Stack

etcd Backup

k3s etcd-snapshot save with automated cron job (3 AM daily, 7-day retention); restore via --cluster-reset-restore-path.

FPGA Bitstream Recovery

Source and compiled bitstream in git repo; re-flash via openFPGALoader -b tangnano9k; SRAM contents volatile (UART dump before power-off).

Tailscale Re-authentication

Restart tailscaled, use auth key from password manager or backup; state stored at /var/lib/tailscale/.

Git Repository Backup

Canonical backup is remote origin; push all changes + tags; add backup remote for redundancy.

sops-nix / age Key Backup

Backup age keys from /etc/age/keys.txt; re-encrypt secrets with new key as last resort.

DNS/Porkbun Recovery

Regenerate Porkbun API key, update k8s secret, restart Caddy for renewal.

Recovery Priority Order

Tailscale → Git → age keys → k3s cluster → DNS/Porkbun → FPGA → Services.

Summary: Disaster recovery procedures for all Research Stack components: etcd backup/restore, FPGA re-flash, Tailscale re-auth, git remote backup, sops-nix age keys, DNS/Porkbun API key recovery; recovery priority order documented.


Ops Runbook — Research Stack

k3s Health Check

kubectl get nodes/pods, journalctl -u k3s, rollout restart for pod restarts, force delete for stuck pods.

FPGA Debug

LED state interpretation (all off=halted, blinking=running, LED0 solid=trap), UART debug via picocom at 115384 baud, re-flash procedure.

Tailscale Debug

tailscale status/ping, funnel restart on 361395-1, relay detection, direct-peers-only mode.

GPU/Ollama Ops

nvidia-smi monitoring, Ollama restart (k3s pod or systemd), model pull/manage, NodePort access at 31434.

DNS/TLS Ops

LE cert check (valid until 2026-08-18), Caddy renewal trigger, Porkbun DNS verification.

Escalation Matrix

Pod down→rollout restart, Node down→SSH+systemctl, FPGA→re-flash, Tailscale→auth key, DNS→Caddy, GPU→nvidia-smi.

Summary: Quick-reference operational procedures for k3s cluster, FPGA Tang Nano 9K, Tailscale mesh, GPU/Ollama, and DNS/TLS with escalation matrix for common failures.


FPGA Programming Guide — SUBLEQ on the Blitter

SUBLEQ Instruction

3-word instruction: [src][dst][next]; mem[dst]-=mem[src], if≤0 PC=next else PC+3; next==0 is HALT.

Memory Map

$0000-$0FFF program+data, $8000-$800F Q16 LUT registers, $8010 voltage controller, $8011 scale space, $8020-$8025 HiGHS pivot, $FF00-$FF03 UART, $FFF0 LED, $FFF1 button.

Q16 LUT Operations

8 opcodes: add, sub, mul, div, sqrt, abs, min, max; 2-cycle latency (74ns @ 27MHz); operands written to $8000-$8003, result read from $8008-$8009.

Q16.16 Encoding

value = integer_part × 65536 + fraction_part; 1.0=65536, 0.5=32768, 3.14=205887, -1.0=-65536.

Voltage Controller Modes

4 BRAM modes: STORE (direct R/W), COMPUTE (Q16 LUT), APPROX (fast), MORPHIC (morphic field).

UART Loading

Programs loaded via UART at 115384 baud; each word as 2 bytes big-endian; also via openFPGALoader SRAM/flash.

SUBLEQ Example Programs

Blink LED (toggle loop), Q16 Addition (hardware LUT), UART Send Character (poll + write).

Summary: FPGA programming guide for SUBLEQ CPU on Tang Nano 9K: instruction format, memory map ($0000-$FFFF), Q16 LUT operations (8 opcodes, 74ns), voltage controller modes, UART loading, and 3 example programs.


API Documentation — Research Stack Services

Authentik OIDC

Web-facing endpoints use Authentik OIDC SSO at auth.researchstack.info; scopes: openid, profile, email, groups.

Bearer Token Auth

API endpoints (/api/*) use Bearer token authentication managed by Credential Server.

Cluster Dashboard API

FastAPI+Vite at /server/dash/; endpoints: /api/status (cluster health), /api/metrics (Prometheus), /ws/live (WebSocket events).

Credential Server API

Endpoints: /health, /tokens (list), /issue (create), /validate; Bearer token auth.

Registry API

Artifact registry with CRUD; filters by type (bitstream, lean-build, receipt), since timestamp, limit.

Jobs API

Job queue with create/list/cancel/logs; types include lean-build; SSE for log streaming.

Blobs API

Binary blob storage with upload (multipart+SHA-256 verification), download, existence check, delete, list.

Rate Limits

100 req/min for cred, 200 for registry, 50 for jobs, 100 for blobs; X-RateLimit headers.

Summary: API documentation for 5 services: Cluster Dashboard (FastAPI+Vite), Credential Server, Registry API, Jobs API, and Blobs API; all use Authentik OIDC or Bearer token auth; rate limits documented.