rplc-sheaf

RPL-C / CycleSheaf / RPL-ISA — restriction–projection under audit with sheaf obstruction.

License: Proprietary source-available. Evaluation and academic citation only without a written commercial grant. See LICENSE and COMMERCIAL.md. Not open source.

Author: Blake A. Jones (JtechAI) · b.jones@jtech.ai
Related: protein-rpl-validation (domain application of the same operator series)

---

Design law

restrict → measure obstruction → audit vs controls → OPEN or STOP
if STOP: refine cover / rotate → remeasure

Residue is defined by failure to open — never forced.

This posture matches a broader engineering discipline: adversarial verification of computational claims, certificate trails, and refusal to promote structure that does not survive controls.

Abstraction

Layer	Role
Hardware	Feature matrix X
Software	RPL-ISA instruction words
ALU	Sheaf Laplacian under matched controls
Domains	Payloads only (FRB-style, materials, CSV, …)

Install

pip install -r requirements.txt
# place rplc_sheaf.py on PYTHONPATH, or run from this directory

Quick start

import rplc_sheaf as m

X, rows = m.synthetic_frb(160)
cert, report = m.run(X, seed=0)
assert report["ok"]  # schema + replay verify

cert, report, rows = m.run_domain("materials", n=160, seed=0)

Custom ISA program

cert, report = m.run(X, program=[
    {"op": "CORE"},
    {"op": "STEP", "max": 4},
    {"op": "ROTATE"},
    {"op": "HALT"},
], seed=0)

CLI

python rplc_sheaf.py --domain frb --n 160 --steps 3
python rplc_sheaf.py --domain materials --seed 1 --out cert.json
python rplc_sheaf.py --domain csv --csv data.csv --features f1,f2,f3 --out cert.json

Core capability map

#	Capability
1	RPL-C loop (restrict → audit → open → rotate)
2	Sheaf Laplacian L = δ₀ᵀ δ₀
3	Holonomy / twist audit
4	Sheaf-audited OPEN
5	ROTATE branch (delay embed / low-recurrence; approximate OPEN)
6	CycleSheaf-style (k, θ) maps
7	Multi-cover filtration + nested persistence
8	RPL-ISA vocabulary + isa_exec bytecode
9	Serializable certificates + verify/replay
10	Domain loaders (FRB / materials / CSV)
11	Front-end: run / run_domain / CLI

Mathematics (short)

• Stalks — feature vectors at vertices
• Restriction maps F_v→e — stiffness from edge length, rotation from local displacement
• Coboundary δ₀; sheaf Laplacian L = δ₀ᵀ δ₀
• λ₁ — first positive eigenvalue (obstruction energy)
• Audit — compare stratum λ₁ to random subsets of equal size
• OPEN only if obstruction survives controls

Certificate schema (illustrative)

{
  "n0": 160,
  "dims": 4,
  "opened_steps": 2,
  "remainder_n": 80,
  "ladder": [{"step": 1, "n": 40, "branch": "core", "lam1": 0.05, "survives": true}],
  "trace": ["CORE", "SHEAF_AUDIT", "OPEN", "...", "HALT"],
  "program": [{"op": "CORE"}, {"op": "STEP", "max": 3}, {"op": "ROTATE"}, {"op": "HALT"}]
}

verify_certificate checks schema markers, program equality under replay, remainder bounds, optional exact remainder indices, and rejects fatal halt reasons (no_core, unknown_op).

Operational envelope

Dense eigh on an nd×nd Laplacian is O((nd)³). Prefer n ≲ 300 for interactive use. Sparse / shift-invert path is a documented follow-on (see docs/CODE_REVIEW_v1.md).

Claims posture

Status	Claim
OPEN	Design law enforced in code: OPEN only under control-matched audit
OPEN	Certificates are JSON-stable; verify/replay rejects fatal halt paths
OPEN	Domains are payloads; operator series is the product
RESIDUE	Sparse ALU for large n (catalog-scale)
RESIDUE	Domain-calibrated audit_margin (default 0.1 is a fixed heuristic)
RESIDUE	Exact (non-approximate) ROTATE point correspondence

What this is not

Not a domain decoder for FRB, SuperCon, ClinVar, or protein structure. Those are test payloads. Not a medical device or diagnostic.

Domain applications of the same operator series:
protein-rpl-validation

Tests

python tests/test_smoke.py
# → all smoke OK

Docs

• docs/RPL_ISA_CARD.md — instruction card
• docs/CODE_REVIEW_v1.md — structural V&V prior to external review
• docs/CLAIMS.md — OPEN / RESIDUE ledger

License

Proprietary source-available — Copyright © 2026 Blake A. Jones (JtechAI / ZuluYokohama).
Evaluation Use and citation permitted. Commercial Use requires a written license: b.jones@jtech.ai
Full terms: LICENSE · Summary: COMMERCIAL.md

Version

1.0.0-operational — standalone RPL-C / RPL-ISA core with certificate front-end.