jlietz93/Phase-Calculus-Research-Corpus

Phase Calculus Research Corpus

The Phase Calculus Research Corpus is the collected working archive of the Phase Calculus research program: papers, mathematical derivations, formal proofs, executable experiments, native runtimes, computational notebooks, validation packages, and the related Cortex, Xi, and VDM research in which the calculus has been developed and tested.

Rather than presenting only finished papers, the corpus preserves the research object around the theory. A result usually arrives with the script that produced it, the symbolic audit that checked it, the Lean surface that formalizes it, the trace log it ran against, and the review record that accepted or rejected it.

The core

At the center is a discrete retained-state calculus built around a recurring B/Q/L evolution:

• B - balanced refinement
• Q - quarter-turn phase transition
• L - domain extension

From this core the research develops the Lifted Object, the Orthad, retained state and memory, quotient and projection structure, Farey and Fibonacci-linked refinement, non-commutative phase geometry, multiscale behavior, and discrete-to-continuous constructions.

Where to start

For the core calculus in plain language, read The-Lifted-Object_Natural-Language-Walkthrough_v1.0.2.pdf at the repository root.

From there, progressively deeper views of the structure:

Next	Directory
The exact B/Q/L recurrence	Publications/Phase-Calculus/CF19_The_Full_Lifted_Object/
Formalization	Publications/Phase-Calculus/Phase_Calculus_Complete_Formalisation/
Farey refinement and orthogonality	Publications/Phase-Calculus/Farey_Remainder_Recursion_and_Orthogonality/
Quotient descent	Publications/Phase-Calculus/Quotient_Descent/
Retained state as memory	Publications/Phase-Calculus/Monodromy_as_Memory/
Non-commutative phase geometry	Publications/Phase-Calculus/Non_Commutative_Phase_Geometry/
Downstream emergent-physics work	Cortex/

To read rather than run, Publications/Non-PC_Specific_CF_Packages/Variation_2/ is a PDF-only set of the CF series.

Quickstart

Large binaries are stored through Xet, so git-lfs must be installed before cloning.

git lfs install
git clone https://huggingface.co/datasets/jlietz93/Phase-Calculus-Research-Corpus

Metadata and text only, with binaries fetched later via git lfs pull --include=<path>:

GIT_LFS_SKIP_SMUDGE=1 git clone https://huggingface.co/datasets/jlietz93/Phase-Calculus-Research-Corpus

A single subtree:

pip install huggingface_hub

hf download jlietz93/Phase-Calculus-Research-Corpus \
  --repo-type dataset \
  --include "Publications/Phase-Calculus/**" \
  --local-dir ./corpus

Packages ship hash manifests, so downloads can be verified in place:

cd Publications/Phase-Calculus/Domesticating_Chaos
sha256sum -c SHA256SUMS.txt

Repository layout

.
├── Corpus_Stabilization/          Recovery ledgers, lineage maps, chronological observation record
├── Cortex/                        Emergent-physics research packages
├── Misc_tex/                      Loose LaTeX sources and shared paper inserts
├── Phase-Calculus_Active-Study/   Phases 2-5: close-read passes, closure work, the review relay
├── Publications/                  Manuscripts and their validation bundles
├── Xi_Exploratory_Work/           Xi engine runtimes, sweeps, instrumentation, sonification
└── The-Lifted-Object_Natural-Language-Walkthrough_v1.0.2.pdf

The collections

Publications/

Manuscripts with their validation bundles, split into two trees.

Publications/Phase-Calculus/ holds the Phase Calculus papers: CF000_Primitive_Distinguishability, CF00_Induced_Geometry, cf10_residual_coefficient_package, CF13_Pi_Transcendence_Chirality_and_NN_Obstruction, CF19_The_Full_Lifted_Object, CG000_Branch_Relative_Origin, Domesticating_Chaos, Farey_Remainder_Recursion_and_Orthogonality, Loop_Generated_Projection_in_TDAHE, Monodromy_as_Memory, Non_Commutative_Phase_Geometry, Operational_Utility_and_Multiscale_Invariance_of_Phase_Calculus, Phase_Calculus_as_Universal_Exact_Grammar_for_Branching_Structures, Phase_Calculus_Complete_Formalisation, Phase_Calculus_Jacobian_Sheet_Custody, Quotient_Descent, Retained_State_Phase_Calculus, The_Orthad_A_Function_of_The_Lifted_State, The_Transcendental_Wall, Unified_Quintic, and two universal-axiom papers.

Phase_Calculus_Complete_Formalisation/packages/ is substantial in its own right, containing the pi spigot iteration series (phase_native_streaming_spigot_bundle_v1 through v5), the two/three/four filter covariance packages, a native symbolic regression engine, and phase_calculus_total_demo_v1.

Publications/Non-PC_Specific_CF_Packages/ holds the CF series that is not Phase Calculus specific, in two forms. Variation_1/ has full packages (LaTeX source, Lean, SymPy, notebooks, provenance manifests) for CF01 through CF18 plus the Infinity Resolution Conjecture, several with an archive/ subdirectory preserving superseded versions. Variation_2/ is the PDF-only set.

Phase-Calculus_Active-Study/

The research process itself, in four phases.

Phase-2_Corpus_Analysis/ holds close-read notes bucketed in tens (1_Thru_10 through 61_Thru_70). Versions v1 through v58 are cumulative reading passes, each adding a numbered file to a growing notes/ directory. From v59 the naming shifts to shadow_residual_v59_correction through shadow_residual_v62_general_shadow_correspondence, which package a specific derivation rather than a reading pass and carry their own proofs, scripts, and patches.

Phase-3_Corpus_Mechanisms_Closure/ contains phase3_v1 through phase3_v6, covering general shadow correspondence, the modular B operator family, the projection loss theorem corpus, ancient Yi carry lift closure, the Wilhelm six-line phase ladder, and a source-sync and Lean preparation pass that assembles the phase's proof surfaces into one Lake project.

Phase-4_Frontier_Expansion/ extends those results across five packages, including a projection-loss formalization with its own Lake project.

Phase-5/ is a multi-agent review relay across three branches:

Branch	Versions	Subject
p5-b1	v1-v7	QBL carry defect, J derivation, symbolic and affine carry language, follower-set closure
p5-b2	v1-v3	Global exact threshold bridge
p5-b3	v1-v23	Hierarchical grammar lift, primary pairing, descriptive articulation boundary, orthad execution

See How the work was reviewed for the conventions in these directories.

Cortex/

Emergent-physics research packages, organized as timestamped self-contained bundles. Two parallel lineages are preserved, cortex-engine_emergent-physics/ and emergent_physics/, which overlap by design and are neither a subset of the other. emergent_physics/ additionally carries canon-ledgers/, accepted-closures/, and an external-research/ set of reference arXiv preprints on causal set theory, fracton gauge theories, quantum cellular automata, and teleparallel gravity.

Packages roughly in dependency order:

light-emergence/                                  Light identification, area biform, first-L cascade
native_operator_closure_20260720T174114Z          QGT coefficients, Dirac wall modes, Ginsparg-Wilson residual
native_lepton_hypercharge_yukawa_...191459Z       Lepton charges, Yukawa mass spectrum
external_native_emergence_search_...201022Z       Endpoint symmetry tower, chiral index
native_color_representation_flux_tube_...203416Z  Flux tube, Casimir, representation inventory
native_first_generation_closure_...211406Z        Anomaly cancellation, first-generation weights
native_color_singlet_composites_...231843Z        Meson and baryon singlet certificates
native_baryon_relation_dynamics_...002435Z        Relation spectra, localization scaling
native_baryon_transport_hydrogen_...005517Z       Baryon dispersion, hydrogen spectrum
native_baryon_hydrogen_spectrum_...031035Z        Spin-flavor channels, 2p-to-1s dipole transition
native_multimode_atomic_emission_...043115Z       Spontaneous emission spectrum, mode convergence
autonomous_gravity_jm_observatory_...092853Z      Gravity defect certificate, JM ratio convergence
autonomous_deep_wide_matter_sweep_...101003Z      Deep relation gap scaling, burden plaquette census
composite_metrology_saturation_sweep_...121607Z   Black hole saturation, hydrogen composite dispersion

Each carries upstream_snapshots/, frozen copies of the summaries it depends on, so a package can be read without resolving the whole chain.

Xi_Exploratory_Work/

Instrumentation and exploratory analysis of the Xi engine, and the most heterogeneous collection here.

• primitive_bifurcation_law_VDM/ - the low-level substrate. Hand-written x86-64 kernels, C harnesses, compiled binaries under bin/, and experiment_runtimes/ holding several independent runtime implementations of the same system.
• P1_full_sweep_revised/, P2_full_sweep/, P1_dry_43200_results_bundle/ - perturbation sweeps with gate logs, null baselines, adversarial row-shuffle controls, and drift envelope figures.
• xi_dark_sonar_v1/ and xi_dark_sonar_v1_live120/ - a packaged detector with a pytest suite and systemd units for a 120-hour live capture.
• Analysis packages - xi_dark_manifold_topology_v1 (persistence barcodes, density isosurface), xi_logic_mosaic_v1, xi_projector_invariance_v1, xi_residual_lattice_filter_v1, xi_transition_probe_v1, xi_transition_extraction_v1, xi_attractor_geometry_quant_v1, xi_phase2_dna_strip_v1.
• Sonification - xi_audio_repro_package, xi_music_scope_package, xi_helical_music_geometry, xi_longform_evolution_package_bundle, and the deep zoom morphology ladders. These render engine state as audio and analyze the result spectrally. v2_repaired and v3_fixed supersede v1, and v2_repaired/out/ includes a direct comparison against the earlier output.

Corpus_Stabilization/

Dated ledgers that index and reconcile the rest of the corpus. Useful when you need to know which variant of a document is current.

File	Purpose
PHASE_CALCULUS_RECOVERY_SOURCE_MAP_v2_*.md	Current source map, superseding the v1 map beside it
CF_VARIANT_LINEAGE_MAP_*.md	Which CF package variant descends from which
CF000_TO_BQL_DERIVATION_LEDGER_*.md	Derivation chain from CF000 through the BQL layer
PHASE_CALCULUS_CHRONOLOGICAL_OBSERVATION_LEDGER_*.md	Time-ordered observation record
CORTEX_CODE_CANDIDATE_COMPARISON_*.md	Comparison of the two Cortex lineages

Misc_tex/

Loose LaTeX sources and the shared proof inserts referenced by several papers.

Package anatomy

Most bundles follow the same internal convention. Once you can read one, you can read all of them.

<package>_<YYYYMMDDTHHMMSSZ>/
├── README.md / FINDINGS.md / lab-journal.md    What it is, what was found, working record
├── MANIFEST.json / SHA256SUMS.txt              File inventory with hashes
├── requirements.txt / REPRODUCE.sh             Dependencies and one-shot rebuild
├── inputs/                                     Frozen copies of everything consumed
│   └── ASSUMPTION_LOCK.md                      Assumptions stated up front
├── source_maps/                                Where each input came from
├── scripts/ or src/                            The derivation code
├── notebooks/                                  Both X.ipynb and X_executed.ipynb
├── proofs/ or lean/ or formal/                 Lean 4 surfaces plus compiler log
├── outputs/ or results/                        Certificates, ledgers, CSV tables
├── figures/                                    Generated plots
├── trace/ or trace_logs/                       JSONL execution traces
└── upstream_snapshots/                         Frozen dependency summaries

To rebuild one:

cd Cortex/emergent_physics/native_operator_closure_20260720T174114Z
python -m venv .venv && source .venv/bin/activate
pip install -r requirements.txt
bash REPRODUCE.sh

Code and formal artifacts

A large fraction of the corpus is executable.

Language	Where	Role
Python	scripts/, src/, sympy/, validation/	Derivations, symbolic audits, figures, package building
Lean 4	proofs/, formal/, lean/, lean4/	Formal proof surfaces
C	primitive_bifurcation_law_VDM/, Cortex/*/source/	Runtime harnesses, observers, contention experiments
x86-64 assembly	*.S, *.s, vdm_runtime.asm	Engine kernels
Shell	REPRODUCE.sh, scripts/run*.sh	Reproduction entry points
Jupyter	notebooks/	Paired source and executed notebooks

Script naming

Filename verbs are consistent and tell you what a script does before you open it.

Pattern	Role
derive_*.py	Produces the primary result
build_*.py	Assembles the package and writes its manifest
verify_*.py, VERIFY_PACKAGE.py	Checks package integrity and hashes
*_audit.py	Independent check, usually SymPy, run separately from the derivation
*_attack*.py	Adversarial script written to break the claim
build_notebook.py, execute_notebook.py, validate_notebook.py	Notebook lifecycle
generate_figures.py, plot_run.py	Figure rendering

The derive / audit / attack split is deliberate. Each is a separate script so the primary derivation, the independent symbolic check, and the attempt to defeat the result stay distinguishable.

Installable packages

Several directories are proper Python packages with pyproject.toml, most following a hexagonal layout (domain/, application/, infrastructure/, presentation/) and exposing a CLI.

Package	Directory	Subject
pc_monodromy_certifier	Publications/Phase-Calculus/Monodromy_as_Memory	Branch monodromy certificates
pc_branch_certifier	.../Phase_Calculus_as_Universal_Exact_Grammar...	Branch grammar compilation
pc_inverse_word_certifier	.../The_Transcendental_Wall	Inverse word certification with interval arithmetic
projection_loss_accounting	.../Domesticating_Chaos	Projection loss accounting
nc_phase_geometry	.../Non_Commutative_Phase_Geometry/nc_phase_geometry_package_v0_3_ALL_FIGURES	Commutator service, Heisenberg and sheet domains
pcsr	.../Phase_Calculus_Complete_Formalisation/packages/pc_native_symbolic_regression	Phase-native symbolic regression
vdm_dynamics_regressor	.../packages/PCVDMFullDynamicsRegressor	Dynamics regression and stress harness
xi_dark_sonar	Xi_Exploratory_Work/xi_dark_sonar_v1{,_live120}	Dark-state detector, footprint and projector

cd Publications/Phase-Calculus/Monodromy_as_Memory
pip install -e .
python -m pc_monodromy_certifier --help
pytest

Native runtimes

Xi_Exploratory_Work/primitive_bifurcation_law_VDM/experiment_runtimes/ holds independent implementations of the same substrate, kept side by side for comparison.

Runtime	Build	Notes
vdm_origin_runtime	make	C, split into core, observe, and witness modules, with tests and NDJSON run logs
am1_symbolic_runtime	make	Symbolic rewriting, term and observer modules
cf000_symbolic_runtime	make	CF000 state machine, plus a_minus_one_single_law.py
assembly_origin	test_vdm.sh	Pure assembly, vdm_runtime.asm

cd Xi_Exploratory_Work/primitive_bifurcation_law_VDM/experiment_runtimes/vdm_origin_runtime
make
bash scripts/run.sh
python scripts/plot.py

Beneath these sits the kernel layer in primitive_bifurcation_law_VDM/src/: hand-written kernels with their C harnesses, plus contention and choke experiments. Prebuilt binaries are committed under bin/, shared objects under shared_libraries/. Cortex carries its own engine kernel and observer under autonomous_gravity_jm_observatory_*/engine_kernel/.

Lean 4

Two forms appear. Lake projects have a lakefile.toml or lakefile.lean plus lean-toolchain and are buildable:

cd Publications/Phase-Calculus/Monodromy_as_Memory/lean
lake build

These sit under Monodromy_as_Memory, Domesticating_Chaos, The_Transcendental_Wall, Phase_Calculus_as_Universal_Exact_Grammar..., Retained_State_Phase_Calculus, Quotient_Descent, Unified_Quintic, Operational_Utility..., two packages under Phase_Calculus_Complete_Formalisation, and the phase-level assemblies in Phase 3 and Phase 4.

Standalone surfaces are single .lean files in a package's proofs/ or formal/ directory with no build harness. Whether one compiled is recorded in the adjacent lean_compiler.log.

Evidence artifacts

These filenames recur throughout and carry consistent meaning.

Artifact	Meaning
gate_matrix.json	Pass/fail status of each acceptance gate
claim_ledger.json	Enumerated claims with their evidence class
closure_certificate.json	Assertion that a derivation closed, with conditions
negative_control_*	A deliberately wrong construction that must fail
falsification_targets.csv	What would break the result if observed
preregistration/PREDICTIONS.md + .sha256	Predictions hashed before the run
independent_symbolic_audit.json	SymPy check run separately from the derivation
lean_compiler.log	Whether the formal surface compiled
ASSUMPTION_LOCK.md	Assumptions frozen before work began
SUPERSESSION_LEDGER.md	What this package replaces

How the work was reviewed

Phase-Calculus_Active-Study/Phase-5/ records a role-separated review protocol, and its filenames encode role rather than content. One agent produced work, a second audited it independently, and a third checked the exchange against a standing rule set.

Suffix	Role
*-operator-response.md	The agent producing the work
*-auditor-response.md	Independent review of that work
*-guardian-response.md	Rule compliance check on the exchange
*_GAURDIAN_RATIFICATION.md	Accepted, work proceeds (spelling as committed)
*_GAURDIAN_RULE_REPORT*.md	A rule was violated, details inside
audit-fails/, operator-fails/	Output rejected at that stage
unratified-attempts/	Complete attempts that never passed review, kept intact

Rejected work is retained on purpose. p5-b3-v10/unratified-attempts/ holds three full attempts at the same result, each with its guardian response, before the ratified version in the parent directory. The same principle appears elsewhere in the corpus: where a later pass corrected an earlier one, both remain, and the correction notice names the specific failure. mi_shadow_orthad_exact_transform_clean_bundle/INVALIDATION_OF_PREVIOUS_LEDGER_ARTIFACT.md is a representative example.

The rules that governed the relay are carried inside the inputs/ of the packages bound by them, as ORTHAD_RATIFIED_RULES_v*.md and QBL_PRIMITIVE_CUSTODY_AND_ORTHAD_LAW_v*.md.

Naming conventions

• YYYYMMDDTHHMMSSZ is the package build timestamp and the primary version key.
• v<n> is an iteration counter within a research line. Later, not necessarily better. Check the SUPERSESSION_LEDGER.md or the stabilization maps.
• Variation_1 / Variation_2 distinguish a full package from a PDF-only extract of the same work.
• archive/ inside a publication directory holds superseded drafts. The current version is the parent.
• NOT-SENT- marks a package that was built but never handed off.
• _executed.ipynb is the notebook with outputs preserved. The bare .ipynb is the source.

Not a conventional ML dataset

This is hosted on Hugging Face Datasets because it is useful as a large machine-readable body of mathematical research, not because it is a tabular training set. It suits reading and study, reproducing experiments, tracing how ideas developed, formal verification, symbolic and numerical analysis, theorem and mechanism mining, retrieval-augmented research, and agent-assisted analysis of the relationship between theory, implementation, and evidence.

The directory structure is part of the corpus. Packages preserve the full context around a result rather than splitting papers, code, outputs, and validation into unrelated repositories.

Storage

Binary content routes through Hugging Face Xet rather than plain Git LFS, configured in .gitattributes at the repository root. git-lfs must be installed before cloning or pushing, and files over 10 MiB are rejected unless tracked. The heaviest subtrees are Xi_Exploratory_Work/ (audio, video, density fields) and Publications/ (PDFs and packaged archives).

Citation

@misc{justin_lietz_2026,
    author       = {Justin Lietz},
    title        = {Phase-Calculus-Research-Corpus (Revision b7b221a)},
    year         = 2026,
    url          = {https://huggingface.co/datasets/jlietz93/Phase-Calculus-Research-Corpus},
    doi          = {10.57967/hf/10127},
    publisher    = {Hugging Face}
}

DOI: 10.57967/hf/10127

Individual publication directories may carry their own CITATION.cff or ZENODO_SUBMISSION_METADATA.md. Prefer those when citing a specific result.

Author

Justin Lietz Neuroca Research

License

Neuroca PRL 2.1. See the license text.

Some bundles carry their own License.txt, LICENSE, or LICENSE_SCOPE.md covering that package specifically. Third-party preprints under Cortex/emergent_physics/external-research/ are retained for reference and remain under their original terms.