Computational Universe Lab

Projective Rule-Space Program · Emergence Boundary Cartography v2

A QA-pruning search over local QCA rule-space for rules whose projections yield law-like
field theories — and an honest map of how far it got. Emergence is not binary; it is a measurable boundary.

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What this is

A computational-physics research repo built around experimental pruning. In the space of local quantum-cellular-automaton (QCA) rules, we use mathematical self-consistency and Maxwell / Einstein / Yang–Mills against real 3+1D experiments as QA gates, searching for rule equivalence classes whose projections yield field theories while retaining diagnosable high-dimensional projection residuals. Fixed 3+1D is the current calibration surface, not an ontological dimension claim; dynamical dimension is deferred past fixed-3+1D.

This is not product engineering. Verification is split into syntax/import checks, symbolic certificates, physics gates, and long-run reproduction — there is no conventional unit-test framework.

Status (2026-07-30)

The program has been upgraded to v2 “Emergence Boundary Cartography”; the authoritative entry is now docsv2/README.md. The v1 North Star (spin-2 emergence M3) was formally sealed on 2026-07-26; docs/ is frozen as v1 history and evidence chain — append-only, history never rewritten. A v3 draft paradigm (causal-identifiable emergence boundary cartography) now exists in docsv3/ as design-review material; it does not rewrite v2.

v2 has closed two complete loops (M0′–M2′) and run the M3′ 30-cell pilot:

Milestone	Content	State
M0′	Instrument migration: basis-invariant calibers (principal-angle spectrum), dual-environment consistency, ε_DOF dimension criterion	✅
M1′	Maxwell full closed loop: one spin-1 rule passes every extreme-language gate; photons exactly 2, ε_DOF=1 measured, zero hand-built	✅ PASS
M2′	Spin-2 coupled loop: R30 hand-built complex geometry sets the stage, emergent Dirac matter plays — (ε_geo=0, ε_mat=1) point on the map	✅ PASS
M3′	Boundary cartography: strict-local real-space q family (Round 0 passed, fp64 symplectic defect 7.77e-16, support radius 4, 64³ BZ max Verlet CFL 3.96396 < 4), 30-cell pilot ran to completion	⏸ HALT-PILOT-UNRESOLVED — no boundary teeth; formal preregistration & scan locked

The 30-cell pilot (q × κ_C = 5 × 6, 30×28=840 real-space impulse runs + 30 verification runs) is fully executed and valid: 30/30 construction cells, N_curv=6, j_hand=4, ε_geo=1/3 on every cell in every direction, σ constant model wins 90/90 direction fits (A=1+O(10^-15)) — the family collapses to a single point (ε_geo, σ)=(1/3, const) with no resolvable boundary teeth. HALT-PILOT-UNRESOLVED is neither an M3′ PASS nor a physical FAIL; it only rules that this construction family carries no resolvable teeth for the frozen M0′ evaluator. formal_preregistration_unlocked=false, formal_scan_unlocked=false. The next permitted move is back to M0′ evaluator / construction-family root-cause. Evidence: docsv2/v2-小报告-M3-30格pilot-2026-07-30.md, data/results/v2m3_pilot.json, visualizations/figs/v2m3_pilot_map.png.

v3 draft paradigm (design review, 2026-07-30): the M3′ no-tooth post-mortem triggered a cross-audit showing the repo was running three different estimators under one ε — construction provenance (R30/R23), thresholded constraint compatibility (frozen walk), and final-propagator geometry (M3′ pilot) — with M0′/M3 and M2 using complementary formulas on the same principal spectrum (ε_A + ε_B = 1). The v3 draft (docsv3/README.md) splits the single axis into (ε_causal, δ_geom, σ) and requires paired actual/ablated runs plus a frozen construction grammar. It is design-review material pending PI sign-off: v2 evidence stays as-is, no rulespace_v3/ implementation, expensive scans remain locked until V3-M0 passes.

The (ε,σ) map now has three complete closed-loop benchmark points: R30 (ε=0, bare geometry), Maxwell (ε=1, M1′), and the coupled point ((ε_geo=0, ε_mat=1), M2′). The coupled point's entire value is accounting honesty — the stage is hand-built, the play is emergent, two integers each in their place; it is not “spin-2 emergence” (ε_geo=0). The forbidden phrase holds.

v1 sealed statement (red line, untouchable): under all four commitments (exact constraint propagation + emergent matter + strict locality + unitarity), spin-2 M3 is structurally unreachable — it dies on polarization count and a stability deadlock (TT₂ axial 76.2° symmetry locks out the band∩ker C; deadlock scaling has no tuning corridor), not on residual. The R30 existence theorem and R26 clearing mechanism are unaffected. See seal-2026-07-26-reachability-campaign.

📄 Visual field log (v2 progress, program-atlas style): visualizations/dashboards/v2-progress-atlas.pdf — a 6-page editorial summary of the M0′→M2′ arc with measured charts (ε_DOF ladder, T_cross prophecy, (ε,σ) boundary map, the sealed-wall ledger).

Figure gallery

All figures below are real experimental artifacts from visualizations/figs/. A PASS in any *_results.json only denotes that file's declared local gate — not M3/M2′. Negative results are logged with the same weight as positive ones.

R36 · R3 two-half verification (v1 seal, three-line support) (a)-half R26 re-certified PASS (τ∈[39,62]≈L/c, clearable residual 2e-15); (b)-half FAIL on all three lines: no stable bidirectional clearing coupling, ±ω 6-fold degeneracy ⟹ N_prop=[1,1,1,1]≠[2,2,2,2], TT₂ symmetry locks out band∩ker C (principal angle 76.2°).	RC3 · chiral-doubling N-N probe Mirror chiral branch located; closing the mirror branch still yields 4 ≠ 2 ⟹ chiral doubling ruled out as the main culprit. The lesion (the lock) is confirmed on the −ω/mirror branch (R31 cross-check holds). Residual obstacle bifurcates; neither half is chiral-fixable.
R25 · static Newton / Eddington candidate certificate Static Newton/Eddington→2.00 candidate certificate, auxiliary Wilson. R25 is a GR-compatible existence construction — must not be read as “GR emerged from the wide rule-space.” Full real-space step, dynamic Newton/Eddington remain unfinished.	R31 · modal spectrum (constraint-row lock localization) The −ω branch carries all constraint-row locks (residual 0.58–0.78, 2–3 angular locks 40–90°); the +ω branch is ~98% inside ker C (2TT+2gauge, residual 0.08–0.16, no locked angles) — cross-check that the lesion sits on the −ω branch.
C1a · instrument (basis-invariant caliber base) M0′ instrument migration product: principal-angle-spectrum invariants (replacing LAPACK-basis-dependent per-mode statistics), ε_DOF subspace-dimension criterion (R30 ε=0, Maxwell ε=1, walk family [0.25,0.5]).	R25 · real-space step The Laurent/de Donder/detour complex on the general walk shell is closed; this is the R25 real-space stepping diagnostic. Usable constraint-shrinkage rate, moving source, live conservation remain unfinished.
M3′ · 30-cell pilot collapse diagnostic (current verdict, 2026-07-30) All 30 strict-local real-space construction cells valid (q × κ_C = 5 × 6, 840 impulse runs + 30 verification runs); every direction gives N_curv=6, j_hand=4, ε_geo=1/3; σ constant model wins 90/90 direction fits with A = 1 + O(10^-15). The family collapses to a single point (ε_geo, σ) = (1/3, A≈1) — no resolvable boundary teeth. HALT-PILOT-UNRESOLVED: not an M3′ PASS, not a physical FAIL; formal preregistration & 10²–10³ scan remain locked. Next move: M0′ evaluator / construction-family root-cause.

Full figure set (PNG/GIF/MP4) in visualizations/figs/; interactive dashboards in visualizations/dashboards/ (dashboard_v2.html for v2, program_atlas.html for the program visual overview, v2-progress-atlas.html for the v2 field log).

⚠️ dashboard_tensor.html and the legacy tensor campaign use the old five-parameter surrogate (cg2,gamma,G,tr_sign,sigma) and cannot back R25/v2. Its 1,470 lawful_tensor entries belong only to that surrogate and constitute no M-gate evidence.

Directory layout

Path	Contents
rulespace/	CPU/numpy reference physics package (kept at top level for import contracts)
rulespace_gpu/	MLX/JAX/numpy multi-backend physics package
rulespace_v2/	v2 frozen physics package (seven files + invariants/spin1)
experiments/	Standalone experiment & certificate scripts; byte-faithful migration preserves SHAs
data/results/	All JSON result files of record (read-only during freeze orders)
data/campaigns/, data/sealed/	campaign and sealed data
data/runtime/	runner-resumable state (has delete semantics; never reset without explicit request)
visualizations/	dashboards, figs, assets (incl. repo cover)
docsv2/	v2 document system (authoritative entry): program, preregistrations, reports, reviews, rulings, closures
docsv3/	v3 draft paradigm (design review): causal-identifiable emergence boundary cartography, (ε_causal, δ_geom, σ) — pending PI sign-off
docs/	v1 history & evidence chain (frozen, append-only)
tools/	campaign runner, local observation server

Quick verification

bash setup_env.sh
source .venv/bin/activate
export RULESPACE_BACKEND=jax

python -m rulespace_gpu.verify      # backend self-check
python -m rulespace_gpu.benchmark   # benchmark
python experiments/exp1_dirac_qca.py
python experiments/r25_laurent_complex.py

Machine-precision certificates use jax/numpy fp64; MLX is for large-scale dynamics and must not be used to claim 1e-12-level gates from fp32.

Run the interactive dashboards:

python tools/campaign_server.py
# open http://localhost:8765/ in a browser
python tools/campaign_runner.py status
python tools/tensor_campaign_runner.py status

Reading order

v2 (current program, authoritative):

1. docsv2/README.md — v2 document-system entry
2. docsv2/v2-纲领-北极星-涌现边界制图.md — thesis, claim tiers, M0′–M4′ gates
3. docsv2/v2-收口-M1-2026-07-27.md — M1′ Maxwell closure
4. docsv2/v2-收口-M2-2026-07-27.md — M2′ coupled-point closure
5. docsv2/v2-小报告-M3-30格pilot-2026-07-30.md — M3′ pilot verdict: HALT-PILOT-UNRESOLVED
6. docsv2/v2-资产重审计-2026-07-26.md — v1 asset triage & v2 inheritance list
7. visualizations/dashboards/v2-progress-atlas.pdf — v2 visual field log

v3 draft (design review, pending PI sign-off):

1. docsv3/README.md — why the single ε splits into (ε_causal, δ_geom, σ)
2. docsv3/v3-裁定草案-从单epsilon到因果可识别双轴-2026-07-30.md — the ε_A + ε_B = 1 audit evidence
3. docsv3/v3-纲领草案-北极星-因果可识别涌现边界制图.md — v3 thesis draft
4. docsv3/v3-设计-V3M0-因果响应与几何距离仪器-2026-07-30.md — V3-M0 instrument design

v1 (history & evidence chain, frozen):

1. seal-2026-07-26 — v1 sealed statement (why v2 exists)
2. docs/status/HANDOFF_02_结果总账.md — results ledger (43-series, row by row)
3. docs/reports/小报告-R30独立复核-张量复形存在性证得.md — R30 existence theorem
4. docs/engineering/REPOSITORY_LAYOUT.md — engineering layout

Working discipline and red lines are in AGENTS.md (on conflict with CLAUDE.md, AGENTS.md and the latest user instruction prevail).

Research discipline

• Verified physics is split into hard gates H, structural priors S, exploratory residuals E. Experimental laws constrain the universality class of the projection; they do not pin a unique UV rule per lattice.
• A PASS in any *_results.json only denotes that file's declared local gate; any M-gate must be passed in a single unified real-space run.
• Negative results, corrections and voided runs are logged with the same weight as positive ones; thresholds are never moved after a run (moving a threshold = moving the goalposts).
• The v1 seal is untouchable; new results go to data/results/, new v2 reports to docsv2/, v1 history status-lines to docs/.
• Certificates are fp64 only; the forbidden phrase “spin-2 emergence” holds permanently in the v2 context.
• Fixed 3+1D is the current testable projection, not an ontological dimension claim; dynamical dimension is deferred past fixed 3+1D.

License

Released under the MIT License. Copyright © 2026 Computational Universe Lab contributors.

The software, experiment scripts, results data, and documentation in this repository are provided for research reproducibility. Negative results, sealed findings, and frozen evidence chains are part of the record and are released under the same terms.