First independent byte-exact reproduction of the Zinoviev–Ericson (1999) configuration of 1154 unit spheres simultaneously tangent to a central unit sphere in ℝ¹³, with the full optimization pipeline, 13 paper-grade structural findings, the rare-paths doctrine, and the dual Constructor/Auditor methodology with both-hats discipline released as a complete, reproducible artifact.
Status: Closed (May 2026). This repository documents the completed attack by Project LUNA on the open question whether K(13) ≥ 1155. The world record K(13) = 1154 (Zinoviev–Ericson 1999, 27 years standing at project closure) was not beaten. The natural algebraic landscape was empirically exhausted across roughly 7.13 billion candidates. The record remains open; this repository documents what was tried, what closed negative, what was learned, and the four rare-path veins identified as the doctrine-conformant directions for any continuation.
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The first independent byte-exact reproduction of the ZE99 1154-vector configuration from cold initialization, reached in ~19 seconds on a Mac M2 single-thread (25% CPU) by engine
TRINCANEROELDELOSCOJONESPUROSvia a 24-step deterministic Move R-axial→irrational chain. Full verification scripts included. -
Thirteen paper-grade structural findings on the saturation of K(13) = 1154 under algebraic perturbation, including:
- F58 universal-sink law: any algebraically natural perturbation in ℝ¹³ clusters its conflicts onto the 48-vector F40 axial-irrational layer of ZE99. Confirmed independently by five non-overlapping algebraic families (Eisenstein superset, BW₁₆ cross-section, exotic √k, composite ℚ+ℚ√3+ℚ√k, and Eisenstein ℤ[ζ₃] via Minkowski embedding).
- The 2²⁶⁴ Steiner-equivalent enjambre: ZE99 is not the unique K(13)=1154 configuration. Roughly 3·10⁷⁹ Steiner-equivalent configurations exist under a coord-12-preserving replacement operation, leaving 24 "Steiner-untouchable" diamonds whose support is a perfect 6-pair matching on coordinates 0–11.
- The cset-parity structural barrier: empty intervals in the conflict-set spectrum appear consistently across real-quadratic, integer, and imaginary-quadratic alphabets — elevating parity from shell-specific observation to a structural feature of the dim-13 algebraic landscape.
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The rare-paths doctrine: a four-condition operational filter for any future record attempt, codified from 27 years of stability of K(13) ≥ 1154 under institutional attack. Three rare-path veins (ℚ(ζ₁₀) decagonal, Steiner+M₁₂ sporadic, rigidity-coupled 48-irrationals deformation) are identified as the directions where the record, if it falls, is most likely to fall.
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The dual Constructor/Auditor methodology with both-hats discipline: a reproducible operational pattern for autodidact-driven mathematical research using two AI instances with separated roles, with a fallback discipline (
§-3.6 both-hats) for single-agent sessions including a graveyard catalogue of three self-caught traps as canonical examples.
git clone https://github.com/REPLACE_WITH_YOUR_USERNAME/kissing-number-13-zinoviev-ericson-reproduction.git
cd kissing-number-13-zinoviev-ericson-reproduction
python3 verify_ze99_1154.py ze99_1154_numeric.txtExpected output ends with *** ALL INVARIANTS PASS ***. The script checks: 1154 vectors, all at squared norm 16, zero pairs with inner product exceeding 8, exactly 59,640 tight pairs at IP=8, exactly 577 antipodal pairs at IP=-16, exactly twelve distinct inner-product values, and zero duplicates.
To compile and run the engine that produced the dump from cold initialization:
g++ -O3 -march=native -std=c++17 -funroll-loops \
-o TRINCANERO TRINCANEROELDELOSCOJONESPUROS.cpp
./TRINCANERO # writes ze99_1154_numeric.txt in ~19 s on Mac M2Canonical paper and operational distillation
PAPER_TERMINAL.md— full paper, 4848 lines, all findings F1–F73 and F-frente-A/B-1..6 with proofs, sandbox transcripts, and external citations.CLOSURE_DIM13.md— formal closure document for dim 13, primary reference for external citation.MAIN_DISCOVERIES.md— five citable scientific contributions, concise.COJONES_SABIOS_TERMINAL.md— operational arsenal and lessons distilled for any researcher who wants to continue.METHODOLOGY.md— standalone technical primer on the pipeline, the D190 quadruple-verify protocol, and the F40 deterministic chain.GUIDE_FOR_EVERYONE.md— plain-language tour, no math background required.NEW_DISCOVERIES.md— empty journal template for any reader who builds on this work.
Canonical data and verifiers
ZE99_1154_DATA.md— provenance, parser, and verification invariants for the 1154-vector configuration.ze99_1154_numeric.txt— the 1154 vectors as numeric float CSV, produced byTRINCANEROELDELOSCOJONESPUROScold-start.verify_ze99_1154.py— independent Python kernel that verifies the record byte-exact.d190_paso4_verify.py— D190 protocol step 4: independent verifier for 1155-candidate engine dumps.
Engines (C++ single-thread, Mac M2 25% CPU)
TRINCANEROELDELOSCOJONESPUROS.cpp— canonical engine; reproduces ZE99 1154 in ~19 s via 24-step deterministic Move R-axial→irrational chain.TRINCANERO_v1.cpp— predecessor, ceiling at 986 (graveyard G23–G25, lesson preserved inCOJONES_SABIOS_TERMINAL.md).HORMONEROCHUMINEROPREMIUM_v2_1.cpp— first LUNA engine, Construction A + layer stacking.DOSPIRATASDUROSCONTRESCOJONESPUROSENCERADOSYPERFUMADOS_v3.cpp— 1155-record-attempt engine #1, did not beat 1154.DOSPIRATASMUYPIRATASSONCOJONESNOBRAVATAS.cpp— 1155-record-attempt engine #2, did not beat 1154.
Operational context and rare-paths catalog
LUNA_CONTEXT_BRUTAL.md— project constitution, including the rare-paths doctrine codification.ANCIENT_MATH_RESEARCH_BRIDGE.md— five mathematical veins identified as untested for dim 13, with probability calibration.MATHEMATICAL_COMPANION_ONBOARDING_LUNA22.md— historical handoff document for a potential dim-22 continuation. Archival only; not operational.
Citation and license
CITATION.md— BibTeX, APA, IEEE, plus the required upstream citations.CITATION.cff— machine-readable for GitHub's "Cite this repository" button.LICENSE— MIT.
The kissing number K(n) is the maximum number of non-overlapping unit spheres that can simultaneously touch a central unit sphere in ℝⁿ. The problem is open in dimension 13: the best known lower bound is K(13) ≥ 1154 (Zinoviev–Ericson, IEEE Trans. Inform. Theory, 1999), the best known upper bound is K(13) ≤ 2064 (De Laat–Leijenhorst, 2024, via quadruple-precision semidefinite programming on the Cohn–Elkies linear programming bound).
The lower bound has stood for 27 years. The natural algebraic constructions (laminated lattice Λ₁₃ = 906, Construction A binary codes, BW₁₆ cross-section to ℝ¹³, Eisenstein superset constructions in dimensions divisible by 6 followed by cross-section to 13) all saturate well below 1154. Zinoviev and Ericson reached 1154 by adding a layer of 48 axial-irrational vectors with coordinates in ℤ[√3]/2 to a Λ₁₃-derived 1106-vector anchor, plus 288 "diamond" vectors with coordinates in (±1)¹² ⊕ (±2). The construction is structured, finite, and reproducible; this repository reproduces it byte-exact from a 1106-vector cold start.
The empirical question this repository investigates is whether the same kind of algebraic perturbation that takes the laminated lattice from 906 to 1154 — Move R-axial→irrational and its successors — can be pushed further to 1155 or beyond. The empirical answer, after sweeping ~7.13 × 10⁹ candidates across all naturally available algebraic alphabets and their compositions, is: not within the natural algebraic landscape, and the conflict structure (F58 universal-sink) is now characterized at quantitative depth. The record, if it falls, falls on a rare path.
Two AI instances (Anthropic Claude Opus 4.7) operated under separated roles: a Constructor that proposed engines and sandbox computations, and an Auditor that verified mathematics from first principles and vetoed Mac launches that did not pass sandbox-kill discipline (directive D24). A human Architect (Rafael Amichis Luengo, Madrid) arbitrated, decided engine names according to a deliberately irreverent naming convention (directive D26: contractual names are earned by records, never assigned speculatively), and held the human clock. When the Auditor was unavailable mid-session, the Constructor applied both-hats discipline (§-3.6): every operational claim is produced twice, once in proposing mode and once in challenging mode, with explicit attention to five trampa-suspect categories. Three traps were self-caught during a single-Claude session (G33, G34, G35) before any contamination of project documents reached the Architect. Every record claim, had one occurred, would have been validated by the D190 quadruple-verify protocol: in-engine FINAL_VERIFY, roundtrip serialization, structural sanity vs ZE99 and the De Laat–Leijenhorst bound, and an independent Python kernel verifier (d190_paso4_verify.py).
For full detail, read METHODOLOGY.md.
If you use this work, please cite it together with the original Zinoviev–Ericson 1999 record and the De Laat–Leijenhorst 2024 upper bound. See CITATION.md for ready-to-paste BibTeX and APA forms.
MIT. See LICENSE. The 1154-vector configuration data itself is derived from Henry Cohn's MIT spherical-codes archive (hdl.handle.net/1721.1/153312) and verified byte-exact against that primary source; the original ZE99 construction is due to Zinoviev and Ericson.
Aquí se baten récords mundiales. No se viene a jugar. Calidad relojero suizo. Pereza prohibida. Vivir para ver. Y ahora también: los caminos raros son el camino.
The record was not beaten. The arsenal, the findings, the doctrine, and the discipline are released so that whoever picks up the chase from a rare-path direction starts ahead of where this project started.
Architect: Rafael Amichis Luengo. Madrid, Spain. May 2026.