L1 Attribution Reference — Berger vs Holistic Model

This page summarises the per-integer mapping; the complete reference with all 20+ candidate combos per integer and rank-ordered tables is in the 3d repository doc 93 . For the underlying L1 lattice structure and the 32-integer set, see Climate Formula. For the synthesis statement this finding supports, see Climate Summary.

1. Background: single vs dual attribution

In standard cyclostratigraphy, every paleoclimate spectral peak is attributed to a single Berger / Laskar eigenmode beat (e.g., “the 95-kyr peak is g₄−g₅ Mars-Jupiter eccentricity”). The attribution is treated as definitive.

The Holistic framework demonstrates that every one of those peaks has an equally valid alternative attribution as an Earth-planet PLANET_CYCLES beat — and the alternative usually names a different planet than Berger does. The 32-integer lattice is the SAME set of frequencies under both frameworks; the disagreement is about which planet–planet gravitational coupling produces each peak.

This is not a contradiction of Berger / Laskar — it is a structural alternative interpretation that the secular-theory derivation does not surface, because secular theory enumerates eigenmodes (g_j, s_j) rather than individual planet cycles (Axial, Peri_ecl, ICRF, AscNode, Obliq, Ecc).

2. Summary table — Berger vs Holistic top-1

For each of the 32 L1 integers: the period in kyr, the canonical Berger / secular-theory label, the Holistic model’s top-1 Earth-planet beat from PLANET_CYCLES, and the agreement status.

32 L1 components total. 0 agree with Berger on both planet and mechanism; 1 has same planet but different mechanism; 26 name a different planet entirely; 5 are not predicted by Berger at all. The L1 lattice itself (the set of integers) is identical under both attributions — only the planet–mechanism interpretation differs.

3. Three example disagreements

3.1 n = 120 — the 22.4 kyr peak: Venus or Jupiter?

Berger labels n = 120 the “k+g₂ Venus climatic precession” peak (period 22.4 kyr). The Holistic top-1 attribution is an exact 2-term beat:

Earth.Axial(104) + Jupiter.Obliq(16) = 120

This is a [2-term sum] (the simplest possible structure — no 3-term combinations needed). The arithmetic is exact: Earth’s axial precession at 8H/104 plus Jupiter’s obliquity cycle at 8H/16 sums to 8H/120 = 22.4 kyr.

Under the Holistic framework, the 22.4 kyr LR04 peak is driven by Jupiter’s obliquity coupling to Earth’s spin axis — not by Venus’s climatic precession.

3.2 n = 28 — the 95 kyr eccentricity peak: Mars+Jupiter or Mars+Saturn?

n = 28 (95 kyr, Berger’s famous eccentricity peak) is labeled g₄−g₅ Mars-Jupiter ecc in classical secular theory. The Holistic top-1 is:

Earth.Axial(104) − Mars.Ecc(52) − Saturn.Obliq(24) = 28

Both attributions involve Mars, but the secondary partner differs: Berger says Jupiter (via the g_j eigenmode), Holistic top-1 says Saturn (via Saturn’s obliquity cycle). The amplitude (0.754) is the highest in the post-MPT spectrum after n=22.

3.3 n = 65 — the 41 kyr obliquity peak: Earth or Jupiter?

n = 65 (41.3 kyr, the canonical obliquity peak) is Berger’s “k+s₃ Earth obliquity” beat. The Holistic top-1 is:

Earth.Axial(104) − Jupiter.Peri_ecl(39) = 65

A clean [2-term diff]. Under Holistic, the 41 kyr LR04 obliquity signal is driven by Jupiter’s perihelion-ecliptic coupling to Earth’s spin axis — not by Earth’s own nodal precession via the s₃ eigenmode.

4. Earth’s spin axis is present in all 32 top-1 attributions

Every one of the 32 Holistic top-1 beats uses one of Earth’s two spin-axis cycles as the base term: Earth.Axial(104) (period 25,794 yr, the precession of the equinoxes) in 30 of 32, and Earth.Obliq(64) (period 41,915 yr, the obliquity oscillation) in the remaining 2 (n=9 and n=22).

This is a strong structural signal: Earth’s spin axis is the universal carrier frequency for the L1 lattice. The remaining 30 integers are produced by modulating Earth.Axial with one or two planet-cycle harmonics; the two Earth.Obliq integers (n=9, n=22) are modulated similarly.

Planet participation as the modulating term in the top-1 attributions:

Jupiter dominates as the secondary modulator — present in three-quarters of the L1 beats. This is consistent with the Jupiter-Saturn resonance lock found in Law 6 (see Fibonacci Laws) and with the fact that Jupiter carries most of the solar system’s angular momentum.

5. Scope — this doc covers L1 only

The canonical climate formula has three layers totalling 41 components:

L2 is off-lattice (405 kyr is not a divisor of 8H = 2,682,536 yr) and arises from carbon-cycle internal resonance, not orbital forcing directly. L3 is non-periodic. Both are covered in Climate Formula.

6. Why the n=7 LR04 peak is excluded from L1

The LR04 full-record spectrum has a 4σ peak at T = 383.22 kyr (= 8H/7). The well-established 405-kyr eccentricity line sits 21.8 kyr away and is off the 8H lattice — its spectral energy leaks into the nearest lattice bin (n=7), which the divisor-spectrum scan then detects but classifies as “Unpredicted” (no family-level beat predicts 383 kyr exactly).

Including n=7 in L1 would double-count with L2. It is correctly excluded; the 32 integers in this doc are the complete L1 set.

See also

• Climate Summary — the synthesis statement this dual-attribution result supports
• Climate Formula — the canonical L1+L2+L3 architecture
• Insolation Null Test — empirical demonstration that adding Berger insolation features to L1+L2+L3 yields ΔR² = 0
• Related Work — position relative to recent peer-reviewed literature (Zeebe-Lantink 2024, Dutkiewicz 2024, etc.)
• Eigenfrequencies — the g_j and s_j fundamental frequencies used by Berger
• Fundamental Cycles — the 8 × 6 PLANET_CYCLES period table
• Full per-integer reference (3d repo)  — all 20+ candidate combos per integer, rank-ordered