The Earth as a two-state recorder: its dipole on the Bloch sphere, the rock that keeps the record, and the clocks inside

1 · A field with two values and a record of them

Seen from far enough away, the Earth's magnetic field is close to the field of a bar magnet at the planet's centre: a dipole. Its axis lies near the axis of rotation, and it can point one of two ways. The present direction is called normal and the other reversed. The field has spent long stretches in each, and it has passed from one to the other many times: by the polarity table this paper uses, it reversed nine times in the last 2.2 million years.

Two things make the Earth a recorder and not only a switch. Its rocks keep the record: lava and new ocean floor take on the direction of the field as they cool, and sediments take it on as they settle, so a column of rock is a tape of the field's state. And the field's strength changes between the reversals, and the strength is recorded too, less directly, in how strongly the rock is magnetised.

A quantity with two values and a strength is what our papers read onto one textbook picture, the Bloch sphere (Bloch 1946): the sphere of states of the simplest system with two levels. A decided answer sits at one of its poles and a weak one sits inside, nearer the middle. In the companion paper on the halo of a decision, a weak answer shares a ring of correlations with a partner, and that ring is its halo. This paper puts the Earth's dipole on that picture, from public records only, and asks one question the picture raises: is the dipole weak where it reverses?

What this paper contributes, losses first, each with its basis and the section that carries it:

1. Measured, one run. The prediction that the dipole carries the periods of the Earth's orbit, registered before the record existed, is refuted band by band, and the prediction that the dipole is weak where it reverses is window-fragile under its registered robustness test (section 4).
2. Prediction. A test of the widening of the dipole's axis tilt from 1900 to 1955 is registered, not run (sections 4 and 8).
3. Measured, one run. As registered, the weak-reversal prediction holds at its threshold, 7 of 9, beside a random-window null that meets the same rule in 19 of 1,000 draws (section 4).
4. Measured, one run. The polarity table and the dipole stack become one margin m for every thousand years, 2,001 values, whose halo radius and information follow in closed form as theorems in the model (section 3).
5. Public data. The Earth's layers, its ringing, its tides, the month and the galactic year as periods and frequencies, with a mean phase of the Moon within 13.5 hours of the true one over 37 new moons (section 5).
6. Reading. Three readings of the picture set beside geophysics: the dipole is the pole reading, the magnetosphere fails as the halo on its size, and the archive is the crust (section 7).

2 · The record and the stack

The ridge writes the polarity. New ocean floor forms at the mid-ocean ridges, where hot rock rises, spreads and cools. As its iron-bearing minerals cool through their Curie point, they lock in the direction of the field of that moment. The floor then moves away from the ridge on both sides, so each reversal leaves a stripe of reversed magnetisation, and the stripes on either side of a ridge mirror each other. That symmetry, read by Vine and Matthews (1963), is one of the observations that established the spreading of the seafloor. Dated lava flows and sediment sections supply the ages, and the result is a table of chrons: the intervals of one polarity, from the present back into the age of the dinosaurs.

The table. This paper uses the polarity time scale of the 2020 geologic time scale (Ogg 2020), in the open transcription the PmagPy project publishes. It lists the boundary ages from the present back to 82.875 million years ago, and the present interval, the Brunhes, began 0.773 million years ago. Over the last three million years it agrees with the earlier table of Cande and Kent (1995) to within 24 thousand years at every boundary the two share; the newer table also lists one short interval, the Cobb Mountain subchron, that the earlier one does not; the comparison is exact, one run.

The stack. The strength comes from a different kind of record. Each sediment core gives a relative intensity, calibrated against the absolute intensities of dated lavas, and many cores are combined into a stack. This paper uses PADM2M (Ziegler and others 2011), a model of the axial dipole moment over the last two million years, evaluated every thousand years: 2,001 values, in units of 10²² ampere square metres. Its value for the present is 7.56, and the International Geomagnetic Reference Field gives 7.60 for the axial dipole of 2020, so two independent records agree on the present to within 1 per cent. A second stack, PISO-1500 (Channell and others 2009), covers 5 to 1,500 thousand years at the same spacing, 1,496 values; it is used here only as a second reading, because the two stacks share many of their input cores. A third stack, from Valet and others (2005), has no open copy that this work could find, so nothing here rests on it.

The polarity table and the stack are separate measurements: one is read from the direction of the rock's magnetisation, the other from its strength. That separation is what makes the question of section 4 a test.

3 · The sphere

Put the two records together and the dipole becomes one number for every thousand years:

m(t) = polarity(t) × moment(t) / (the largest moment in the record)

Here polarity(t) is +1 in a normal chron and −1 in a reversed one, read from the table, and moment(t) is the stack's value, so m lies between −1 and 1. The largest moment in the record is 9.57, from two thousand years ago, and exactly one row sits at a pole. Dividing by today's moment instead would not work: today's value is 0.79 of the largest, so older and stronger rows would land outside the sphere, at values that are not states at all. The normalisation is our choice, made for the sphere: published models of the dipole scale it by its long-term mean or by today's value (Buffett and others 2013).

Each m is a point on the sphere's axis, and the companion paper's picture gives it three readings. The pole: how decided the dipole is, the length |m|. The halo: the ring of correlations a partner could share with it, at height m, of radius √(1 − m²). The event that set it: the information the pair carries, H₂((1 + m)/2) bits, which is zero at a pole and one bit at the middle. One number sets all three at once; the pole's length and the ring's radius are two views of the same m. The standard models of the dipole are not a system with two levels: they treat it as a bistable stochastic oscillator, a continuous quantity that wanders in one of two wells and sometimes crosses to the other (Hoyng and others 2001; Morzfeld and Buffett 2019). The sphere is a projection of that picture, not a replacement for it. Today the dipole reads m = 0.79, with a halo of radius 0.61 and 0.48 bits.

A reversal is m changing sign: the dipole passes the equator. In the record the sign changes at exactly the seven boundaries of the table that fall inside its two million years, as it must, since the sign comes from the table. What the stack adds is the strength on either side. The two records do not keep one clock: the sign flips between two rows where the moment is low but not zero, and a passage that takes a few thousand years at any one site cannot be resolved by a smoothed model sampled every thousand years (Clement 2004; Valet and Fournier 2016). So the figure shows each passage as a jump across the middle line, where the halo is wide but not yet full. The record also has a direction the picture lacks: the dipole decays more slowly than it recovers (Ziegler and Constable 2011).

The record also holds weak spells that are not reversals. With the record's own tenth percentile of |m|, 0.34, as the line, there are 22 runs below it: 8 within 20 thousand years of a boundary, and 14 farther away, where the dipole weakened and recovered without changing sign. These are weak spells of the intensity, not a catalogue of excursions: the field's own definition of an excursion is by the direction the field swings to (Laj and Channell 2015), a stack of sediments under-records them (Roberts and Winklhofer 2004), and naming one needs a source that dates it, so this paper names none.

4 · Two predictions, each run once: one refuted, one window-fragile that holds at its threshold as registered

Four tests of this reading are registered. Three ran once, deterministically, on the records of 4 October 2026, and none of their numbers carries an interval, because nothing was repeated; the fourth has not run. The losses come first.

The orbital periods: refuted. A prediction about this record had been written down in our earlier work, before the record was committed: that the dipole carries the periods of the Earth's orbit, 23, 41 and 100 thousand years, above a background of red noise. We ran it as registered: the spectrum of the moment as the average of 7 tapered spectra, against a background fitted to the record's own memory from one thousand years to the next, at a combined significance of 1 in 100. The 23 thousand year band reaches 0.81 of its line, and the 41 and 100 thousand year bands reach 1.89 and 1.04, so two clear it and one does not. The prediction said all three, so it is refuted. The standard expectation was a null, so the refutation does not separate this reading from the standard models either. Its likely cause, not measured, is resolution: the stack is a smoothed model sampled every thousand years, its effective resolution is unconfirmed, and smoothing removes power at short periods first; it is a limit of this paper (section 8). The usual reading of orbital periods in records of this kind is that the climate leaks into the sediments that record the strength (Xuan and Channell 2008), and nothing here separates that reading from any other.

The weak-reversal prediction under its robustness test: window-fragile. Registered on its own on 7 October 2026, after the result below was public, a robustness test varied only the windows and ran once on the same records. With a window of 10 thousand years on either side of each boundary, 6 of the 9 boundaries are met, and with windows moved 15 thousand years younger, again 6 of 9; with a window of 40 thousand years, or with windows moved 15 thousand years older, 7 of 9. Two of the four variants fall below the 7 the prediction needs, so the record's verdict is window-fragile. The boundary that fails is 1.180 million years: in the registered window its lowest moment, 1.50, sits at the window's older edge, 1,200 thousand years, inside the Cobb Mountain subchron, and the boundary at 1.215 million years is met by the same low. That the older shift meets the rule and the younger one does not is what a delay in the time sediments take to lock in the field would make likely; that delay was not measured here, and the fragility is a limit of this paper (section 8).

The axis tilt's widening: registered, not run. A further test reads the reference field itself. Between 1900 and 1955 the angle between the dipole's axis and the axis of rotation in the reference field widened, while the dipole weakened at every date the field is given for, and the model's waking rule only relaxes a margin toward its pole. The test of whether that widening needs a forcing the rule lacks is registered, not run, so it has no verdict. Its angle is the reference field's axis tilt, not this paper's halo radius.

The weak-reversal prediction as registered. Before any value of the stack near a boundary was read, we wrote down a prediction and committed it to our records on its own: for the nine boundaries of the last 2.2 million years, the smallest moment within 20 thousand years of the boundary is at or below the record's tenth percentile at no fewer than seven of the nine. A boundary with no data in its window counts as a miss. The stack ends at two million years, so the two boundaries of the Réunion subchron, just older, have no data; that was written down before the data as well, and it meant the prediction could hold only if every boundary inside the record was met.

The record's tenth percentile is 3.25, in the same units. The result, in both columns:

The prediction holds at its threshold: seven of the nine, with every boundary inside the record met. It holds with no margin, since one more miss would have refuted it. At two boundaries the weakest point sits 7 and 15 thousand years older than the table's age, close to the earlier table's ages for the same boundaries, and at the base of the Olduvai subchron the moment at the boundary's own age is high: the window carries it. The dipole is known to weaken at a reversal (Valet and others 2005), and the standard stochastic models of the dipole weaken there too (Buffett and others 2013), so the hold is consistent with the textbook expectation. Its power, the chance that the rule meets 7 of 9 on records that such a model generates, was not measured, so the hold does not separate this reading from those models. Sediments take on the field's direction some thousands of years after they settle (Suganuma and others 2010), which is one reason the two records keep different clocks. PISO-1500, read the same way against its own tenth percentile, meets all five of the boundaries whose windows lie inside it. That is a second reading of overlapping data, for reference, not an independent test.

Same observation, three vocabularies. Three fields (information theory, systems and graph theory) describe the same situation in different words, and an insight in one usually has a twin in the other two. This series names a twin only where its own model has the object, and says so where a twin is missing or runs the other way. Each twin is our reading, not an identity, unless a result the paper states makes the two one number. The two stacks are one such observation. In information theory they are correlated readings, so their agreement is not two independent pieces of evidence. Read as a system, they are two parts likely to move together, since some of what each records is the same. Read as a graph, the two stacks are joined to many of the same cores, and the cores they share are likely part of why they agree; how much they share, and how much of the agreement it explains, is not measured here.

The null. Nine window centres drawn at random along the record, with the same rule, the same window and the same line, meet it in 19 of 1,000 draws: a rate of 0.019, with a binomial standard error of 0.004 over the 1,000 draws. The null was registered with the robustness test, after the result above was public and after a reviewer's rough, unregistered estimate had been seen, so it is a check registered after the result, not a test fixed before it.

Settings, from the records.

• The weak-reversal rule: the record's tenth percentile of the moment, 3.25, as the line; a window of 20 thousand years on either side of each of the 9 boundaries; at least 7 met; a boundary with no data a miss.
• The robustness test: windows of 10 and 40 thousand years, and windows of 20 thousand years moved 15 thousand years older and younger; the null draws 1,000 sets of 9 window centres between 20 and 1,980 thousand years, with the seed 20261007.
• The orbital periods: 7 tapers at a time-bandwidth of 4, no padding, the plain mean of the tapered spectra, a lag-one correlation of 0.978, a line at 2.33 times the background over 3 periods, and 2 thousand years standing in for the unconfirmed resolution; the padding and the plain mean were chosen at run time.

5 · The layers as clocks

A body that rings, turns or orbits keeps time. The Earth carries several such clocks, and each is a period and a frequency, one the inverse of the other.

The layers. The Preliminary Reference Earth Model (Dziewonski and Anderson 1981) divides the planet at three main boundaries: the base of the crust at 24.4 km, the top of the core at 2,891 km and the top of the inner core at 5,149.5 km, out of a radius of 6,371 km. A pressure wave crossing each layer straight down takes a fixed time, which we computed exactly from the model's tabulated speeds:

Straight down from the surface to the centre takes 605.2 seconds, a little over ten minutes. The outer core passes no shear wave, which is how it is known to be liquid.

The ringing. After a great earthquake the whole planet rings, and its slowest note, the mode called 0S2, takes 3,231.5 seconds, about 53.9 minutes, a cycle: 309.45 microhertz observed, and 309.28 in the reference model (Masters and Widmer 1995). Between earthquakes the planet still hums at a low level, driven by the oceans (Rhie and Romanowicz 2004).

The Moon and the Sun. The principal lunar tide, M2, has a period of 12.4206 hours, half a lunar day. The mean solar day is 86,400 seconds, and the mean synodic month, from new moon to new moon, is 29.530589 days. We computed the Moon's mean phase from the standard formula (Meeus 1998) and checked it against the U.S. Naval Observatory's table of the true phases for 2024 to 2026: over 37 new moons the mean phase is never more than 13.5 hours from the true one, which is the accuracy a mean phase has. The same formulas give the rate of the M2 tide's equilibrium phase, and it matches the speed NOAA's tables give, 28.9841042 degrees an hour. That phase is the equilibrium tide's and not a harbour's. A harbour's tide lags the Moon by an amount of its own, which only that harbour's measured constants give, so nothing here says when the water is high anywhere. The month itself is slowly lengthening as the Moon recedes, which lunar laser ranging measures (Williams and Boggs 2016). None of these clocks is known to set the dynamo's timing. Stirring of the core by the tides and by the wobble of the axis is a minority hypothesis about the dynamo's power (Malkus 1968; Andrault and others 2016), and a direct test of orbital control of reversals and excursions found none (Kent and Carlut 2001).

The Galaxy. The Sun orbits the centre of the Galaxy once in a quoted range of 225 to 250 million years, the galactic year. It is a period and not a clock the rocks are known to record: no imprint of it on the Earth's record is established (Bailer-Jones 2009). Every clock of this section, each as a period and a frequency:

6 · What the Earth prints and sorts

The Earth makes no element. Its iron, silicon and oxygen were made in stars before the Sun formed, and the planet inherited them. What the Earth does is sort and print. Early on, the dense iron sank to form the core and the lighter rock above it became the mantle and crust. The sorting goes on: new crust is made at the ridges and returned at the trenches, so the ocean floor, and the magnetic record it carries, is printed continuously at one edge and erased at the other. That is why the record of section 2 is read from young ocean floor and from sediments: the ocean floor keeps only a young part of the record, and none of it reaches back to the Earth's beginning. This paper calls this sorting and printing "the Earth printer".

A further hypothesis goes beyond the record: that a planet keeps what it prints because its field holds it, the dipole shielding the upper atmosphere from the solar wind and so helping the planet keep its air and water. The evidence is against it at the rates measured today: two studies of escape find that a planet's own field does not protect its air (Gunell and others 2018; Ramstad and Barabash 2021). Venus has no dipole and keeps a thick atmosphere, which is the standing counterexample. Mars lost its dynamo and most of its air, but its loss is put down mainly to its small mass and the young Sun's activity (Jakosky and others 2018). So the hypothesis stands only for earlier times, untested, and this paper states it as nothing more; it is one of the limits of section 8.

7 · Three readings on the Earth

The companion paper reads a pair in three ways: on the variable, on the ring it shares, and on the event that set it. On the Earth the three readings have places one can point to, though only the first is measured; each is read here as a reading, and two are checked against geophysics.

The pole: the dipole. The pole reading is the dipole itself. The International Geomagnetic Reference Field gives its moment for 2020 as 7.71 × 10²² A m², of which 7.60 lies along the axis of rotation. That is the m of section 3, read on the field of today.

The halo: the magnetosphere, as a reading that fails a first check. In the picture, the halo is the ring a weak dipole shares with what surrounds it, and the place where the Earth's dipole meets its surroundings is the magnetosphere. Read that way, the reading fails at once on its size: the halo's radius grows as the dipole weakens, but the magnetosphere shrinks, since its distance from the planet on the day side goes as the cube root of the moment (Siscoe and Chen 1975). Its compression on the day side and its long tail on the night side are made by the solar wind, not by the dipole alone. So the magnetosphere is not the halo; at most it is where a halo would be looked for, and nothing here measures it.

The archive: the record, and the base of the mantle. The third reading is the record the event leaves. On the Earth that record is literal: the seafloor's stripes and the sediment cores this paper reads. Deeper down, at the base of the mantle above the core, seismology finds piles and patches of anomalously slow material, whose origin is debated (Garnero and others 2016). None of it is a record of the field's polarity: the archive of polarity is the crust, on the ocean floor and in the rocks of the continents. The heat the core loses to the mantle, which powers the dynamo, is set by the mantle as a whole and not by a thin layer at its base (Lay and others 2008).

8 · Limits, and what this paper does not say

The open limits come first, each with what would close it.

• The weak-reversal prediction is window-fragile on a single stack. Narrower windows, or windows moved younger, meet 6 of the 9 boundaries where 7 were needed (section 4). It would close with the same rule re-run on a stack that shares no cores with this one, registered first.
• The stack's effective resolution is unconfirmed, and it is the likely cause of the orbital-period refutation, not a measured one. It would close with the resolution quoted from the stack's authors, or with a test that plants the three periods in a record smoothed the same way and counts how often the registered rule finds them.
• The picture is symmetric and the record is not. The dipole decays more slowly than it recovers (Ziegler and Constable 2011), and reversals do not arrive at a steady random rate (McFadden and Merrill 1984; Gallet and Hulot 1997); nothing in the sphere carries either. It would close with a registered test of the recovery timescale after a reversal.
• No phase is measured. The halo's angle is the model's clock, and nothing in the Earth's records reads it. It would close with a recorded run whose phase is read and compared with the clock.
• The Earth's halo has not been measured at all: the magnetosphere of section 7 is a reading, and it fails a first check. It would close with a recorded reading of the magnetosphere's size or shape set against the dipole's margin over the same years, with the method written down first.
• The hypothesis that a field keeps a planet's air is contradicted at today's rates and untested for earlier times, with Venus as its standing counterexample. It would close with a comparison across bodies of field and retained atmosphere, registered before the data, with Venus counted.
• The dipole stack's terms for commercial use are still to be confirmed with the archive that holds it: it is used for research under the source's published terms, with its authors credited and written confirmation pending. It would close with the archive's written terms.

The standing statements, which no measurement closes:

• The Earth is not a qubit. The series takes as a postulate, its fourth, that a field with two values and a strength can be read on the sphere. This paper shows only the projection of section 3, a reading of how the record moves and not an identity, and the words of the picture are used in their information sense.
• The bits are the picture's. The information of section 3 is the model's reading of a margin, not a count of anything the dynamo stores, and no claim about the Earth as an efficient recorder is made.
• No method. How our engine reaches an answer is not described here, and will not be.
• Qualified, not denied. "The inner core only grows" is too strong: it grows on balance as the outer core freezes onto it, but the whole core also cools, its boundary can melt locally, and a dynamo ran before there was an inner core. A recent study (Hansen and others 2023) found widespread patches of slow material beneath one region of the Southern Hemisphere and proposed, from models, that they are crust carried down from the surface; it is a regional observation with modelling, not an observed global layer. Heat in the core's iron is carried by its electrons, and how well they carry it is debated (Pozzo and others 2012; Olson 2013). The Moon's long ringing after a quake is mostly scattering in its broken surface layer, not only low damping. Hearing the Earth's ringing as sound is a mapping, not a result.

This paper reads the Earth's dipole onto the textbook picture of a two-way choice and runs the tests registered for that reading, on public records: one refuted, one window-fragile that holds at its threshold as registered, and one not yet run. It claims no new geophysics and no measurement of the Earth's halo. The records are as of 4 October 2026; the robustness test and the null ran on them on 7 October 2026.

9 · How this was made: the method and the chain of records

The question was set on 4 October 2026 as a written brief: put the Earth's field on the picture the companion paper draws, and add it to the series under the series' scope rules, which are public records only, the picture in textbook terms, the engine's method not described, and nothing claimed beyond what was measured. The lineage is the series' fourth postulate, the two-state recorder: assumed, never derived; no theorem of this paper rests on it beyond the closed forms of section 3, and the tests under it are the ones in section 4.

Day read the two public records into one margin and computed the clocks from the public tables. Claude (Anthropic), the consultant named in the byline, designed and built the rest from the engineering side: the reading of the two records as one margin, the prediction and its commitment before the data, the code that reads the records and the clocks, the check of the Moon's phase, the figure, the tests that pin every number on this page to its record, and the draft of this paper.

The chain of records, in the order they were committed:

• the weak-reversal prediction, committed alone at a617281c1, before any Earth record existed;
• the orbital-period prediction, committed alone at c69ab6bbc, before the record it is tested on;
• the Earth records, committed at 2cbca0b67, after both;
• the robustness test and the null, committed alone at 4fbe6a1f7, after the result was public and before their own run;
• the tests that hold every number on this page to its record and hold the order of the commits above, and this page, generated from its source.

10 · Companion papers

Seven papers published beside this one take the same approach: each traces its figures to a recorded measurement and says what it did not measure.

• The Operational Unit: the model behind the engine, and how it was built.
• The periodic table as a ground-state ladder: each element read as the lowest-energy filling of its electrons, with every answer NIST lists checked against it.
• Closing the gaps: four sustainability problems an engine can schedule, and what it cannot do about them.
• Sense, remember, act: what the engine senses, remembers and learns.
• The halo of a decision: a two-way choice, the partner it is tied to and the event that tied them, in textbook terms, with what an experiment could measure.
• HOPE: recall in a library of Hilbert spaces: recall as settling to the nearest stored state, in a library of small spaces kept one per model, with the measured answer that they do not make one large space.
• The unit of work: a receipt for one settled problem, booked on a hash-chained ledger, and what it is not, with the economy's measured losses first.

Acknowledgements

• Masters & Widmer 1995, AGU, cited. Used for research under the source's published terms; written confirmation pending.
• PREM: Dziewonski and Anderson 1981; NOAA CO-OPS; U.S. Naval Observatory; IGRF: Alken et al. 2021. The layer table is the TauP project's.
• EarthRef PADM2M (Ziegler, Constable, Johnson and Tauxe 2011), used for research under the source's published terms; written confirmation pending. From the EarthRef.org Digital Archive.
• PISO-1500 (Channell, Xuan and Hodell 2009), used for research under the source's published terms; written confirmation pending.
• GTS2020 polarity time scale, Ogg 2020, via PmagPy (BSD-3-Clause).
• IGRF-14, IAGA/NOAA NCEI, Alken et al. 2021. Used for research under the source's published terms; written confirmation pending.

Replicate this paper, or tell us what is wrong

We invite replication and correction. The measured results come from records committed in our repository. The records are not yet published; until they are, write to us through the contact page, naming the paper and the number you want to rebuild or the error you found. We correct an error we can reproduce on the paper's web page, with its date.

The tests this paper registered before reading their data are frozen, each with the rule that would fail it, in docs/EARTH_PREDICTION_2026_10_04.md, docs/FALSIFY_SIM_1_2026_10_04.md, docs/PAPERS_DUALFIELD_1_2026_10_04.md, docs/PAPER_EXPERIMENTS_REGISTRY_2026_10_07.md and docs/EARTH_P1_SENSITIVITY_2026_10_07.md.

How to cite this paper

Please cite this paper as:

Agile Integrations LLC. 2026. "The Earth as a two-state recorder: its dipole on the Bloch sphere, the rock that keeps the record, and the clocks inside." Version 1, 4 October 2026. https://agileintegrations.net/blog/the-earth-as-a-two-state-recorder.html

Citation file: CITATION.cff.

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