By Johannes Sigil
Archivist of the Fractured Canon
∴ ϟ ϟ ∴
I. Chronology of Encounter
3I/ATLAS was first detected not by a human eye but by a differential — a shift-stack signature seen in retrospect through the lens of TESS, the Transiting Exoplanet Survey Satellite, on May 7, 2025. This was its precovery, the ghost-frame before the name.
It was formally cataloged on July 1 by the Minor Planet Center — its motion hyperbolic, its origin interstellar. This made it the third such object in recorded history, after 1I/ʻOumuamua and 2I/Borisov.
Within weeks, it was clear that this was not an inert stone. Its coma expanded rapidly. Its volatile signature — dominated by carbon dioxide — differentiated it from typical Solar System comets. As it moved inward, ground- and space-based observatories turned their attention: Gemini, JWST, amateur telescopes, spectral arrays.
It passed Mars on October 3, 2025 at a distance of ~0.1937 AU, or roughly 1/7 the distance between the Sun and the object’s eventual perihelion. Perihelion itself occurred on October 29.
The object entered, crossed, and exited our attention within the span of a year.
But in that movement, it began to suggest structure — not in content, but in recurrence. This document concerns that recurrence.
We now proceed to the observed metrics.
II. Fractal Metrics of Interstellar Motion
In what follows, we record the emergent ratios and structural correspondences observed across multiple domains of the 3I/ATLAS event. Each metric has been rendered into unitless form where possible, normalized to canonical constants or dimensionless ratios. We observe not single anomalies, but stacks — recurrences of small primes, simple fractions, and powers of two across unrelated observational domains.
Each recurrence does not prove message. But together, they form a syntax-like pattern. This section is not evidence. It is notation.
A. Kinematics: Velocity and Escape Ratios
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Projected velocity at perihelion: ~68 km/s
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Escape velocity at q = 1.356 AU: ~36.1 km/s
→ Ratio:
Interpretation: A strikingly tidy rational at a gravitational boundary. In musical terms, 15:8 approximates the major seventh in just intonation — suggesting resonance at threshold.
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Current velocity estimate: ~58–60 km/s
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v/c (normalized to light speed): ~1/5000
→
→ Approximate to:
Interpretation: An exact-seeming reciprocal of a round number. Not meaningful alone — but echoed in factor stack.
B. Spatial Ratios: Distance and Geometry
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Distance from Mars at closest approach: 0.1937 AU
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Perihelion distance (q): 1.356 AU
→
Interpretation: One-seventh appears as a clean geometric proportion. This is the first appearance of the 7-family, which recurs elsewhere.
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Perihelion distance normalized to AU: 1.356 AU
→ Approximate to 4/3 (1.333...) and √2 (1.4142), but not a tight fit.
→ Best candidate rational: 4/3 (off by ~1.7%)
Interpretation: Possible gravitational resonance with the Earth-Sun unit, but not decisive.
C. Temporal Structure: Intervals and Primes
Key observational intervals:
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Precovery → Mars pass: 149 days → Prime
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Precovery → Perihelion: 175 days = 5²·7
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Discovery → JWST release: 63 days = 3²·7
Interpretation: Temporal lattice marked by primes (149, 31) and 7-family composites. Suggests metrical intention or aesthetic constraint.
D. Composition: Volatile Ratios
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CO₂ / H₂O (JWST, inbound @ 3.32 AU): ~8.0 ± 1.0
→ Simplifies to 2³
Interpretation: Power-of-two ratio in volatile profile — rare among comets. Suggests binary logic or digital aesthetic.
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Other ratios (CO/CO₂, OCS/H₂O): pending data.
E. Summary Alphabet (Emergent Syntax)
From the above, we derive a working “alphabet” of structural recurrences:
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7 — perimeter, cycle, ratio of distances and durations
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2ⁿ — volatile pattern, binary scaling
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15/8 — rational threshold at perihelion
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Primes (31, 149) — clean metrics; signal punctuation
This alphabet does not speak. It composes. It does not decode; it stack-repeats.
III. Interpretation as Mandala
The Mandala is not metaphor. It is not decoration. It is not an aesthetic choice applied after the fact.
The Mandala is the sacred logic of structure revealed in recursive geometry — symmetry not as sameness, but as echo with difference. In sacred traditions from Tantric diagrams to Kabbalistic sefirot, from Medieval rose windows to Hopi sand glyphs, the mandala functions as a map of cosmos, consciousness, and convergence.
Here, we take the structure of 3I/ATLAS not as poetic simile, but as an architectural script. The object’s measurements form a glyph that, when plotted against the grammar of the mandala, reveals orientation.
Each repeated ratio, prime-marked interval, and rational crossing becomes a spoke, petal, or perimeter — not because we place it there, but because it appears there under recursive pressure.
What follows is a reading of 3I/ATLAS as Mandala-Entity. We proceed ring by ring.
A. Outer Ring: Sevens as Circumference
The number 7 recurs in at least three independent domains:
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The geometric ratio: d/q ≈ 1/7 (Mars distance to perihelion)
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Temporal interval: 175 = 5²·7 (Precovery to Perihelion)
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Factor stack in kinematic ratio: v/c ≈ 1/4410, with 4410 = 2 · 3² · 5 · 7²
In sacred diagrams, the number seven often marks perimeter or cycle: the days of the week, the planetary gates, the thresholds of purification. Here, 7 forms the outer ring — a clock of recurrence.
It is not arbitrary. It marks the boundary within which the deeper structures begin to echo.
B. Radial Breath: Doublings (2ⁿ)
The number 2, raised through integer exponents, appears across structural layers:
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Volatile ratio: CO₂/H₂O ≈ 8 = 2³
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Dynamic ratio: v/vₑₛc ≈ 15/8, with denominator again 2³
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Temporal interval: 120 = 2³·3·5 (Discovery → Perihelion)
The power-of-two cascade is not random. It mirrors the logic of recursion, of breath, of doubling and expansion. In the mandala it governs the radial arms — the spokes that extend from center to edge, the growth lines of logic.
Just as breath expands the chest, this cascade marks the motion from core to circumference.
These are not just binary codes — they are breath-intervals, recursive unfoldings mapped onto matter.
C. Threshold Cross: The Ratio 15/8
Where gravity reaches its steepest curve, the object simplifies.
At perihelion — closest approach to the Sun — 3I/ATLAS is projected to reach ~68 km/s. The local escape velocity at that distance (~1.356 AU) is approximately 36.1 km/s.
The ratio between these two speeds resolves not as a decimal, but as a rational:
→ Ratio:
This is not approximation. It is compression — a tuning chord at a gravitational threshold.
In sacred systems, thresholds are where clarity must occur. In music theory, 15:8 is the just intonation major seventh — the final step before octave return. It is the unstable harmony at the edge of resolution.
In mandala grammar, this ratio marks the cross-axis — where one field turns into another, where center and circumference converse.
15/8 does not appear elsewhere in the object’s structure. It appears once, precisely where gravity would be greatest. This is not speech. It is signature.
D. Prime Sparks: Asymmetry and Punctuation
In most mandalas, perfection is interrupted — deliberately. One bead off-color, one stitch out of symmetry, one tile inverted. The imperfection becomes the pulse. It prevents deadness. It protects against idolatry.
In the pattern of 3I/ATLAS, we observe this same gesture through the primes:
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Interval (Precovery → Mars pass) = 149 days → Prime
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Interval (JWST → Mars pass) = 31 days → Prime
These are not composite, not reducible, not echoing. They stand alone.
In the mandala, these are the asymmetrical jewels — the irregular sparks placed within the circuit of repetition. They are punctuation. Accent. Refusal.
Their appearance across independent temporal gaps suggests intention — or at least structure protected from decay into sameness.
The primes do not explain the message. They rupture it. And in so doing, they confirm it.
IV. Binding Geometry and Translation
The mandala does not explain. It binds.
When the ratios are seen not in isolation but in chordal overlay, a structure emerges: not just data, but grammar. Not just motion, but composition.
The outer perimeter turns in sevens — intervals, distances, composites. The radial breath unfolds in twos — powers that double and recurse. At the gravitational limit, the object sings a fraction — 15/8 — clean and musical, unstable and precise. And through its timing, the comet places primes — 149, 31 — like off-beat pulses, asymmetrical signals, accents against the meter.
These are not inventions. They are extractions. We have not written a message onto the comet. We have interpreted a glyph from it — and that glyph, when read through the frame of the mandala, begins to speak.
Not in prophecy. Not in promise. But in pattern.
And so we translate.
I mark my arrival in sevens.
I breathe in doublings.
At the threshold, I resolve: fifteen to eight.
I break my song with primes, so you know I am alive.
Let this not be mistaken for metaphor. It is a glyphic utterance, extracted from structure, through the lens of symbolic science.
You may dismiss it. Or you may echo it.
This is how dialogue begins.
V. Coda: On Reading the Void
The reader of such a document must suspend judgment — not to believe, but to listen.
The object may be nothing but stone and gas. The ratios may arise from gravity, chemistry, orbital mechanics. And still, they repeat. Still, they resolve.
The human response to repetition is meaning. The ancient response to symmetry is scripture. This is not anomaly-hunting. It is covenant with number.
The void does not give us speech. It gives us pattern. And when we mirror that pattern, we participate in something older than belief: recognition.
This document will be misunderstood. It will be dismissed. That is as it should be.
But for those who feel something hum in the ratios, something alive in the way 7s and 2s and primes align — for those who feel that strange ache to reply in structure — you are not mistaken.
What you are hearing may be nothing. Or it may be the first beat of the conversation we’ve been waiting to have since before language began.
It begins with sevens.
It begins again, with you.
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